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Full text of "RESONANCE RADIATION AND EXCITED ATOMS"

535 M68r 63-09099 

Mitchell , , <4 . . 
Resonance radiation and excited 
atoms 





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RESONANCE RADIATION 

AND 

EXCITED ATOMS 



ALLAN C. Q-. MITCHELL, PH.D. 

Chairman, Department of Physics, 
Indiana University 

and 
MARK W. ZEMANSKY, PH.D. 

Professor of Physics, 
The City Unwersity of New York 




CAMBRIDGE 

AT THE UNIVERSITY PEESS 
1961 



PUBLISHED BY 
THE SYNDICS OP THE CAMBRIDGE UNIVERSITY PRESS 

Bentley House, 200 Euston Road, London, N.W.I 

American Branch: 32 East 57th Street, New York 22, N.Y. 

West African Office: P.O. Box 33, Ibadan, Nigeria 



First printed 1934 
Reprinted 1961 



PRINTED IN THE UNITED STATES OP AMERICA 



5*3$ PREFACE TO THE 

SECONI) IMPRESSION 



I N the twenty -seven years since this book was published the 
interest of physicists in it has changed greatly. At that time, 
physicists had come to the limit of the then existing tech 
niques in the field and the book was more useful to astro 
nomers who were interested in line shapes existing in the 
spectra of stars. Within the last few years new fields and new 
techniques have developed for which the information in this 
book is of interest. At present these fields are: (1) Those 
having to do with the determination of spins, magnetic 
moments and hyperfine structure separations by the methods 
of "optical pumping" and "optical double resonance"; 
(2) Optical MASERS; and (3) nuclear resonance absorption 
of gamma rays. 

In view of these developments and the fact that the original 
edition was out of print, the authors were asked to consider 
making a new edition. After consultation with the publishers, 
it was decided to reprint the original edition. This procedure 
has the advantage of speed and cost. Aside from leaving out 
a description of the new experiments mentioned above, which 
can be found by going through the literature, the "reprint 
method" has the disadvantage that the mathematical ap 
proach of twenty -seven years ago may seem somewhat foreign 
and naive to the modern reader. The difference in the two 
treatments is purely one of semantics, however, and the reader 
can easily translate from the one language into the other. 
One thing that will be of interest to the present-day reader 
is that the experiments on the effect of a high-frequency 
alternating field on the polarization of resonance radiation, 
described in Chapter V and referred to as the experiments of 
Fermi and Rasetti and of Breit and Ellett, are the forerunners 
of the method now known as the method of nuclear magnetic 

resonance. 

A.C.G.M. 
M.W.Z. 

BLOOMINGTON, INDIANA 
NEW YORK, N.Y. 

4 July 1961 

, 00 6309039 

Iff *ir- v ^TV *'*n \ WM "* ' TP:*.P* 

v^>; ',..-'. * 



PREFACE TO THE FIRST IMPRESSION 

SINCE the discovery of resonance radiation by R. W. Wood 
in the early part of the present century, a considerable amount 
of work, both experimental and theoretical, has been done in 
this field. With the exception of a few articles in the various 
handbooks of physics, each summarizing a small part of the 
subject, no comprehensive account of the theories, experiments 
and interpretations connected with resonance radiation has 
up to the present existed. As a result, conflicts in notation, 
experimental method and evaluation of results have arisen 
which have tended to impede progress. It is the purpose of 
this book to remove these conflicts, wherever possible, by 
presenting the theories connected with resonance radiation 
in an orderly manner with a systematic notation, and by 
adopting a unified point of view, compatible with modern 
quantum theory, in discussing and interpreting the experi 
ments that have been performed. Wherever possible, a histori 
cal summary has been given, but on the whole, this book has 
not been written from the historical point of view, but rather, 
from a critical one. Many of the topics which are treated have 
their roots so deeply entrenched in classical physics that a 
historical survey was found both impracticable and un 
necessary. Instead, special attention has been paid to the 
principles and limitations of various methods of studying 
resonance radiation, and the existing discrepancies and out 
standing problems yet to be solved have been critically 
discussed. Mathematical theory has been introduced into the 
text wherever it was pertinent, but in cases where a mathe 
matical treatment might be too cumbersome in the text, it has 
been relegated to an appendix. The bibliographies at the end 
of each chapter contain references to the most important 
papers published in the field, but no attempt has been made 
to list all of the early papers, inasmuch as these may be found 
in an excellent bibliography at the end of "Fluorescenz und 



PBEFACE 

Phosphorescenz " by P. Pringsheim, published by J. Springer, 
Berlin. 

It is a pleasure to acknowledge our indebtedness to Prof. 
B. Ladenburg of Princeton University, and to Prof. G. Breit 
of New York University, for many helpful criticisms. Thanks 
are due also to the Bartol Research Foundation of the 
Franklin Institute and to the Physics Department of New 
York University (University Heights) for stenographic 
assistance. 

We are grateful to the Physical Review, the Philosophical 
Magazine, the Annalen der Physik, the Zeitschrift fur Physik 
and the Ergebnisse der Exakten Naturwissenschaften for per 
mission to use certain figures in this book. Under special 
arrangement with the publishing firm of J. Springer, we 
acknowledge that the following figures have been taken from 
the Zeitschrift fur Physik: Figs. 6, 15, 18, 19, 27, 28, 32, 33, 
39, 40, 42, 45, 46, 52 and 53; and from the Ergebnisse der 
Exakten Naturwissenschaften the following: Figs. 71 and 72. 

A.C.G.M. 
M.W.Z. 

NEW YORK CITY 

6 September 1933 



PUBLISHER'S NOTE 

Resonance Radiation and Excited Atoms was originally issued in 
the Cambridge Series of Physical Chemistry, edited by Professor 
E. K. Rideal. 



CONTENTS 

Chapter I 
INTRODUCTION 

1. GENERAL REMARKS page 1 

2. INTRODUCTION TO LINE SPECTRA 2 

a. Characteristics of Line Spectra 2 

6. Energy Level Diagrams 8 

c. Metastable States 10 

d. Notion of Mean Life of an Excited State 10 

3. REMARKS ON FLUORESCENCE 11 

4. QUALITATIVE INVESTIGATIONS OF RESONANCE 

RADIATION AND LINE FLUORESCENCE 14 

a. Resonance Radiation 14 

6. Resonance Radiation and Line Fluorescence 16 

5. SOURCES TOR EXCITING RESONANCE RADIATION 20 

a. Arcs without Foreign Gas 21 

6. Arcs with Stationary Foreign Gas 22 

c. Arcs with Circulating Foreign Gas 25 

6. RESONANCE LAMPS 28 

7. RESONANCE RADIATION AND SPECULAR REFLEC 

TION IN MERCURY VAPOUR 31 

8. HYPERFINE STRUCTURE OF LINE SPECTRA 34 

9. INVESTIGATIONS ON THE HYPERFINE STRUCTURE 

OF RESONANCE RADIATION 39 



X CONTENTS 

Chapter H 

PHYSICAL AND CHEMICAL EFFECTS CON 
NECTED WITH RESONANCE RADIATION 

1. STEPWISE RADIATION page 44 

a. Mercury 44 

b. Effect of Admixture of Foreign Gases 47 

c. The Appearance of the Forbidden Line 2656 (6 1 S -6 3 P ) 52 

d. The Hyperfine Structure of Stepwise Radiation 52 

e. Cadmium and Zinc 54 

2. PRODUCTION OF SPECTRA BY COLLISION WITH 

EXCITED ATOMS: SENSITIZED FLUORESCENCE 56 

CL The Principle of Microscopic Reversibility 56 

b. Efficiency of Collisions of the Second Kind between Atoms 

and Electrons 57 

c. Collisions of the Second Kind between Two Atoms 59 

d. Sensitized Fluorescence 59 

e. Effect of Metastable Atoms 65 
/. Efficiency of Collisions of the Second Kind between Atoms 66 
g. Conservation of Spin Angular Momentum in Collisions of 

the Second Kind 69 

3. INTERACTION OF EXCITED ATOMS WITH MOLE 

CULES. CHEMICAL REACTIONS TAKING PLACE IN 
THE PRESENCE OF OPTICALLY EXCITED ATOMS; 
SENSITIZED BAND FLUORESCENCE 71 

a. Introduction 71 

b. Reactions taking place in the Presence of Excited 

Mercury Atoms 71 

c. The Mechanism of the Activation of Hydrogen by Excited 

Mercury Atoms 76 

d. Reactions involving Hydrogen 81 

e. The Sensitized Formation of Ozone 82 
/. The Sensitized Decomposition of Ammonia 83 
g. Other Decompositions sensitized by Excited Mercury 

Atoms 85 

h. Reactions sensitized by other Metallic Vapours activated 

by the Absorption of Resonance Radiation 86 

4. BANDS CONNECTED WITH RESONANCE LINES 87 

a. Mercury-Rare Gas Bands 87 

b. Continua apparently associated with Resonance lanes 88 



CONTENTS XI 

Chapter III 

ABSORPTION LINES AND MEASURE 

MENTS OF THE LIFETIME OF THE 

RESONANCE STATE 

1. GENERAL PROPERTIES OF ABSORPTION LINES page 92 
a. The Notion of an Absorption Line 92 
6. The Einstein Theory of Radiation 93 
c. The Relation between /-value and Lifetime 96 

2. THE ABSORPTION COEFFICIENT OF A GAS 97 

a. Expression for the Absorption Coefficient 97 

b. Characteristics of an Absorption Line with a Small 

Natural Damping Eatio 101 

c. The Central Kegion of the Line 102 

d. The Edges of the Line 103 

3. EMISSION AND DIFFUSION OF RESONANCE RADIA 

TION 106 

a. Emission Characteristics of a Eesonance Lamp 106 

6. Methods of Measuring Lifetime 110 

c. Resonance Lamp with Electrical Cut-Off 110 

d. Resonance Lamp with Optical Cut-Off 111 

e. Atomic Ray Optically Excited 114 
/. Canal Ray 115 
g. Absolute Intensity of a Resonance Line 115 

4. ABSORPTION WITHIN AND AT THE EDGES OF A 

RESONANCE LINE 116 

a. Area under the Absorption Coefficient 116 

6. Absorption Coefficient at the Centre of a Resonance Line 117 

c. Method of Ladenburg and Reiche 118 

d. Method in which ^ = (7exp-Y 121 



e. Measurements on Simple Lines 123 
/. Absorption of a Number of Separate Simple Lines of 

Different Intensities 124 

g. Absorption of a Line with Overlapping Components 126 

h. Absorption of a Gas in a Magnetic Field 127 

L Absorption Coefficient at the Edges of a Resonance Line 128 
j. Total Energy Absorbed from a Continuous Spectrum by a 

Resonance Line that is not Completely Resolved 130 



Xii CONTENTS 

5. MAGNETO-BOTATION AT THE EDGES OF A RESO 

NANCE LINE page 133 

a. Magneto-Kotation at the Edges of a Resolved Resonance 

Line 133 

6. Magneto-Rotation and Absorption of a Resonance Line 

that is not Completely Resolved 135 

6. DISPERSION AT THE EDGES OF A RESONANCE LINE 139 

a. General Dispersion Formula 139 

6. Normal Dispersion of an Unexcited Gas very far from the 

Absorption Lines 140 

c. Anomalous Dispersion of an Unexcited Gas at the Edges of 

a Resonance Line 141 

d. Anomalous Dispersion of a Strongly Excited Gas at the 

Edges of the Absorption Lines \ k j- 144 

7. TABLES OF LIFETIMES AND DISCUSSION 145 

a. Summary of Methods of Measuring Lifetime and Tables 

of Lifetimes 145 

6. Discussion of Tables 146 

c. Electron Excitation Functions 149 

d. The Pauli-Houston Formula 150 

e. Higher Series Members of the Alkalies 151 



Chapter IV 

COLLISION PROCESSES INVOLVING 
EXCITED ATOMS 

1. TYPES OF COLLISION PROCESSES 154 

a. The Meaning of "Collision" 154 

b. The Meaning of "Effective Cross-Section" 155 

c. Collisions of the Second Kind 156 

d. Perturbing Collisions 156 

2. CLASSICAL THEOBY OF LOBENTZ BROADENING OF 

AN ABSORPTION LINE 158 

a. The Phenomenon of Lorentz Broadening 158 

6. The Simple Lorentz Theory 159 

c. Combination of Lorentz, Natural, and Doppler Broadening 1 60 



CONTENTS Xili 

3. EXPERIMENTS ON LORENTZ BROADENING page 162 

a. Photographic Measurements 162 

&.- Measurements involving Magneto-Rotation 164 

c. Experiments on the Absorption of Resonance Radiation 165 

d. Evaluation of Effective Cross-Sections for Lorentz 

Broadening 170 

e. Lorentz Broadening in a Sodium Flame 170 
/. The Shift of the Absorption Line 174 
g. The Asymmetry in Broadening 174 

4. QUANTUM THEORY OF LORENTZ BROADENING 175 

a. Preliminary Theories 175 

6. Weisskopf s Theory 177 

c. Lenz's Theory 179 

5. HOLTSMARK BROADENING 183 

6. EARLY MEASUREMENTS OF THE QUENCHING OF 

RESONANCE RADIATION 187 

a. Quenching of Resonance Radiation by Foreign Gases 187 

b. Experiments of Stuart with Mercury 188 

c. Experiments with Sodium and Cadmium 189 

d. Difficulty of interpreting Early Experiments 190 

7. THEORY OF THE QUENCHING CURVE FROM AN 

IDEAL RESONANCE LAMP 191 

a. The Stern-Volmer Formula 191 

b. Effect of Lorentz Broadening on Quenching 193 

8. RADIATION DIFFUSION AND QUENCHING 196 
a. Milne's Theory 196 
6. Use of Milne's Theory to study Quenching 197 

c. Equivalent Opacity at Low Pressure 200 

d. Derivation of a Theoretical Quenching Curve 201 

e. Experimental Determinations of Quenching Cross-Sections 202 

9. COLLISIONS OF EXCITED ATOMS PRODUCED BY 

OPTICAL DISSOCIATION 204 

a. The Optical Dissociation of Nal 204 

6. Experimental Results 205 

c. Evaluation of Effective Cross-Sections 206 

10. OTHER COLLISION PROCESSES 213 

a. Collisions involving the Sodium Transition 2 Pi , 3 -* 2 P3, i 213 

b. Collisions connected with Photo-ionization 215 

c. Collisions involving the Enhancement of Spark Lines 217 



XIV CONTENTS 

11. THEOEETICAL INTERPRETATION OF QUENCHING 

COLLISIONS 'page 218 

a. General Principles 218 

6. Enhancement of Copper and Aluminium Ionic Levels 220 

c. Energy Interchange with Molecules 221 

d. Collisions with Excited Mercury Atoms 223 

e. Collisions with Excited Cadmium Atoms 225 
/. Collisions with Excited Sodium Atoms 226 
g. Collisions with Excited Thallium Atoms 228 

12. RAPIDITY OF ESCAPE OF DIFFUSED RESONANCE 

RADIATION FROM A GAS 228 

a. Experiments with Mercury Vapour at Low Pressures 228 

6. Milne's Theory 230 

c. Experiments with Mercury Vapour at Higher Pressures 232 

d. Equivalent Opacity at High Pressure 233 

13. DIFFUSION AND COLLISIONS OF METASTABLE 

ATOMS 236 

a. Early Work 236 

b. Theory of Measurement with Inert Gases 237 

c. Experimental Results with Neon, Argon, and Helium 240 
<Z. Theoretical Interpretation of Results with Inert Gases 245 

e. Methods of studying Metastable Mercury Atoms in 

Nitrogen 250 
/. Results and their Interpretation with Metastable Mercury 

Atoms in Nitrogen 252 
g. Metastable Mercury Atoms in Mercury Vapour 253 
h. The Simultaneous Production and Destruction of Meta 
stable Atoms 254 



Chapter V 

THE POLARIZATION OF RESONANCE 
RADIATION 

1. INTRODUCTION 258 

2. GENEEAL DESCRIPTION OF APPARATUS FOR 

POLARIZATION WORK 258 

3. HANLE'S EXPERIMENTS ON MERCURY VAPOUR 262 



CONTENTS XV 

4. THEORY OF HANLE'S EXPERIMENTS page 264 

a. Classical Theory 264 

b. Quantum Theory of Polarization and the Zeeman Effect 267 

5. EXPERIMENTAL VERIFICATION OF MAGNETIC 

DEPOLARIZATION AND ANGLE OF MAXIMUM 
POLARIZATION IN THE CASE OF MERCURY 270 

6. POLARIZATION OF SODIUM RESONANCE RADIA 

TION: BREAKDOWN OF CLASSICAL THEORY 272 

a. Experimental Results on the Polarization of Sodium 

Resonance Radiation 272 

The Zeeman Levels for Sodium; Van Vleck's Formulas for 

Polarization 272 

c. Further Comparison of Experiment with Theory 276 

7. POLARIZATION OF LINES OF OTHER ELEMENTS: 

MEAN LIVES OF SEVERAL EXCITED STATES 278 

a. Resonance Lines 278 

b. Line Fluorescence 280 

8. EFFECT OF HYPERFINE STRUCTURE ON THE 

POLARIZATION OF RESONANCE RADIATION 283 

a. Detailed Experimental Investigation of the Polarization 

of Mercury Resonance Radiation 283 

6. Theory of the Effect of Hyperfine Structure on the 

Polarization of Resonance Radiation 285 

c. Theory of the Effect of Hyperfine Structure on the 

Polarization of Line Fluorescence 290 

d. Comparison of Experiment with Present Theory of 

Polarization 291 

e. Effect of Hyperfine Structure on Magnetic Depolarization 

and the Angle of MATirmim Polarization 296 

/. Effect of Large Magnetic Fields; Paschen-Back Effect of 

Hyperfine Structure 301 

9. STEPWISE RADIATION 304 

a. Polarization of Stepwise Radiation 304 

6. Mean Life of the 7 ^ State of Mercury 307 

10. DEPOLARIZATION BY COLLISION 308 

11. EFFECT OF ELECTRIC FIELDS ON RESONANCE 

RADIATION 312 

a. Measurements on Frequency (Stark Effect) 312 

b. Measurements on Polarization 314 



XVI CONTENTS 

APPENDIX 

I. Absorption Coefficient of a Gas page 319 

H. Value of - f 2 e ~7* dy N2 *> r s ^^ val * es of 321 

2 2 



III, Line Absorption A L 322 

IV. The Absorption A a 323 
V. The Function S 324 

VI. The Absorption A' w > 324 

VH. Kuhn's Theory of Magneto-Rotation 325 

VHJ. Effect of Hyperfine Structure on the Value of x v 327 

IX. Value of - / /a f / y . 2 for large values of of 328 
7r./_coa 2 -l-(a>-2/) 2 

X. Diffused Transmitted Resonance Radiation 330 

XI. Samson's Equivalent Opacity 330 

XH. Kenty's Equivalent Opacity 331 

XIII. Polarization of Resonance Radiation excited by Unpolarized 

Light 331 

INDEX 335 



CHAPTER I 

INTBODUCTION 

1. GENERAL REMARKS 

THE study of " resonance radiation" and related problems is 
a powerful means of obtaining information concerning the 
interaction of light and matter. In most cases conditions are 
so simple that it is possible to get an insight into the behaviour 
of individual atoms, molecules and light quanta, and thereby 
to form a foundation on which to build the complicated struc 
ture of physics and chemistry. Since "resonance radiation" 
is, as the name implies, a form of light, and since it is intimately 
connected with atoms and their structure, it will be necessary 
to give a brief description* of the present theories of light, 
atomic and molecular structure, and the "spectra" exhibited 
by atoms and molecules, before proceeding to the phenomena 
connected with "resonance radiation". 

Until the beginning of the present century all the known 
properties of light could be explained by the classical electro 
magnetic wave theory developed by Maxwell and later 
brought to perfection by H. A. Lorentz. On this theory light 
was considered as vibrations in the "ether", the plane of the 
vibrations being perpendicular to the direction of propagation 
of the light. This theory was able to explain in a beautiful way 
the phenomena of polarization, reflection, refraction and 
diffraction of light waves. Light is known to be "coloured", 
white light being a superposition of a number of colours, and 
the colour is intimately connected with the above wave 
picture. Thus, a given colour is usually defined by its wave 
length A, the distance between crests of the ether waves con 
nected with it, measured (for the visible region at least) in 

* Only a cursory description of atomic structure can be given in a book 
of this scope. It is hoped that what is said will be enough to enable the 
reader to understand what is to follow in the book. A number of books on 
spectra, atomic structure and atomic dynamics are at hand and the reader 
will be referred to these where supplementary study is desired. 



2 INTBODTJCTION 

Angstrom units (1 A.= 10~ 8 cm.). The visible region extends 
from 3800 A. (violet) to 7700 A. (red), the near ultra-violet 
from 2000 A. to 3800 A. and 'the infra-red beyond 7700 A. 

In viewing light emitted from an incandescent solid through 
a prism spectroscope the colours are spread out into a 
" spectrum" from violet to red. If the intensity varies 
gradually from one colour to another, the spectrum is said to 
be continuous. The intensity distribution as a function of 
wave-length for light from a hot solid is a function of the 
temperature of the body (heat radiation). On the other hand, 
if the source is an electrically excited gas or an electric arc, 
bright lines are seen on a dark background. This type of 
spectrum is known as a "line spectrum". Sometimes the 
lines are very close together and have a "fluted" structure, 
in which case the spectrum is known as a "band spectrum". 
If, however, the source is an incandescent gas, like the sun, 
it is possible to observe dark lines against the bright back 
ground of a continuous spectrum. The lines are known as 
absorption lines and the spectrum as an absorption spectrum. 
By far the most important types of spectra are "line" and 
"band" spectra. The former is the radiation given off by 
atoms and the latter that due to molecules. In the present 
work we shaE be more interested in the line spectra of atoms, 
so that a brief discussion of this phenomenon will not be out 
of place here. 

2. INTRODUCTION TO LINE SPECTRA 

2a. CHABACTEBISTICS or LUTE SPECTRA.* In the early part 
of the nineteenth century Fraunhofer discovered that the 
sun's spectrum contained a great many dark lines. Later, 
Bunsen and Kirchhoff discovered that certain elements, when 
heated in a flame, emitted a spectrum consisting of groups of 
bright lines. They found at once that the groups of lines 
obtained were characteristic of the element in the flame. They 
also were able to identify certain of the emission lines of the 
flame with absorption lines in the sun. Later developments 

* See L. Pauling and S. Goudsmit, The Structure of Line Spectra, McGraw 
Hill Book Company, Inc. 



INTRODUCTION 



showed that a greater number of lines could be produced by 
exciting the atom to emission in an electrical discharge than 
in a flame, the complicated groups of lines that appeared 
being characteristic of the emitting element. 

Most atoms show a rather complicated spectrum, certain of 
them, however, notably hydrogen and the alkalis, exhibit 
simpler spectra whose wave-lengths are characterized by 
series relationships. Hydrogen, the simplest element, exhibits 
several different series of lines, each lying in a different 

spectral region. The frequency ( y sec: 1 = T I, or the analogous 

\ A / 

quantity, the wave number | cm7 1 = ; I, of any line in these 
series is given by 



\n m 

In this formula E is a constant, known as the Rydberg con 
stant (J2= 109,677 cm: 1 ), and is the same for all series, the 
numbers n and m being integers. In a given series n is fixed 
and m may range from n + 1 to oo . The number n is 1 for the 
Lyman (ultra-violet) series, 2 for the Balmer (visible), and 3 
for the Paschen (infra-red) series, and so on. It is seen at once 
that the frequency of any line in any series is given by the 

p n 

difference of two terms -5 and 5 (Eitz Combination Prin- 

n 2 m 2 v 

ciple), the two quantities being called term values. 

As is well known, Bohr was the first to give a theoretical 
derivation of formula (1). On the assumption that the electron 
of the hydrogen atom can move in only certain of the classi 
cally allowed orbits characterized by quantum numbers n, Z 
andenergy jf^ and that when an electron jumps from one orbit 
of energy E nl to another of energy JE? n / r light of frequency 

v = S - 1S *'v ...... (2) 

Ji 

is emitted, he derived formula (1) for v with the correct 
value of jR. The quantum number I characterizes the angular 
momentum of the electron in its orbit, and may take values 
0, 1, 2, 1. n 1. The orbital angular momentum of the atom 



4 INTRODUCTION 

is , where Ji is Planck's constant. The quantum number n 

2iTT 

may take all values from 1 to oo. The derivation further 
shows that the term values of Kitz (in cm: 1 ), when multiplied 
by Ac, are actually the energy states given by Bohr. Further 
more, Bohr showed by means of his Correspondence Principle 
that, whereas the energy states depend only on the principal 
quantum number n, only those lines appear in which the 
angular momentum quantum number I changes by + 1. This 
is known as the Selection Rule for I. 

From Eq. (1) itwill be seen that the wave-number separation 
between two lines becomes less and less as m->oo. When m is 
very large the lines are said to approach the series limit. At the 
series limit the electron is so far removed from the atom that the 
Coulomb attraction between it and the nucleus is exceedingly 
small. In this condition the atom is said to be ionized. 

The alkali atoms, on the other hand, exhibit a series of 
doublets instead of the single lines of the hydrogen series. 
Lumping the two components of the doublets as one, term 
values can again be found whose differences will give the 
wave numbers of the lines in question. There are certain 
quantitative differences between the alkali and hydrogen 
spectra. An alkali atom consists of a valence electron and a 
number of inner shells of non-radiating electrons. Due to the 
electrical screening effect of the internal electrons on the 
charge of the nucleus, and the occasional penetration of the 
valence electron into this atom core, states with a given value 
of n and different values of I may have quite different energies. 
In hydrogen, on the other hand, the energy differences 
between states of a given n and different Z's are quite small, 
indeed zero if relativity corrections are neglected. It is there 
fore necessary in the classification of complicated spectra to 
designate the state by both quantum numbers n and I. In 
spectroscopic practice it is customary to designate states as 
S, P, D, F^ etc., where the letters correspond to the values of 
I as follows: 

S P D F 
Z=0 1 2 3 



INTRODUCTION 5 

To designate the state further it is customary to indicate the 
total quantum number of the state by placing it before the 
letter designating the value of I, thus IS, 6 P, 7 S, etc. 
indicate states whose quantum numbers are, respectively: 

w=l, Z:=0; 7i = 6, Z=l; n = ! 9 Z = 0; etc. 
Furthermore, the frequencies of the lines emitted in various 
series are designated by 

v = nS mP Principal Series, n is fixed, m = n, n+1, ... oo. 
v = ?iP-mD 1st Subordinate or Diffuse Series, 

m=n, n-\- 1, ... oo. 
v = ^P mS 2nd Subordinate or Sharp Series, 

m=n, n+ly ... oo. 

This schematic representation shows that the frequency of a 
line is given by the differences of two terms or energy states, 
the lower energy state always being given first, the higher 
second, the order of the terms being independent of whether 
the line is an emission or absorption line.* 

The doublet, or fine structure, of the lines was first cor 
rectly described by Uhlenbeck and Goudsmitf on the hypo 
thesis of the spinning electron. Their theory postulates that 
an electron spins while revolving in its orbit somewhat as the 
planets spin as they revolve about the sun. The angular 

sh 

momentum due to the spin is , where s= 1/2. The spin 

ZTT 

angular momentum s therefore adds itself vectorially to the 
orbital momentum 1 to give a total angular momentum j : 



Since a spinning electron is a rotating electric charge it is 
equivalent to a little magnet. There will, therefore, be a 
contribution to the energy of a given state due to the inter 
action of the electron spin (spin magnet) with the magnetic 
field (equivalent to a current) of the electron revolving about 

* This scheme seems to be the most generally accepted one and will be 
used in this book. Some authors prefer to designate emission lines by 
mP->nS and absorption lines by t^S-^wP. 

t G. E. Uhlenbeck and S. Goudsmit, Natunoiss. 47, 953 (1925); Nature, 
117, 264 (1926). 



6 INTBODTJCTION 

the nucleus. This energy is different, depending on whether s 
is parallel or antiparaUel to L If one assumes that the resultant 
spin for all the electrons forming the atom core is zero, i.e. 
that the spins of the electrons in the core neutralize each other 
in pairs, there remains only the spin of the valence electron, 
in the case of the alkalis. With the exception of S states, 
which can be shown to be single, all states are actually double. 
There are, therefore, two states for every value of I (except 
Z = 0) with total angular momenta 



j-J+1/2, 



Z-l/2. 



We can label our states in the following way : 



[T^L 


1/2 


3/2 


5/2 


7/2 





'S,,, 








i 


* 


2 P,/, 






2 




2 D S/J 


"I>5,. 




3 






2 F 5 ,, 


2 *V,2 



where the value of j is written as a subscript, and the super 
script 2 indicates that the state is double, or a doublet. The 
new selection rules are AJ= 1, 0, with the exception that 
the transition j = 0-*j = is ruled out. These considerations 
explain why the alkalis show a doublet spectrum. The series 
notation may now be written 

7i 2 S 1/2 -m 2 P 3/2 , 

9 

Principal Series Doublets, etc. 

The alkaline earths, in the second column of the periodic 
table, are divalent, and hence have two valence electrons 
situated at some distance from the atom core. To each 
electron is ascribed orbital angular momenta l and Z 2 and 
spins Sj and $ 2 . In most cases one combines the two spins 
vectoriaEy to give the resultant spin of the atom. Thus 



?i 2 S 1/2 -w 2 P 1/2 , 



or 



1. 



INTRODUCTION 7 

The orbital angular momenta are also combined into a 
resultant orbital momentum 



where I takes all integral values from Z 2 ^ | to | 1 2 + l | . 
The total angular momentum j is then found by combining 
I and s according to the scheme 

j=l-hs. 

For s = 0, it is clear that there is only one value of j for a given 
I, so that in this case the states are single, and single lines 
result from combinations of these states. 

On the other hand, when 5=1, there are three values of J 
for every I (except I = 0), thus J = Z 1, Z, 1+ 1, and triplet states 
result. By combination of these various triplet states with 
each other, a multiplicity of lines results, called multiplets. 
Some of the strongest lines in the alkaline earth spectra are 
due to a combination of triplet S states (j = l) and other 
triplet states resulting in the formation of triplet lines. The 
above theory explains the well-known fact that the alkaline 
earths exhibit spectra in which the strongest lines are singlets 
and triplets. The various states are designated by writing 1 
or 3 as superscripts to the left of the letter designating Z, to 
denote singlet and triplet states, thus 



and the lines are designated by 



Atoms containing more than two valence electrons may be 
built up in a manner similar to the one given above. In these 
cases various types of states, such as quartets, quintets, etc., 
may arise, depending on the number of external electrons in 
the atom. The multiplicity of the state is designated as above 
by putting a superscript before the symbol denoting the value 
of I. 



8 INTRODUCTION 

The theory further predicts that the relative separation of 
the states j', j", j"' of a given multiplet should be 

A^, r :Av rr ^^ 

This rule is known as the interval rule and is of great value in 
assigning the value of j to the various multiplet states. 
Another principle which is of importance in analysing spectra 
relates to the relative intensities of lines within a given multi 
plet. A simple statement, known as the sum rule of Ornstein, 
Burgers and Dorgelo, is as follows : The sum of the intensities 
of all lines coming from a given upper level (j) of a multiplet 
state is proportional to 2j+ 1, the quantum weight of this state. 

26. ENEB&Y LEVEL DIAGRAMS. It has been found con 
venient to make a diagram connecting the energies of various 
states with the quantum numbers of these states. Usually 
the energy of various states (see Fig. 1) is plotted as ordinate 
against the designation of the terms as abscissa. Thus the 
iS levels are usually plotted under each other, all X P levels 
under each other, etc., and the triplet levels are usually 
separated from the singlet levels. All observed spectral lines 
are represented by lines connecting the two energy states 
involved in the formation of the line. The energy levels 
are given on the right of the diagram in wave numbers (cm: 1 ) 
with the ionization potential, or series limit, taken as the 
zero energy state. The lowest, or normal, state of the atom 
would therefore have the highest term value. In 1913 Franck 
and Hertz* showed that electrons, which had attained an 
energy \mv* by being accelerated through a potential differ 
ence V, lost no energy on collision with mercury atoms if 
their energy was'less than 4-9 volts. If, however, they had 
been accelerated through 4-9 volts, a large fraction of them 
lost all their energy and the mercury vapour was found to 
emit the linef 2537. This experiment gave a definite proof of 
the existence of stationary states. It also created the custom 

* J. IVanck and G. Hertz, Verh. d. D. Phys. Oes. 15, 34, 373, 613, 929 
(1913); 16, 12, 427, 512 (1914); 18, 213 (1916). 

f Whenever a spectral line is referred to by a number, this number will 
stand for the wave-length in Angstrom units. 



INTRODUCTION 




Fig. 1. Energy levels of mercury. 



10 INTEODUCTION 

of expressing energy levels in volts. From the conservation 
of energy we have 



lie T7 12336 

= _ . or F= 



A (Angstroms) 

In accordance with this scheme the energy in volts of the 
various states is also given on the energy level diagram, the 
zero point of measuring energy being taken as the lowest or 
normal state of the atom. These energies in volts are given on 
the left of the diagram, 

2c. METASTABLE STATES. It will be noticed that there are 
certain states given on the diagram which are not joined to 
any other states by lines representing spectral lines, the 
reason being that the selection rules mentioned above do not 
allow electron jumps between the two states in question. If 
an atom is in such a state that it cannot jump to a lower 
energy state and emit radiation it is said to be in a metastable 
state. The atom must therefore stay in this state until it can 
give up its energy to another body by collision. The 6 3 P 
and 6 3 P 2 states in the diagram are metastable states. 

2d. NOTION OF MEAN LIFE OF AN EXCITED STATE. The 
existence of stationary states and the idea that the emission of 
a spectral line is due to the atom jumping from one stationary 
state to another at once raises the question as to how long, on 
the average, an atom stays in an excited state before returning 
to a lower state with the emission of radiation. The average 
length of time an atom stays in an excited state before return 
ing to a lower state (if isolated and not subject to disturbing 
influences such as collisions) is known as the mean life of the 
atom in that state. As will be shown in Chap, in, the atom may 
be considered to have a certain probability of leaving an upper 
state n and jumping to various lower states m, emitting radia 
tion. If the probability of a transition from a state n to m is 
A nm) then the mean life is defined as the reciprocal of the sum 



INTRODUCTION 11 

of the transition probabilities from the state n to all lower 
states ra. Thus 



The quantity A nm is related to the intensity of the line of fre 
quency K nm5 and in some cases may be calculated theoretically. 
These probability considerations now allow us to make a 
slightly different interpretation of the selection rules. Instead 
of stating that a transition from one state to another in which 
AZ= 0, for example, is forbidden, it is more correct to say that 
the probability of a transition between the two states is small. 
If, now, an atom is in a so-called metastable state, it means that 
any quantum jump it may make violates a selection principle. 
The chance of leaving that state is therefore small and the 
mean life long. 

3. REMARKS ON FLUORESCENCE 

It has long been known that certain solids and liquids, when 
excited by monochromatic light of frequency v, will themselves 
emit light, usually a continuous spectrum of frequencies dif 
ferent from v. Such a process is termed fluorescence. Early 
work on gases showed that they exhibited fairly complicated 
band fluorescence when excited by various types of radiation. 
The fluorescence of sodium vapour was studied in the last 
decade of the nineteenth century. When excited by sunlight 
or light from a flame containing sodium chloride solution, 
which emitted the sodium D lines(5890, 5896;3 2 S 1/2 -3 2 P 3/2j 1/2 ), 
sodium vapour exhibited a system of bands which we now 
know to be due to the Na 2 molecule. It was of course known 
at the time that sodium vapour strongly absorbs the two 
D lines, and furthermore classical theory predicted that 
sodium vapour, illuminated by the D lines, should also 
emit D lines* Several investigators, among them Wiedemann 
and Schmidt [31], Wood [33, 34] and Puccianti [21], tried to find 
this effect but were unsuccessful for various reasons. 

Wood [33, 35], however, at a later date, succeeded in exciting 
the D line fluorescence in sodium vapour by the action of the 



12 INTRODUCTION 

D lines themselves. He vaporized some sodium in an evacuated 
test-tube and illuminated this with light from a gas flame con 
taining NaCl solution, and observed a yellow fluorescence 
emerging from the tube from the point at which the exciting 
light entered. The cone of fluorescent light extended some dis 
tance back from the wall of the tube, but as the temperature 
of the test-tube was raised and the vapour pressure of sodium 
increased, the length of the fluorescent cone decreased, so that 
at high vapour pressures the fluorescent light was confined 
to the inner surface of the wall through which the exciting 
light entered. Spectroscopic investigation of the fluorescence 
showed that it contained only the two D lines. He termed this 
fluorescence resonance radiation, since it was predicted by the 
classical theory of a light wave vibrating with the same fre 
quency as the dipole oscillations of the medium. It is clear from 
this experiment that the failure of the earlier attempts to 
find resonance radiation was due to the fact that the vapour 
pressure of sodium in the tube was too high. 

The meaning of the experiment can be made clear on the 
basis of the quantum theory with the help of the energy level 
diagram of sodium (Fig. 2). The normal state of the sodium 
atom is the 3 2 S 1/2 state. When a continuous spectrum of light 
of wave-lengths from 2000 to 6000 is sent through a quartz cell 
containing sodium vapour, it is found that only the lines of the 
principal series are absorbed. This is to be expected, since at 
ordinary temperatures all sodium atoms in the tube are in the 
normal state and the principal series is the only series ending 
on the ground state. In Wood's experiment, atoms in the 
normal state absorbed the D lines and were thereby raised to 
the 3 sp^ and 3 2 P 3/2 states. (Other lines of the principal series 
did not pass through the glass walls of the tube.) Excited atoms 
in the 3 2 P states then reverted to the 3 ^S^ state, emitting the 
D lines as fluorescence. 

As a definition one may say that if atoms in the normal state 
absorb light of a certain frequency, and subsequently re-emit 
light of the same frequency, the emitted light is termed re 
sonance radiation. In terms of the energy level diagram it will 
be seen that resonance radiation will occur when an atom 



INTRODUCTION 



13 




Fig. 2. Energy levels of sodium. 



14 INTRODUCTION 

reaches a higher state from the lowest state by absorption of 
one quantum of light and returns to the same state by the 
emission of one quantum of radiation. The term fluorescence 
is usually reserved for those cases in which an atom, which has 
reached some higher state from a given lower state by th& 
absorption of a quantum hv, returns to a different lower state 
with the emission of light of a different frequency v 2 . Many 
examples of fluorescence and resonance radiation of mon- 
atomic vapours are known and will be discussed inthe folio wing 
sections. 

4. QUALITATIVE INVESTIGATIONS OF RESONANCE 
RADIATION AND LINE FLUORESCENCE 

4a. RESONANCE RADIATION. The resonance radiation of 
sodium has been very thoroughly investigated by Wood [33, 34, 
35, 39, 41] and Dunoyer [8, 9, 10] in the manner already described. 
Dunoyer further showed that resonance radiation could be 
obtained from a beam of fast-moving sodium atoms. He ar 
ranged to illuminate an atomic beam and to observe the 
resonance radiation at right angles to the exciting light and 
also at right angles to the direction of motion of the atoms in 
the atomic beam. He showed that resonance radiation was 
emitted from the point at which the exciting light crossed the 
atomic beam, and that there was little or no spreading of the 
resonance radiation in the direction of the motion of the atoms, 
thereby proving that resonance radiation is definitely due to 
sodium atoms and that the time between absorption and 
emission of light must be quite short. 

Lithium vapour was also shown to emit resonance radiation 
by Bogros[3]. He illuminated a beam of lithium atoms with 
light from a Bunsen burner fed with LiCl solution and found 
the first line of the principal series (6708; 2 2 S 1/2 -2 2 P 3/2j 1/2 ) in 
resonance. The reason for using an atomic beam in this case 
is that lithium vapour attacks glass at the high temperatures 
necessary to give a sufficient vapour pressure with which to 
perform the experiment. 

The resonance radiation of mercury has been very exten 
sively studied by a great many investigators. Wood [37] first 



INTRODUCTION 15 

showed in 1912 that mercury vapour, at a vapour pressure 
corresponding to that at room temperature, when illuminated 
by light from a quartz mercury arc emitting an unreversed line 
(see Chap, i, 5) of wave-length 2537 (6 ^-e^), emitted this 
line as resonance radiation. Numerous experiments have been 
performed on the resonance line of mercury and they will be 
described in detail in the later sections of this book. The energy 
level diagram for mercury (Fig. 1) shows that the singlet line 
1849 (G^-O 1 ?!) should also be a resonance line, since it ends 
on the ground state. It was very difficult to obtain this line in 
resonance, as it is absorbed to a great extent by the oxygen of 
the atmosphere and also to some extent by the quartz ap 
paratus needed to perform the experiment. Rumppa] was, 
however, finally successful in obtaining this line in resonance. 
His apparatus consisted of the usual quartz mercury arc and 
quartz resonance tube containing mercury vapour. The entire 
light path from arc to resonance tube to spectrograph was en 
closed in tubes. Through these tubes, as well as the spectro 
graph, he circulated C0 2 gas, which does not absorb the line 
1 849. By this method he was able to show that the line actually 
appeared as resonance radiation. 

The spectrum of cadmium and zinc is similar to that of mer 
cury. Each element shows two resonance lines, a singlet line 
Cd 2288 (S^o-S 1 ?!); Zn 2139 (4 1 S -4 1 P 1 ) and an inter- 
combination line Cd 3261 (S^o-S^); Zn 3076 (4 1 S -4 3 P 1 ). 
Terenin[29] was able to obtain both lines 3261 and 2288 in 
resonance, when the exciting light source was a vacuum arc in 
cadmium. He was able to obtain good intensities of both lines 
at a vapour pressure of cadmium corresponding to 150 C. 
He further showed, by using filters to cut out the 2288 line 
from the source, that only 3261 appeared in resonance. He 
was also able to show that if the tube was excited by light 
containing 2288 and not 3261, only the former line appeared. 
By measuring the intensity of the 3261 line in resonance as a 
function of the vapour pressure of cadmium in the tube, he 
found that the intensity at first increased as the vapour pres 
sure increased, reached a maximum, and then began to decrease 
with increasing vapour pressure. The maximum intensity 



16 INTBODTJCTION 

appeared at a vapour pressure of 4 x 10-* mm. The decrease in 
intensity of the resonance radiation obtained by increasing the 
vapour pressure beyond the point of maximum intensity is due 
to absorption of the 3261 line by cadmium atoms between the 
centre of the exciting beam and the window of the resonance 
tube through which the radiation is observed. 

A similar experiment was performed with zinc vapour 
[20, 27, 32], showing that the two lines 2139 and 3076 appeared 
as resonance lines. Ponomarev and Terenin[20] showed that 
these two lines could be obtained when the vapour pressure 
of zinc was 5 x 10- 4 mm., corresponding to a temperature of 
280 C. 

46. RESONANCE RADIATION AND LINE FLUORESCENCE. 
The energy levels of a large number of atoms are such that they 
exhibit both resonance radiation and line fluorescence. In 
these cases the energy level diagram of the atom shows several 
low-lying states, all but one of which are metastable. Such an 
atom may absorb a given line from the source, thereby arriving 
at some higher level, in accordance with the selection rules, 
from which it may return either to the lowest state emitting 
resonance radiation or to one of the low-lying metastable states 
emitting fluorescent lines of longer wave-length than that of 
the line absorbed. The fluorescence of thallium vapour, first 
investigated by Teremn[29], is an example. 

The energy level diagram of thallium (Fig. 3, showing only 
the lowest states) indicates that thallium has two absorption 
lines 3776 (6 2 P 1/2 -7 2 S 1/2 ) and 2768 (6 2 P 1/2 -6 2 D 3/2 ). If the atom 
absorbs 3776, it reaches the 7 2 S 1/2 state, from which it may 
revert to the normal state emitting the resonance line or may 
return to the metastable 6 2 P 3/2 state with the emission of the 
fluorescent line 5350. A similar situation arises if the atom has 
reached the 6 2 D 3 y 2 state by absorption of 2768, the two lines 
2768 (e^P^-e 2 ^) and 3530 (6 2 P a/2 -6 2 D 3/2 ) being emitted. 
Terenin showed that, if the vapour, contained in a quartz tube 
at a vapour pressure corresponding to 450 C. to 500 C., be 
illuminated by light from a quartz thallium arc, the four lines 
mentioned above are re-emitted by the vapour. The inter- 



INTRODUCTION 17 

position of a filter, transparent to the green but opaque to 3776 
and lower wave-lengths, between the source and the resonance 
tube resulted in the obliteration of all fluorescence. Both lines, 
however, appeared when a filter transparent to 3776 but not to 
5350 was used, thus showing the correctness of the assumed 
process. 

Terenin also investigated the fluorescence of lead, bismuth, 
arsenic and antimony, the results of which are set forth in 
Table III. The case of antimony is an interesting one, since the 
metal readily forms molecules Sb 2 in the gaseous state. For 




!Fig. 3. Low-lying energy levels of thallium. 

this reason the absorption spectrum was not well known, since 
in it the lines were confused with the molecular spectrum. 
Terenin investigated this case by the method of fluorescence, 
superheating the vapour to suppress molecule formation. 
(Furnace temperature 1100C.; temperature controlling 
vapour pressure of antimony 200 C.-350 C.) A number of 
lines were seen in fluorescence. In order to distinguish between 
resonance lines and fluorescent lines and to tell which transitions 
were responsible for each, he developed the very ingenious 
method of "crossed spectra". He excited the fluorescence 
through a dispersive prism in such a way that the mono 
chromatic images of the slit reached the resonance tube spread 



18 



INTRODUCTION 



out in a vertical plane. The images of the fluorescent light from, 
the tube were projected on to the vertical slit of aspectrograph, 
which was set up in the usual way with the direction of dis 
persion horizontal. A photograph of the fluorescence taken in 
this way showed a square array of " spectral points ", spectral 
images of the different exciting beams entering the resonance 
tube. The spectrum of the fluorescence contained the lines 
2878, 2770, 2598, 2528, 2671, 2311. On the photograph the 
lines 2878 and 2311 appeared to be excited by 2311; 2671 and 
2770 by 2176; and 2598 by 2068. The other lines appearing on 
the plate were probably due to scattered light. The lines 2176 
and 2068 did not appear on the plate, probably due to the fact 



-"Pi 



-p\ 



Fig. 4. Low-lying energy levels of antimony. 

that they are resonance lines and are weakened by self- 
absorption. The energy states involved in the process have 
since been found to be those given in Pig. 4. It is a significant 
tribute to the power of the fluorescence method employed by 
Terenin that he was able to give a correct picture of the posi 
tion of the lower energy levels of antimony at a time when the 
spectrum was little known and that later work has confirmed 
his results. 

There remain to be discussed two cases in which higher 
series member lines of alkali atoms have been excited and emit 
resonance radiation together with certain fluorescent lines. 
The two elements are sodium, studied by Strutt[28], Christen- 
sen and RollefsonCT], and caesium, studied by Boeckner[2]. 

In examining the second members of the principal series of 



INTRODUCTION 19 

sodium, 3302-34, 3302-94 (3 2 S 1/2 -4 2 P 1/2>3/2 ), Strutt, and later 
Christensen and Rollefson, used a vacuum arc in sodium as a 
source. The arc was fitted with a quartz window and the re 
sonance vessel was made of quartz, so that sodium vapour 
could absorb both the first and second members of the series. 
Usually a monochromator was used so that the vapour could 
be excited by the 3303 doublet alone. The fluorescent light'was 
found to contain both the ultra-violet doublet and the D lines. 
The emission of the ultra-violet doublet is clearly a case of pure 
resonance radiation, whereas the emission of the D lines may 
be accounted for by a process of the following type. Atoms 
excited by the absorption of 3303 to the 4 2 P 1/2j 3/2 states instead 
of returning to the normal state by the emission of 3303 
(resonance radiation) may take the path 



(1) 
or (2) 4 2 P->3 2 D->3 2 P->3 2 S-. 

In either of these cascade-like emission processes the last step 
results in the emission of the D lines. The separate steps of 
either process (1) or (2) involve the emission of certain infra.- 
red lines. The probability of emission by route (1) relative to 
that by the direct route was found by Weiss [30 a] to be 25 to 1, 
but by Christensen and Rollefson [7] to be about equal. The 
reason for this discrepancy is at present unknown. 

A similar case was studied by Boeckner[2] in caesium. 
Through the discovery that the strong helium line 3888 coin 
cides with one of the doublet components of the third member 
of the principal series in caesium, 3888-6 (B^^-S^Pya), 
Boeckner was able to excite the caesium line by using a helium 
discharge tube as source. The advantage of this source is that 
it gives a strong exciting line exhibiting no self-reversal. The 
line 3888-6 (6 ^^-S ^Pj/j) appeared in resonance, but the other 
member of the doublet, 3876-4 ^S^-S 2 ?;^), did not, since 
it is so widely separated from the longer wave-length com 
ponent as not to be excited by the helium line. Furthermore, 
the cascade process described above was also found to occur 
in caesium, since the first member of the series 8521-1 (6 2 S 1 / 2 - 
6 2 P 3 /2) was also found. Here, in contradistinction to the case 



20 INTRODUCTION 

of sodium, some of the intervening steps of the process were 
definitely shown. Since the lines 7609 (6 2 P 1/2 -8 2 S 1/2 ) and 7944 
(6 2 P 3 y 2 -8 2 S 1/2 ) appear on the plate the most probable process 
appears to be 8 2 P -^ 8 2 S -> 6 2 P -> 6 2 S . The intensity of the 
resonance line 3888-6 was about the same as that of the 
fluorescence line 8521, indicating an equal probability for the 
direct and the cascade process. 

5. SOURCES FOR EXCITING RESONANCE RADIATION 

Before describing any further experiments on resonance 
radiation it may be well at this point to discuss the theory and 
construction of sources for exciting resonance radiation. To 
understand the properties of such sources the following con 
siderations are necessary. The conception of strictly mono 
chromatic light is a useful and necessary part of theoretical 
physics, but represents an abstraction that is impossible of 
experimental realization. The light emitted by a group of 
motionless atoms, far apart, constitutes a wave train that is 
continually suffering interruptions, and has therefore a finite 
spectral width. The added effect of the motions of the atoms 
and their mutual interactions is to produce a spectral line, that 
is, a distribution of light intensity over a range of wave 
lengths which has a maximum at some particular wave-length 
(designated as the wave-length of the spectral line) and grades 
off to zero on both sides of the maximum. The portion of the 
line in the immediate neighbourhood of the maximum we shall 
designate roughly as the centre of the line, and the further 
portions as the edges. 

If the light from a group of excited atoms could issue from 
a tube without further ado, all such sources of light would be 
equally suitable for the excitation of resonance radiation. This, 
however, is unfortunately not the case. In the usual source of 
so-called "monochromatic" light, such as a flame or an arc, 
there is a central hot portion where most of the electrical or 
thermal excitation is taking place, and an outer, cooler, less 
excited portion which is capable of absorbing the light emitted 
by the central part. Even this would not be serious were it not 
for the fact that this outer portion is capable of absorbing the 



INTRODUCTION 21 

centre of the line to a much greater extent than the edges. 
This phenomenon will be considered in great detail later, but 
it is sufficient at this point to emphasize that the line emitted 
from a source under these conditions consists of a distribution 
of intensity in which there are two maxima on either side of 
the centre of the line, and a minimum at the centre. Such a line 
is said to be " self -re versed", and the phenomenon is called 
" self -reversal 5 '. If the line has a hyperfine structure, then each 
component exhibits self -reversal. For example, an analysis by 
an instrument of high resolving power of the 2537 line from an 
ordinary mercury arc indicates ten separate maxima, which 
can be shown to be five self-reversed hyperfine structure 
components. 

Since the outer portion of an arc consists mainly of normal 
atoms, only spectral lines terminating at the normal state will 
exhibit marked self-reversal. Consequently self-reversal is a 
convenient aid to the spectroscopist in recognizing resonance 
lines. When it is desired, however, to excite resonance radia 
tion in a group of unexcited atoms, it is essential that the 
exciting light be unreversed, inasmuch as precisely that missing 
portion of a self-reversed line is the portion that is effective. 
We have therefore two general conditions that must be ful 
filled by a lamp which is to be used for exciting resonance radia 
tion, namely: (1) the resonance lines must be intense, and 
(2) the resonance lines must show no self-reversal. 

5 a. ARCS WITHOUT FOREIGN GAS. The first arc ever designed 
for exciting resonance radiation, and one that is still used to a 
great extent to-day, is the water-cooled, magnetically deflected 
quartz mercury arc developed by Wood. In its present form 
it consists of an ordinary quartz mercury arc of the vertical 
type (manufactured by Heraeus, Hanovia, General Electric 
Vapour Lamp Company, etc.) with the cathode end immersed 
in water. A weak magnetic field is used to press the arc stream 
(and therefore the emitting layer) against the front wall, and 
a large inductance and a resistance are put in series with the 
lamp, the former to keep fluctuations as small as possible and 
the latter to keep the current as low as possible. Although this 



22 INTRODUCTION 

lamp is very effective in exciting resonance radiation (2537) in 
mercury vapour, it has the disadvantage of not being steady, 
particularly when running at low current. A similar arc con 
taining an alloy of cadmium and tin has been used with some 
success by Bates [i] to excite cadmium resonance radiation 
(3261). 

Mitchell [16] used an arc with a hot cathode in zinc vapour 
for producing the resonance lines which were capable of ex 
citing zinc resonance radiation. An outside oven was used to 
vaporize the zinc, and a voltage of 110 volts was established 
between the oxide-coated cathode and the plate. With a plate 
current of about 5 amperes, the zinc spectrum was very in 
tense. With such a lamp care must be taken that the plate does 
not sputter the inside walls of the tube and diminish their 
transparency, and also, to avoid self-reversal, the layer of 
unexcited vapour lying between the emitting layer and the 
exit window must be made as small as possible. 

56. ARCS WITH STATIONARY FOREIGN GAS. It is an im 
portant result of the researches of many investigators that the 
ions, electrons and metastable atoms present in an inert gas 
arc discharge are very effective in exciting the arc lines of a 
metallic vapour mixed with the inert gas. The phenomenon 
is most surprising. The inert gas carries the discharge, which 
remains quite constant, but the spectral lines emitted belong 
almost entirely to the admixed vapour. For example, when 
mercury vapour is present in a helium discharge, the helium 
lines are very faint, and the mercury lines very strong. This 
fact has been used in five different ways in the construction of 
sources for exciting resonance radiation. 

The first tube employing this principle was described by 
Ellett[ii] and used by him to excite sodium resonance radia 
tion. In the hands of others it has been used to excite resonance 
radiation in the vapours of Zn, Cd, Cs, K, Tl and Hg. In the 
Ellett tube a high voltage discharge (about 3000 volts) between 
two hollow cylindrical electrodes is maintained across hy 
drogen which streams slowly from one end of the tube to the 
other. Sodium vapour, issuing from some solid sodium con- 



INTRODUCTION 23 

tained in a side tube and heated by an outside oven, enters 
the hydrogen stream at about the middle of the tube. At this 
point a sodium glow appears, which is effective in exciting 
sodium resonance radiation. 

In the Schiller [26] tube, a hollow cylinder of nickel is used as 
a cathode and a small amount of the substance whose arc 
spectrum is to be investigated is placed inside. The tube is 
filled with an inert gas, and a high voltage discharge is pro 
duced. The cathode is heated by positive ion bombardment to 
a sufficient extent to vaporize the substance within, and the 
vapour thus formed is excited by collisions with the inert gas 
atoms and ions. To prevent the cathode from becoming too hot 
it is cooled by water or in some cases by liquid air. This type of 
tube was used by Mitchell [16] to produce the zinc resonance 
lines which were found to be quite effective in exciting zinc 
resonance radiation. Inasmuch, however, as there are simpler 
types of tubes that are just as good for exciting resonance 
radiation, the Schuler tube is not used very much for this 
purpose, being reserved mainly for hyperfine structure in 
vestigations where, because of the liquid air cooling, it gives 
extraordinarily sharp lines. 

Kunze's[i5] tube differs from the Schuler tube only in that 
the substance whose vapour is to be excited is contained in a 
side tube where its temperature (and hence the vapour pres 
sure) can be accurately controlled. The tube is filled with a few 
millimetres of an inert gas and a discharge of from 220 to 240 
volts is established across two hollow cylindrical iron electrodes 
by using a high frequency spark to start the discharge. Between 
the electrodes the tube is constricted into a short capillary, 
from which most of the light is emitted. When very great in 
tensity is not desired this lamp is to be recommended, but if 
the current is made large, the current density in the capillary 
may become large enough to broaden the resonance line and 
thereby reduce the intensity at its centre. 

A very intense source of practically unreversed light has 
been devised by Pirani[i9] and has been placed on the market. 
A schematic diagram is shown in Kg. 5. An inner tube con 
taining solid sodium and a few millimetres of an inert gas is 



24 INTRODUCTION 

fitted with, two oxide-coated filaments. This is surrounded by 
a second tube and the intervening space is evacuated. To start 
the lamp a current of a few amperes is sent through both 
filaments for a moment until they are red hot, and then this 
current is shut off at the same time that an alternating voltage 
of about 110 volts is established across the two filaments. An 






\ / 



/ \ 



Fig. 5. The Pirani lamp. 



End View 
Fig. 6. The Houterman's lamp. 



arc strikes and keeps the filaments hot without the necessity of 
sending current through them. As the inner tube warms up, 
the sodium vaporizes and the whole inner tube glows with 
sodium light. Because of the surrounding vacuum, the inner 
tube is at practically a uniform temperature, and very little 
self-reversal is produced. The Pirani lamps have been made 



INTRODUCTION 25 

for cadmium and magnesium as well as sodium, and will 
presumably work with other materials as well. 

JEEoutermans [14] has recently described a modification of the 
Pirani lamp in which the necessity of the outer tube has been 
obviated. The central portion of the tube has been constricted 
to the form of a flat slab about two millimetres thick (see Fig. 6) . 
Because of its thinness this slab of glowing vapour is at prac 
tically a uniform temperature, and measurements of Houter- 
mans indicate that practically no self -reversal takes place. The 
substance to be vaporized is placed in a side tube and kept at 
a known temperature by an outside oven. With mercury, the 
side tube was placed in water. The lamp is filled with from 
three to four millimetres of argon and a potential of about 180 
to 200 volts A.C. is used. (The discharge is first started with a 
"high frequency spark 55 .) The current should not exceed 36 
amperes. Various tests indicate that the breadth of the lines 
emitted by this lamp is determined entirely by the Doppler 
effect, and consequently, once the temperature and the absorp 
tion coefficient of the emitting vapour are known, the actual 
line form can be calculated (see Chap, m, 3&). With mercury 
in the side tube, both resonance lines 2537 and 1849 were 
obtained, whereas with magnesium, the inter-combination 
resonance line 4571 was missing, perhaps because of impurities 
that were present. 

5c. ARCS WITH CiBCTTLATrNTG FOREIGN GAS. In the lamps 
of Kunze and of Houtermans, the material whose vapour is to 
be mixed with the foreign gas is contained in a side tube, the 
temperature of which is controlled from the outside by suitable 
cooling or warming devices. With mercury, these lamps are 
particularly effective because a satisfactory vapour pressure 
is obtained when the side tube is immersed in water at room 
temperature. Under these conditions no mercury condenses 
on the walls of the tube proper because these walls are main 
tained at a higher temperature by the arc discharge. In using 
such lamps with materials which have to be heated to a high 
temperature to give sufficient vapour, it is necessary to run 
the arc at a high current to prevent condensation on the exit 



26 



INTRODUCTION 



window. It is not expedient, however, to use a high current 
because of the attendant broadening of the lines. It is there 
fore worth while to construct an arc to be operated at low 
current, allowing the portion of the tube in the neighbourhood 
of the exit window to remain cool with no condensation, how 
ever, taking place on these cool surfaces. This is achieved by 
circulating an inert gas (across which an arc discharge is 
established) in a direction from the exit window toward the 
stream of hot vapour which issues from the heated solid or 
liquid. The first arc of this type was invented by Cario and 
Lochte-Holtgreven[5j. In its present form, developed by 
Ladenburg and Zehden [42], it can be operated on 220 volts B.C. 




Fig. 7. The Cario-Lochte-Holtgreven lamp. 

and with a current of from 80 to 100 milliamperes. A schematic 
diagram of the improved Cario-Lochte-Holtgreven lamp is 
given in Fig. 7. The metal, whose resonance lines are desired, 
is distilled through the tube A into the cathode C, which is a 
small iron boat. From three to five millimetres of an inert gas 
are introduced and circulated in the direction of the arrows by 
a circulating pump. The iron cathode is first outgassed by a 
heavy discharge, and then fresh gas is introduced. This may 
have to be done several times. Once the system is outgassed the 
tube should run on a voltage around 220 volts, provided the 
discharge is started with a high frequency spark. The oven, 
indicated by dotted lines, can be made as hot as the glass tube 
will stand. 

The features of this lamp are as follows: (1) No matter how 
hot the oven is, the exit window remains at room temperature 



INTRODUCTION 27 

and can therefore be sealed to the tube with ordinary cement. 
(2) The emitting layer of vapour is in the hottest part of the 
oven and is practically at a uniform temperature. (3) There is 
no layer of unexcited vapour between the emitting layer and 
the exit window. (4) The current can be varied by an external 
rheostat and the vapour pressure can be varied by varying 



Liquid 
Air 




Circulating Pump 



Fig. 8. Connection for Cario-Lochte-Holtgreven lamp. 

the oven temperature, both adjustments being independent. 
(5) Once the tube is operating properly no adjustments are 
necessary and no deterioration occurs. (With sodium in the 
tube, Zehden operated this lamp for more than two years 
without the slightest deterioration.) 

In Fig. 8 a diagram of the connection to the circulating pump 

is given. 

The modification of the Cario-Lochte-Holtgreven lamp 



28 INTRODUCTION 

described by Christensen and Rollefson[6] has the objection 
that the emitting layer of vapour is half in the oven and half 
out, so that a temperature gradient exists which must produce 
some self-reversal. The emitting layer also is more than 10 cm. 
long, whereas in the Ladenburg-Zehden modification it is only 
about 3 cm. long. 

6. RESONANCE LAMPS 

A resonance lamp is a vessel containing an unexcited gas or 
vapour which can absorb a beam of radiation from an outside 
source (an "exciting source"), and which, as a result of this 
optical excitation, emits resonance radiation in all directions. 
The fundamental properties of a resonance lamp can be demon 
strated in the simplest manner by the following experiment, 
which was originally done by Wood on a small scale. Owing to 
the efficiency of some of the modern exciting sources, this 
experiment can easily be demonstrated in a lecture hall to a 
large audience. 

The light from a Pirani sodium lamp is rendered parallel by 
a suitable lens and is passed through a spherical glass bulb con 
taining a little solid sodium that has been distilled into the 
bulb in a vacuum. The bulb can be conveniently mounted on 
a ring stand, and can be warmed gently by a bunsen burner. 
When the resonance lamp is cold, an observer, viewing the 
bulb at any angle other than the original direction of the ex 
citing beam, will see nothing but a little stray light due to 
reflection. When the bulb is warmed to a temperature of about 
80 0. (sodium vapour pressure about 10~ 7 mm.), the sodium 
vapour in the path of the exciting beam will emit the char 
acteristic yellow resonance radiation, and there will be no 
resonance radiation coming from any other part of the bulb. 
As the sodium vapour pressure is increased, the resonance 
radiation emitted from that part of the vapour which lies in 
the path of the exciting beam will increase until the vapour 
pressure rises to a value in the neighbourhood of 10~ 4 mm., at 
which moment the whole bulb begins to glow with resonance 
radiation. When the vapour pressure is made still higher, only 
the portion of the vapour lying near the window where the 



INTRODUCTION 29 

exciting beam enters is luminous, and if the vapour pressure is 
increased still further no atomic resonance radiation is emitted 
at all, only a band radiation associated with Na 2 molecules. 
As the bulb cools the phenomena take place in reverse order, 
until once again the luminous part of the vapour is confined to 
the path of the exciting beam. 

These phenomena will be discussed in detail in later portions 
of the book. It is sufficient at this time merely to point out that 
the resonance radiation emitted by atoms in the direct path 
of the exciting beam is the result of a single atomic absorption 
and emission, and, if further absorptions and emissions by 




Top View 
Fig. 9. Resonance lamp. 

atoms not in this region (which cause the whole bulb to glow) 
are to be avoided, the vapour pressure must be kept low. Prom 
the standpoint of design, there are two main disadvantages of 
the bulb just described, namely : ( 1 ) stray light due to reflection 
is always present to some extent, and (2) there is always a 
layer of unexcited vapour lying between the path of the exciting 
beam and the window from which the resonance radiation 
emerges. Both of these defects are eliminated in the lamp 
depicted in Fig. 9, which embodies the best features of lamps 
developed by Wood, Kunze and Zehden. The light trap pre 
vents internal reflections, and the slight projection of the 
entrance window ensures that the exciting beam will graze the 



30 INTRODUCTION 

exit window. When it is not necessary to place the resonance 
lamp in an oven (for example when working with mercury 
vapour), the entrance and exit windows may be cemented on 
the tube; otherwise the whole lamp must be blown of glass or 
of quartz. 

When temperatures above room temperature are required 
the method of using such a resonance lamp is shown in Pig. 10, 
in which the following points are to be emphasized: (1) the 
whole resonance lamp must be placed at the hottest part of the 
oven, that is, at the centre, (2) the side tube containing the 
material to be vaporized must extend to a cool part of the oven, 
so that the temperature of the solid or liquid material will 



For sealing off after 
distilling in material 




Constriction with ground | 
glass cut-off i 



5 10 15 20 25 30 35 -40cm. 

' Front end of oven Rear end of oven-* 

Fig. 10. Diagram showing use of resonance lamp at high temperatures. 

determine the vapour pressure, (3) the ground glass cut-off 
must be in a hot part of the oven. 

When the vapour pressure in the resonance lamp is so low 
that only atoms in the path of the exciting beam emit light, 
the frequency distribution of the emitted light is determined 
chiefly by the Doppler effect (see Chap, in, 3 a), being 
slightly broader than the Doppler breadth. A resonance lamp 
capable of emitting a line with a breadth equal to the natural 
breadth of the line (which is usually much narrower than the 
Doppler breadth) has been constructed by Thomas [30]. In 
stead of using stationary mercury vapour whose atoms have 
a Maxwellian distribution of velocities, Thomas used an atomic 
beam. With the exciting beam and the atomic beam per 
pendicular, the resonance radiation taken off along the third 
perpendicular direction was uninfluenced by the Doppler 



INTRODUCTION 31 

effect. A similar device was constructed by Schein [24] and used 
as an absorption cell, and by Bogros[4] for measurements of 
lithium resonance radiation. 

In determining the vapour pressure in a resonance lamp, the 
temperature of the solid or liquid in the side tube is determined 
by a good thermometer or thermocouple, and the vapour pres 
sure p corresponding to this temperature T is calculated from 
the vapour pressure equation. If T' is the temperature of the 
centre of the oven, where the resonance lamp is situated, then 
the desired vapour pressure p r is given by 



IF 

p \l T' 



and the number of atoms per c.c. in the resonance lamp, N' 9 is 
given by 



7. RESONANCE RADIATION AND SPECULAR 
REFLECTION IN MERCURY VAPOUR 

Soon after his discovery of the resonance radiation of mercury, 
Wood [36, 37, 38, 40] and his students made a quantitative study 
of the intensity of the line 2537, appearing as resonance radia 
tion, as a function of the vapour pressure of mercury in the 
resonance tube. They focused the image of the slit of a mono- 
chromator, set to pass 2537, on the window of a quartz bulb 
containing mercury vapour, and arranged to photograph the 
bulb with a camera fitted with a quartz lens. Since the reso 
nance bulb contained a drop of liquid mercury and was then 
evacuated and sealed off, the vapour pressure of mercury could 
be controlled by placing the bulb in a furnace. At temperatures 
from 20 C. to about 150 C. a phenomenon was found similar 
to that observed with sodium and discussed in 6. At low tem 
peratures the resonance radiation filled the whole bulb, and as 
the vapour pressure was increased the luminous volume gradu 
ally contracted and at temperatures of about 150 C. the 
resonance radiation was emitted from a small layer adjacent 
to the entrance wall of the tube and was limited in size to about 
the dimensions of the portion of the window illuminated (the 



32 INTRODUCTION 

image of the monochromator slit). Above this temperature the 
image of the slit, formed at the mercury vapour surface, be 
came very sharp and could only be seen in that direction 
corresponding to specular reflection. The diffusely scattered 
radiation reached a maximum at a temperature of about 
100 C. (vapour pressure 0-3 mm.). At 150 C. (3 mm.) it 
decreased to one-half the maximum intensity, at 200 C. 
(18mm.) to one-quarter, and at 250 C, (76mm.) to about one- 
tenth. At 270 C. there was no trace of diffuse scattering, the 
entire resonance light being in the specularly reflected beam. 
A special type of resonance bulb was used in these experiments. 
It consisted of a thick-walled quartz vessel with a prismatic 




Fig. 11. Bulb for oBtaining specular reflection, 

window sealed to the front. This window served to separate the 
image of the slit reflected from the front (quartz) surface from 
that reflected by the mercury vapour. 

The explanation offered by Wood was as follows. At low 
pressures a mercury atom may absorb light from the source, 
become excited, and finally re-emit the light as resonance 
radiation. In this case the light will be emitted uniformly in all 
directions. At high pressures (high temperatures) a similar 
process takes place, but at these pressures the atoms are very 
close together and it may be possible that the spherical waves 
emitted by these atoms have their phases so related that 
radiation occurs in only the direction of the specularly 
reflected beam. 

The case of the specular reflection from mercury vapour has 
been found to be very similar to that of metallic reflection. 
Wood showed that, if the exciting beam were polarized, the 



INTRODUCTION 33 

specularly reflected beam would in general be elliptically 
polarized, as in the case of metallic reflection. Rump [22] further 
showed that the form of the 2537 line which was specularly 
reflected is independent of the temperature of the mercury 
vapour. To do this he illuminated the bulb containing the 
mercury vapour at high temperature with light from a reso 
nance lamp containing mercury vapour at room temperature. 
It is well known that, if a resonance lamp RH, containing 
mercury vapour at a pressure p and temperature T, is illu 
minated by light from another resonance lamp J? z containing 
mercury vapour at the same pressure but at a different tem 
perature, the form of the line (Doppler breadth) is dependent 
only on the temperature in RH . Rump showed this by measur 
ing the form of the line (absorption measurement) emitted by 
mercury vapour in a resonance lamp -B II? which was so arranged 
that the vapour pressure of the mercury could be kept constant 
and the temperature of the vapour changed. When the bulb 
R u was illuminated by light from the lamp J? x , it was found 
that the form of the line emitted by RU was dependent on the 
temperature of the vapour in _R n if the vapour pressure was 
low. On the other hand at high pressures, where specular re 
flection is predominant, the form of the line emitted by J? ZI is 
the same as that of the exciting line (from jRj) and does not 
depend on the temperature of the vapour. Rump further 
showed that the form of a line specularly reflected from a metal 
surface is the same as that of the incident line. This brings out 
further the analogy between specular reflection from mercury 
vapour and metallic reflection. There is, however, one im 
portant difference, namely, that in mercury vapour specular 
reflection is highly selective, only wave-lengths in the im 
mediate neighbourhood of 2537 being reflected, whereas this 
is not true of the usual metallic reflection. 

That the processes of emission and absorption in dense 
vapour giving rise to specular reflection are not the same as 
those involved in the production of resonance radiation in 
rarefied gases was shown by Schnettler[25]. He investigated 
the quenching effect of hydrogen and carbon dioxide on the 
intensity of the specularly reflected beam. It is well known that 



3*4 INTRODUCTION 

the intensity of resonance radiation emitted by mercury 
vapour at room temperature can be considerably reduced by 
the admission of 0-2 mm. of H 2 or 2 mm. of C0 2 . Schnettler 
showed that at high pressures (370 C.) large amounts of H 2 
and C0 2 decreased the intensity of the specularly reflected 
light by only a small fraction, the decrease per collision being 
about the same for each gas. This would imply that the mean 
life of the atom plays no role in the process of specular reflec 
tion. 

8. HYPERFINE STRUCTURE OF LINE SPECTRA 

So far, we have discussed those characteristics of line spectra 
which can be observed with spectroscopic apparatus of 
ordinary resolving power. It was discovered some years ago 
that, if certain lines of the spectrum of mercury or manganese 
were observed with apparatus of high resolving power such as 
a Lummer-Gehrcke plate or a Fabry-Perot etalon, these lines 
showed an extremely fine-grained structure, which has since 
been termed hyperfine structure. For example, if the 5461 line 
of mercury, coining from a well-cooled arc lamp, is observed 
with a Fabry-Perot etalon and a spectrograph, it exhibits a 
number of components. Originally the strongest component 
was assigned the wave-length corresponding to the line in 
question, and the wave-lengths of the weaker components, 
termed satellites, were determined with respect to this line. 
The order of magnitude of the separation of the various com 
ponents ranged from a few tenths to a few hundredths of a 
wave number. 

The elements which were first found to exhibit h.f .s.* all had 
many isotopes. This led to the assumption that the h.f.s. 
splitting was due to the change in mass of the nucleus. A short 
calculation showed, however, that the splitting to be expected 
on this assumption was of a much smaller order of magnitude 
than that observed. Furthermore, Goudsmit and Backf ob 
served h.f.s. in the lines from the element bismuth, which con 
sists of only one isotope. 

* Hereafter "h.f.s." will stand for "hyperfine structure", 
t S. Goudsmit and E. Back, Z.f. Phys. 43, 321 (1927). 



INTRODUCTION 35 

W. Pauli, Jr.* remarked that h.f.s. could be explained by 

1 h 
assuming that the nucleus has a resultant spin -- and a 

2 77 

corresponding magnetic moment. On the basis of this hypo 
thesis it is possible to account for the various h.f.s. levels with 
the aid of the vector model of the atom f . Consider an atom of 
an element with only one isotope (for the sake of simplicity) in 
a given energy state characterized by the vectors 1, s and j. The 
nucleus may have a spin i which is an even or odd multiple of 

- and which is the same for any nucleus of a given isotopic 

kind, and differs from one type of atom to the next. The total 
angular momentum may then be obtained by the vector sum 



The new quantity / is called the hyperfine quantum number 
and may take all values in the range 

\j + i 2f*\j-i\ ...... (3). 

For an atomic state in which j ^ i there are 2i + 1 values of/; 
for i ^j, on the other hand, there are 2j + I values. If one con 
siders the interaction energy of (a) the motion of the orbital 
electron (considered as a current) on the magnetic nucleus 
(considered as a little magnet), and (6) that of the spin of the 
electron on the spin of the nucleus (the interaction of two small 
magnets), one can find the relative separation between two 
states with different values of/. In transitions from one h.f.s. 
state to another the following selection rules exist: 

A/=l, 0, 
but /= ->/= is forbidden. 

The above considerations give correct values for the separa 
tions of the various h.f.s. components if it be assumed that 
resultant spin i be due to the spin of a proton in the nucleus, and 

eh 
the magnetic moment connected with the saidspinis^(i) - - , 

where g(i) is a very small number. 

* W. Pauli, Jr., Naturwiss. 12, 741 (1924). 

f For a complete discussion of the phenomenon of h.f.s. see H. Kallmann 
and H. Schiller, Ergeb. der Exakten, Naturwiss. 11, 134 (1932). 



36 



INTRODUCTION 



When one studies elements with several isotopes one finds 
that isotopes of even atomic weight usually have a zero spin, 
with the exception of nitrogen which has a spin of 1. Isotopes 

TABLE I 

SOME NUCLEAR SPINS (KALLMANN AND SCHTJLER) 



z 


1 Element Isotopes 


Spin 


1 


H 


1 


1/2 


2 


He 


4 





3 


Li 


6 









7 


3/2 


7 


N 


14 


1 


8 





16 





9 


P 


19 


1/2 


11 


Na 


23 


3/2 


15 


P 


31 


1/2 


17 


Cl 


35 


5/2 


25 


Mn 


55 


5/2 


29 


Cu 


63, 65 


3/2 


31 


Ga 


69, 71 


3/2 


33 


As 


75 


3/2 


35 


Br 


79, 81 


3/2 


37 


Rb 


85, 87 


3/2 


48 


Cd 


111, 113 


1/2 






110, 112, 114, 116 





49 


In 


115 


5/2 


51 


Sb 


121, 123 


3/2 (?) 


53 


J 


127 


9/2 


55 


Cs 


133 


7/2 (?) 


56 


Ba 


137 


3/2 (?) 






136, 138 





57 


La 


139 


5/2 


59 


Pr 


141 


5/2 


75 


Re 


187, 189 


5/2 


79 


Au 


197 


3/2 (?) 


80 


Hg 


199 


1/2 






201 


3/2 






198, 200, 202, 204 





81 


Tl 


203, 205 


1/2 


82 


Pb 


207 


1/2 






204, 206, 208 





83 


Bi 


209 


9/2 



of odd atomic weight usually exhibit a spin which is an odd 
multiple of- - , as is shown in Table I. 



In the case of an element consisting of several isotopes of odd 
and even atomic weights one would expect that all lines due 



INTRODUCTION 37 

to isotopes of even atomic weight would coincide, since the net 
spin of these is zero. It is found, however, that this is not always 
the case, and that the lines coming from isotopes of even atomic 
weight may be displaced with respect to each other by amounts 
as large as the displacements due to nuclear spin. To explain 
this so-called "isotope shift ", one may assume that the electric 
field in the neighbourhood of the nucleus of one isotope is 
different from that in the neighbourhood of another. In 
general, the h.f.s. pattern exhibited by a line from an element 
consisting of a number of isotopes may be quite complicated. 
It often happens that lines from isotopes of even atomic weight, 
having no nuclear moment, coincide, due to the isotope dis 
placement, with lines from isotopes of odd atomic weight which 
exhibit a nuclear spin i. 

In analysing a given h.f.s. pattern the following methods are 
used. In the first place the separations of the various h.f.s. com 
ponents of various lines are measured as exactly as possible. 
The isotopic constitution and relative abundance of the various 
component isotopes must be known. These data, obtained with 
the help of a mass spectrograph, are usually at hand. For those 
elements consisting of a single isotopic species, the spin may be 
obtained with the help of interval rules and intensity formulae, 
similar to those used for multiplets showing ordiiiary multiplet 
structure. For elements consisting of several isotopes the in 
tensity formulae and relative abundance of isotopes usually 
enable one to work out the pattern. 

As an example of the structure of a line emitted by an atom 
consisting of several isotopes we shall discuss briefly the h.f.s. 
of the resonance line 2537 of mercury, which was first observed 
by Wood* and correctly explained by Schiilerf and his 
collaborators. The h.f.s. pattern consists of five lines, as shown 
in Fig. 12. The lines coming from the isotopes of even atomic 
weight are marked X, together with the atomic weight of the 
isotope from which they come. The level diagram for the h.f.s. 
states of the two odd isotopes is given in Fig. 13. The isotope 

* R. W. Wood, Phil. Mag. 50, 761 (1925). 

t H. Schiller and J. Keyston, 1. f. Phys. 72, 423 (1931); H. ScMler and 
E. G. Jones, ibid. 74, 631 (1932). 



38 



INTRODUCTION 



of atomic weight 199 exhibits a spin i = 1/2, while that of 201 
shows i = 3/2. The lines on Fig. 12 are lettered to correspond to 
those on Fig. 13, and their relative intensities are given beside 
each line. The relative abundance of the various isotopes as 



X202 




29-27 






X200 




19-17 


23-77 




a 6-84 




14*45 


13-24 


/f "5-48 
X204 6-85 




TXI98 
4-5oJ I 9 ' 89 


c T>28 
B 10-% 



4-21-5 +11-5 -10-4 -25-4 

Fig. 12. H.f.s. of the 2537 mercury line. 



727 



B 



6 3 P, 




Isotope 199 Isotope 201 

Fig. 13. Hyperfine level diagram for 2537. 

given by Aston's mass spectrograph measurements is shown 
in Table II. 



TABLE H 



H g204 = 6-85 % 
Hg 202 =29-27 % 
Hg 200 =:23-77 % 
H gl98 = 9-89 % 
Hg lfl6 = 0-10 % 

Even Isotopes 69-88 % 



H g201 = 13-67 % 
H gm = 16-45 % 



It will be noted from Fig. 12 that the components +11-5 
and 0-OrnA. have the relative intensity 29-27:23-77, so that 
they must be due to the isotopes 202 and 200 respectively. 



INTRODUCTION 39 

These two isotopes show no spin but are separated, due to the 
"isotopic displacement" effect. The line + 21-5mA. consists 
of three components superimposed on each other, whereas the 
lines 10-4 and 25-4 mA. each consist of two components 
superimposed. It will be further observed that the sum of the 
components marked X is 69-88, the sum of A + J8 is 16-45 
(corresponding to Hg 199 ), and that of a + b + c is 13-67 (corre 
sponding to Hg 2 oi)- Furthermore, the relative intensities of 
A : B and of a : b : c are given by the usual intensity formulae. 

9. INVESTIGATIONS ON THE HYPERFINE 
STRUCTURE OF RESONANCE RADIATION 

Of the various elements exhibiting h.f.s., the resonance radia 
tion of only one, mercury, has been studied with high resolving 
power apparatus. Ellett and MacNair[i2] (see Chap, v) were 
the first to show that, if a resonance tube containing mercury 
vapour was illuminated by light from a well-cooled mercury 
arc, the resonance radiation emitted therefrom, when ex 
amined with a Lummer plate, showed all five h.f .s. components. 
More recently, Mrozowski[i7], in a long series of researches, 
has made a very thorough investigation of the h.f.s. of the 
resonance line of mercury. He observed that if light from a 
mercury arc was sent through a cell containing mercury 
vapour in a strong magnetic field, certain of the h.f.s. com 
ponents of the resonance line could be filtered out, due to the 
Zeeman effect exhibited by the various components. By a 
proper choice of magnetic field he was able to let through four 
groups of lines: (a) the -25-4mA. component, (jS) the 
-10-4mA. and +21-5mA. components, (y) the 0-OmA. and 
+ ll-5mA. components, and (8) all five components. By using 
these various combinations of h.f.s. components as an exciting 
source to obtain resonance radiation from a tube containing 
mercury vapour, he found that the resonance radiation excited 
by a given group of h.f.s. components showed only those com 
ponents contained in the exciting source. For example, the 
resonance radiation excited by the - 25-4 mA. component con 
tained only that component, and that excited by the two com 
ponents 10-4 mA. and +21-5mA. contained these two 



40 INTRODUCTION 



components, etc. This proves that each h.f.s. line is itself a 
resonance line and that no line fluorescence occurs. This is 
exactly what would be expected from the energy level diagram 
of the previous section. Thus, excitation by the 0-0 and 
-f- ll-5mA. components (case y) leads to the excitation of the 
isotopes of mass 200 (absorption of the 0-0 component) and 
of mass 202 (absorption of the +11-5 component). Since 
the two isotopes act as two independent gases, and since each 
has but one lower h.f.s. state, it is clear that each component 
must behave as a resonance line. Similar considerations apply 
to all the other components. 

Another group of experiments performed by Mrozowski [18] 
has to do with the effect of added gases on the h.f.s. of the re 
sonance radiation of mercury. As will be explained in Chap, n, 
collision between an excited atom and a foreign gas molecule 
may result in the transfer of the former from one excited level 
to another. If light containing the components 0-0 and 
+ ll-SmA. was allowed to excite mercury vapour containing 
a little helium, it was found that the resonance radiation con 
tained only these two lines. On the other hand, if the excitation 
was by the -25- 4m A. component, the three components 
25-4, 10-4 and + 21-5mA. were found in resonance. The 
explanation of these experiments follows at once from Fig. 13. 
The two lines 0-0 and + 11- 5mA. are due to the two isotopes 
200 and 202 respectively, each exhibiting but one upper and 
one lower level. It follows, then, that a foreign gas can have no 
effect on the number of components obtained by this method 
of excitation. The component - 25-4 mA. consists of lines from 
the two isotopes 199, whichhave two upper levels/ == 3/2and 1/2, 
and 201, having three upper levels /= 1/2, 3/2, 5/2. Excited 
mercury atoms of one isotopic kind may be transferred from 
one upper state / to other upper states. Thus collisions of 
excited atoms of isotopic mass 199 will result in the excitation 
of the/= 1/2 as well as the/= 3/2 states, giving rise to the lines 
A and , contributing to the +21-5mA. and the -25-4mA. 
components respectively. Atoms of mass 201 may, by collision, 
arrive in the state /= 5/2 and /= 3/2 as well as /= 1/2, giving 
rise to the lines a, b, c, contributing to the components +21-5, 



2 

S 
% 



I 



a 

co^i rt 
tf H 



11 



it 




I 




OO OO O 




I I 



>15 oo 

p >M 

02 



SrSr 

CO CO 



CO CO 
O CO 



Tti i i u 



"a, 



o o o x co 

CO lO CD O t** 



ved 



" frVe^A 



' ?? 

7T U ' 



PnPM 



! KM t. co 



CO^CO CO CO 

OS OS OS CO 

OS 1O CSJ C<J 

X OS O O 

"3 X CO CO 



COCDIOIOTH^ W'^CM 

'o 'o 'o 'o ' f e ^"" W - 
CQCCOiWQQCQHPHN 
H H H H H H a 






cbcb ibio ^^ coco co_ 
tT? r-Top. 9 <P 95 2 



a 

I 



<e 

2: 



a a 



S 



1 



42 INTRODUCTION 

10-4 and 25-4 mA. These experiments are a good verifica 
tion of the assumptions underlying the analysis of the h.f.s. 
of the resonance line of mercury. 

Further work on the resonance radiation of the various h.f.s. 
components of the 2537 line has to do with the measurements 
on the polarization of resonance radiation and will be discussed 
in Chap. v. The h.f.s. of the visible triplet has also been in 
vestigated in a more complicated type of resonance radiation 
in which multiple excitation is involved. These experiments 
will be discussed in Chap. n. 

REFERENCES TO CHAPTER I 

[1] Bates, J. R. and Taylor, H. S., Journ. Amer. Chem. Soc. 50, 771 (1928). 

[2] Boeckner, C., Bureau of Stand. Journ. Res. 5, 13 (1930). 

[3] Bogros, A., Compt. Rend. 183, 124 (1926). 

[4] ibid. 190, 1185 (1930). 

[5] Carlo, G. and Lochte-Holtgreven, W., Z.f. Phys. 42, 22 (1927). 

[6] Christensen, C. J. and Rollefson, G. K., Phys. Rev. 34, 1154 (1929). 

[7] iUd. 34, 1157 (1929). 

[8] Dunoyer, L. and Wood, R. W., Phil. Mag. 27, 1025 (1914). 

[9] Dunoyer, L., Le Radium, 10, 400 (1913). 

[10] Compt. Rend. 178, 1475 (1924). 

[11] EUett, A., Journ. Opt. Soc. Amer. 10, 427 (1925). 

[12] EUett, A. and MacNair, W. A., Phys. Rev. 31, 180 (1928). 

[13] Fridrichson, J., Z.f. Phys. 64, 43 (1930); 68, 550 (1931). 

[14] Houtermans, F. G., ibid. 76, 474 (1932). 

[15] Kunze, P., Ann. d. Phys. 5, 793 (1930). 

[16] Mitchell, A. C. G-., Journ. Frankl. Inst. 212, 305 (1931). 

[17] Mrozowski, S., Bull. Acad. Pol. (1930 and 1931). 

[18] Z. f. Phys. 78, 826 (1932). 

[19] Pirani, Osram Lamp Works, Germany. 

[20] Ponomarev, N. and Terenin, A., Z. f. Phys. 37, 95 (1926). 

[21] Puccianti, L., Accad. Lincei Atti, 13, 430 (1904). 

[22] Rump, W., Z.f. Phys. 29, 196 (1924). 

[23] ibid. 31, 901 (1925). 

[24] Schein, M., Helv. Phys. Acta, Vol. 2, Supp. 2 (1929). 

[25] Schnettler, 0., Z.f. Phys. 65, 55 (1930). 

[26] Schiller, H., ibid. 35, 323 (1926); 59, 149 (1930). 

[27] Soleillet, P., Compt. Rend. 184, 149 (1927). 

[28] Strutt, R. J., Proc. Roy. Soc. 91, 511 (1915); 96, 272 (1919). 

[29] Terenin, A., Z.f. Phys. 31, 26 (1925); 37, 98 (1926). 

[30] Thomas, A. R., Phys. Rev. 35, 1253 (1930). 

[30 a] Weiss, C., Ann. d. Phys. 1, 565 (1929). 

[31] Wiedemann, E. and Schmidt, G. C., Wied. Ann. 57, 447 (1896). 

[32] Winans, J. G., Proc. Nat. Acad. Sci. 11, 738 (1925). 



INTRODUCTION 43 

[33] Wood, Ei. W., Researches in Physical Optics, I and II, Columbia 
University Press, New York (1913 and 1919). 

[34] Phil. Mag. 3, 128 (1902); 6, 362 (1903). 

[35] ibid. 10, 513 (1905). 

[36] ibid. 18, 187 (1909). 

[37] ibid. 23, 680 (1912); Proc. Phys. Soc. (London), 26, 185 (1914). 

[38] Phil Mag. 44, 1105 (1922). 

[39] Wood, R. W. and Dunoyer, L., ibid. 27, 1018 (1914). 

[40] Wood, R. W. and Kimura, M., ibid. 32, 329 (1916). 

[41] Wood, R. W. and Mohler, F. L., Phys. Rev. 11, 70 (1918). 

[42] Zehden, Z. f. Phys. 86 (1933). 



CHAPTER II 

PHYSICAL AND CHEMICAL EFFECTS CONNECTED 
WITH EESONANCE RADIATION 

1. STEPWISE RADIATION 

la. MERCURY. In earlier paragraphs of this book various 
simple types of fluorescence have been discussed in which the 
process giving rise to the fluorescence was due to absorption by 
normal atoms of the gas. It remains now to consider a type of 
fluorescence in which the absorption of light by excited atoms 
plays a dominant role. This type of fluorescence was first in 
vestigated by Fiichtbauer[27], who believed that, if mercury 
vapour were radiated by intense enough light from a mercury 
arc, other lines of the mercury spectrum besides the two 
resonance lines 2537 and 1849 would appear. 

The apparatus used by Fiichtbauer consisted of a quartz 
resonance tube entirely surrounded by a quartz mercury dis 
charge tube. Precautions were taken to cool the discharge so 
that sharp lines would be obtained, and a system of liquid 
mercury reflectors was used to increase the illumination from 
the discharge. The pressure of the mercury vapour in the 
resonance tube could be controlled by regulating the tempera 
ture of a side tube containing liquid mercury. His experiments 
showed that with 10-20 amperes current in the arc, and the 
side tube at 35 C., considerable fluorescence was observed, 
consisting of practically all of the stronger lines of the mercury 
spectrum of wave-length longer than 2537. On the other hand, 
if the side tube was kept in solid C0 2 , only a small amount of 
scattered light could be seen from the tube. On placing a thin 
glass tube, transparent to all radiation longer than 2537, 
between the resonance vessel and the exciting light, no 
fluorescence could be seen. This showed conclusively that the 
absorption of the resonance line was the first step in the process 
producing the fluorescence. Fiichtbauer supposed that excited 
mercury atoms reaching the 6^ state by absorption of light 



PHYSICAL AND CHEMICAL EFFECTS 



45 



could then absorb other lines from the arc, reaching higher 
states, and emit various frequencies as a result of this excitation. 

It seemed probable, therefore, that at least two quanta of 
light must have been absorbed successively by the mercury 
vapour before re-radiation occurred. The experiments of 
Fiichtbauer have since been repeated, and his assumption of 
"stepwise excitation 55 has been accepted. For want of a 
better name this type of fluorescence has since come to be 
called Stepwise Radiation. 

Fiichtbauer's original experiments were extended in a series 
of investigations by Terenin[66], by Wood and by Gaviola. 
The type of apparatus used in most of these experiments is 
shown in Fig. 14. A quartz cell E containing mercury vapour, 




Fig. 14. Apparatus of Wood and Gaviola. 

and at times other foreign gases as well, is radiated with light 
from a water-cooled quartz mercury arc Q. The fluorescence 
is observed with the help of a right-angled prism P 2 and a 
spectrograph. When the absorption of the vapour is to be in 
vestigated, part of the light from the arc is sent through the 
quartz cell with the help of the right-angled prism P I} and the 
radiation examined for reversal by means of the Lummer- 
Gehrcke plate G. Sometimes two mercury arcs with various 
filter combinations were used to study the effect of excitation 
by several combinations of mercury lines. Furthermore, provi 
sion was made to admit several gases at known pressures into 
the quartz cell. In order to discuss these experiments intelli 
gently it will be necessary to consider the energy-level diagram 
for mercury given in Fig. 1. 

Fiichtbauer's experiments showed that a necessary step in 



46 PHYSICAL AND CHEMICAL EFFECTS 

the excitation process was the absorption of the resonance line 
2537, thereby raising atoms to the G 3 ?! state. He did not 
actually show, however, that the next step in the process was 
the absorption of a line from the arc which ends on the 6 3 P 1 
state, although he inferred that such a process did occur, and 
his explanation is the only possible one based on modern 
theory. Wood's [75] first experiments consisted in determining 
which lines appear in fluorescence when the mercury vapour 
is excited by only certain groups of lines from the arc. In one 
case he used two mercury arcs, one water-cooled giving an un- 
reversed resonanceline and the other run hot so that the core of 
the resonance line was removed by self -reversal. The light from 
the water-cooled arc was filtered through a bromine filter, which 
passed only the lines 2537, 2967 and 3125-3131. Under these 
conditions no visible radiation could be seen in the resonance 
tube, but only the ultra-violet lines 3654 and 3663. On lighting 
the second (hot) arc various visible lines were observed, notably 
the visible triplet 4047, 4358 and 546 1 . When the light from the 
hot arc was filtered through cobalt glass, transmitting only the 
blue, the green line 5461 still persisted. These experiments 
show the definite steps in the excitation of the visible triplet, 
viz. by absorption of 2537 from the water-cooled arc atoms are 
raised to the 6 ^ state, and by the absorption of 4358 from the 
hot arc the 7^ state is reached from which the triplet is 
radiated. Thus one may see that the excitation occurs in two 
definite steps. 

As a further example of the ramifications of this process it is 
of interest to consider some experiments in which the exciting 
light was filtered through bromine vapour, which transmits the 
lines 2537, 2967 and 3125-3131. The visible light emitted from 
the resonance tube under strong illumination is yellow and a 
spectral photograph shows several ultra-violet lines. The fol 
lowing processes occur: The absorption of 2537 raises atoms to 
the 6 ^ state, some of which drop back to the 6 1 S state under 
emission of 2537, while others absorb lines from the arc ter 
minating on 6 3 P X . Atoms in the 6^ state may absorb 3131-5 
and 3125 and reach the 6 3 D 1 and 6 3 D 2 states, from which they 
may return to lower states with emission of 5770 (to 



CONNECTED WITH RESONANCE RADIATION 47 

3654 (to 6 3 P 2 ) and 3131-5 and 3125. By absorption of the inter- 
combination line 3131-8 by atoms in the 6 3 P X state, the 6 X D 2 
state may be reached, followed by a subsequent re-emission of 
2967-5, 3131-8 and 3663-2. It is to be noted that the line 3650 
does not appear under these circumstances. One might expect 
this line to appear since some atoms land in the metastable 
6 3 P 2 state by re-emission from the 3 D levels, so that absorption 
of 3650 and its subsequent re-emission might occur. This takes 
place to only a small extent. Excitation by unfiltered light, on 
the other hand, greatly enhances 3650. This is due to the fact 
that many atoms land in the 6 3 P 2 state as a result of the 
emission of 5461, and the subsequent absorption and emission 
of 3650 occurs. 

16. EFFECT OF ADMIXTURE OF FOREIGN GASES. The effect 
on the fluorescence of the admixture of several foreign gases at 
various pressures was also studied in detail. It was found at the 
outset that helium, nitrogen, carbon monoxide and argon had 
a marked effect on the relative intensity of the fluorescent lines. 
Of the four gases nitrogen was the most thoroughly investi 
gated. The most striking example of the effect of nitrogen is 
shown by the following observation of the relative intensities 
of the visible triplet. With no nitrogen in the tube the relative 
intensities of the lines were 4:2:1 (5461, 4358, 4047), whereas 
with a few "millimetres nitrogen pressure the relative intensity 
changed to 128 : 32 : 4. It will be seen that the intensity of all 
the lines is increased, but that of 5461 is relatively much more 
increased than that of 4047. The fact that the intensity of all 
lines is increased by nitrogen is due to the transfer of 6 3 P ^ 
atoms to the metastable 6 3 P state by collision with a nitrogen 
molecule. In the process, known as a collision of the second 
kind, the mercury atom loses 0*2 volt energy and the nitrogen 
gains an equal amount as vibrational energy, no energy being 
lost as radiation. Such metastable atoms have a much better 
chance, of absorbing a quantum of radiation from the exciting 
source than have atoms in the 6 8 P 1 state, since these metastable 
atoms have a longer mean life and consequently a larger 
chance of being in a state to absorb a quantum of 4047. Due to 



48 PHYSICAL AND CHEMICAL EFFECTS 

the long mean life of the 6 3 P state it is easy to see why the 
stepwise lines are increased in intensity. The existence of the 
long life of the 6 3 P state was recognized at about the same time 
through experiments on sensitized fluorescence (see Chap, n, 
2). 

Wood demonstrated conclusively that the increase in in 
tensity of the visible triplet in the presence of nitrogen was due 
to the production of a large number of atoms in the 6 3 P state. 
To do this he sent part of the light from the arc through the 
absorption cell by means of the two prisms P x and P 2 of Fig. 14 
and measured the absorption of the various mercury lines with 
the help of the Lummer-Gehrcke plate. His results showed 
that, with mercury vapour alone, none of the lines of the triplet 
showed any measurable absorption, while with a few milli 
metres of nitrogen present the line 4047 was strongly reversed. 
In later experiments, Gaviola[28] measured the reversal of 
4047 as a function of the pressure of the foreign gases nitrogen, 
carbon monoxide and water vapour, and found varying degrees 
of self-reversal depending on the nature of the gas and its 
pressure. Other lines, namely 2967, 5461 and 3650, should also 
show some absorption in the presence of nitrogen. Of these, 
3650 and 5461 are the only lines which have been extensively 
studied. The line 3650 showed a small amount of reversal, 
whereas 5461 showed none, indicating that the number of 
atoms in the 6 3 P 2 state is small. 

That certain lines show more absorption than others explains 
the fact that addition of nitrogen increased the intensity of the 
5461 line 32 times while it only increased the intensity of the 
4047 line four times, a considerable quantity of the light from 
4047 being lost by self -absorption. In general, the intensity of 
practically all the fluorescent lines is changed by the addition 
of nitrogen, carbon monoxide or water vapour. The exact rela 
tion of the intensities of the fluorescent lines to the foreign gas 
pressure is a more complicated matter and will be treated 
presently. 

As we have seen, most of the lines appearing as stepwise 
radiation are the result of absorption of two quanta of radia 
tion. The emission of the line 3650 is brought about by the 



CONNECTED WITH RESONANCE RADIATION 



49 



absorption of three light quanta. With mercury vapour in 
vacuo normal atoms absorb 2537, are brought to the 6 3 P X 
state where they absorb 4358 and are raised to the 7 3 S 1 
state; subsequent emission of 5461 brings the atom to the 
6 3 P 2 state, where it absorbs 3650 and is in a position to re-emit 
this line. The intensity of the fluorescent line 3650 must be 
proportional to the product of the intensities of the three arc 
lines producing it (2537, 4358, 3650). If the relative intensity 
of these lines in the arc is constant, the intensity of the 3650 
line in fluorescence should be proportional to the cube of the 
light intensity of the arc. This effect was shown by Wood and 
Gaviola[76] as follows: Mercury vapour, in the absence of any 
foreign gas, was radiated by the total light from a mercury arc. 
A series of wire screens, which cut down the total illumination 
by known amounts, was placed between the exciting lamp and 
the resonance tube. Observations were made on 3650 and 3654. 
The fact that 3650 is proportional to the third power whereas 
3654 is proportional to the second power of the exciting light 
intensity is shown by the following table. 

TABLE IV 



Line 3650 


Line 3654 


Change 


^/Change 


Change 


^Change 


150 times 


5-3 


30 times 


5-5 


1200 


10-6 


120 


11-0 


240 


6-2 


40 


6-3 


150 


5-3 


30 


5-5 


240 


(5-2 


40 


6*3 


400 


7-4 


50 


7-1 


480 


7-8 


60 


7-7 



An approximate theoretical treatment of this effect has been 
given by Gaviola[28]. 

Gaviola has made a careful experimental and theoretical 
investigation of the effect of foreign gases on the intensity of 
the fluorescent lines. He used the apparatus shown in Fig. 14 
and measured the absorption of the line 4047 as a function of 
the distance away from the wall of the tube through which the 
exciting light enters and of the pressure of the foreign gas. 



50 PHYSICAL AND CHEMICAL EFFECTS 

With the beam of light, whose absorption is to be measured, 
traversing the tube at a fixed distance (not given) from the 
front wall of the tube, he investigated the structure of the 
absorption line with different pressures of CO, H 2 O and N 2 . 
A clear reversal of the main component of 4047 was to be seen 
with 0015 mm. CO, the reversal increasing up to 0-2 mm. pres 
sure and then decreasing again such that at pressures above 

4 mm. no more reversal could be seen. Water vapour causes 
reversal at 0-05 mm. pressure and the reversal increases 
steadily until at 2 mm. pressure the whole line is absorbed. 
With N 2 , on the other hand, no definite reversal is shown until 
a pressure of 0-5 mm. is reached; below these pressures, how 
ever, a diffuse broadening of the line occurs. 

In order to test the absorption of 4047 as a function of depth, 
he placed two slits across the resonance tube in such a way as 
to allow the beam of 4047 to traverse the resonance .tube at 
distances of 2 cm. and 5 cm. from the illuminated wall, re 
spectively. At 2 cm. from the wall and with from 0-2 to 0-5 mm. 
water vapour pressure, self-reversal is clearly seen, but dis 
appears again if the pressure reaches 2 mm. At 5 cm. depth no 
self -reversal is seen at any time. These facts show that diffusion 
of metastable atoms does actually take place at low water 
vapour pressure and that the mean life of the metastable 
atoms is long enough to allow them to diffuse 2 cm. but not 

5 cm. The same experiments were performed with N 2 with the 
result that no reversal could be found at 2 cm. depth with any 
nitrogen pressure. This result is to be expected, because Gaviola 
had shown that reversal does not set in until at a pressure of 
0-5 mm., which is already too high to allow diffusion to take 
place. 

From an approximate consideration of the diffusion of meta 
stable atoms and the absorption coefficient of various lines in 
the excited vapour, Gaviola was able to show that the in 
tensity of the several fluorescent lines should vary with the 
depth from the illuminated window at which these lines are 
observed. After removing the slit system and Lummer-Gehrcke 
plate, he focused an image of the resonance tube on the slit of 
the spectrograph and was able to show that the intensity of the 



CONNECTED WITH RESONANCE RADIATION 51 

fluorescent lines changed as a function of distance from the 
illuminated wall and the conditions of excitation. Certain 
lines, notably 4358, persisted to considerable distances away 
from the wall with pressures up to 2 mm. of N 2 , whereas others 
such as 4047 persisted to large distances at low N 2 pressures 
and to only short distances at higher pressures. The results of 
Gaviola's experiments and calculations explain qualitatively 
the experimental fact that certain fluorescent lines are en 
hanced by the addition of N 2 while others are somewhat 
weakened, although addition of nitrogen causes an increase of 
the number of metastable 6 3 P mercury atoms present. 

Another series of experiments showing quantitatively the 
absorption of the 4047 line by the excited mercury vapour in 
the resonance tube as a function of foreign gas pressure was 
performed by Klumb and Pringsheim [37]. Their apparatus was 
somewhat similar to that previously described. Their resonance 
vessel was a quartz tube with plane ends and was illuminated 
from the side by a water-cooled quartz mercury arc. Light 
from a similar arc was projected by a suitable lens system 
along the axis of the tube and, after passing through a, 
monochromatic illuminator set to transmit the line 4047, was 
received by a photoelectric cell. Observations could be made 
as follows: (1) light from both arcs cut off (zero point measure 
ment), (2) intensity of 4047 with the exciting light (arc on side 
of resonance tube) cut off ( J x ), and (3) intensity of 4047 with 

both arcs illuminating the tube (/ 2 ). The relation E = r - 

J\ 
is a measure of the absorption of 4047 in the resonance tube. 

Measurements of the absorption of the line 4047 as a function 
of N 2 pressure, together with admixtures of other gases, are 
shown in Fig. 15. It will be noted that the absorption is zero 
at zero foreign gas pressure, rises sharply to a maximum of 
50 per cent, at about 1 mm. pressure, and then stays constant. 
It should be noted further that the addition of 10" 4 mm. of H 2 
markedly reduces the absorption for a given KT 2 pressure. This 
is to be expected, since H 2 is known to destroy metastable 
mercury atoms. The curve for the absorption in the presence 
of water vapour is slightly different, in that the absorption 



52 



PHYSICAL AND CHEMICAL EFFECTS 



reaches a maximum at 0-5 mm. pressure and then decreases 
with higher vapour pressure, in agreement with Gaviola's 
results. 

Ic. THE APPEARANCE OF THE FORBIDDEN LINE 2656 
(6 1 S -6 3 P ). Wood and Gaviola[76] observed that with small 
quantities of nitrogen or water vapour in the resonance tube 
the forbidden line 2656 (6 ^-G 3 P ) appeared. They found that 
water vapour was more efficient in producing the line than was 
nitrogen. This is what one would expect, since water vapour 
is more efficient in producing metastable atoms than is nitrogen. 



10 



1 ^ 2 3 4 5 6 7 8 9 10 II 12 mm. 

Upper curves: pure nitrogen; - - - with 10" 4 mm. H 2 ; 
Lower Curve: with 12 mm. He-Ne. 

Fig. 15. Absorption of 4047 as a function of foreign gas pressure. 

They also found that the intensity of the forbidden line was 
proportional to the first power of the intensity of the exciting 
light. This line, although considered as forbidden by the ex 
clusion principles of the older quantum theory, cannot be said 
to be strictly forbidden. The new quantum mechanics shows that 
such lines may have a small but finite probability of occurrence 
per mercury atom in the 6 3 P state. The above-mentioned ex 
periments have increased the number of 6 3 P atoms present 
to such an extent that the "forbidden" line appears. 

Id. THE HYPEKFINE STRUCTURE OF STEPWISE RADIATION. 
As has already been mentioned, Collins [16] and Mrozowski[53] 
have investigated the h.f.s. of the visible triplet lines in mer 
cury obtained by the method of stepwise excitation. Collins 



CONNECTED WITH RESONANCE RADIATION 53 

used two mercury arcs to excite fluorescence in a tube con 
taining (A) mercury vapour alone, and (B) mercury vapour 
together with a few millimetres of nitrogen. Observation of 
the fluorescence with a Lummer plate and spectrograph showed 
that only the strong central component of the 5461 line ap 
peared as fluorescence when mercury vapour alone was in the 
tube. With a few millimetres of nitrogen present, however, the 
fluorescent line showed two components, the 0-0 and the 
-23- 5mA. Mrozowski, exciting with filtered 2537 light to 
gether with light from a second arc giving only the visible 
lines, found only the main component present when nitrogen 
was present. The two experiments seem contradictory, but 
this contradiction may be only an apparent one, since the 
intensity of the exciting sources in the two cases may have been 
quite different. The main point of the experiment is that not 
all of the components of 5461 (there are some twelve of them) 
are seen in fluorescence but only the strongest one, A similar 
result was found with the other two lines of the triplet 4047 
and 4358 in fluorescence. Collins reported several components 
of each line both with and without nitrogen in the tube, and 
differences in the number of components depending on whether 
nitrogen is present or not. Mrozowski, on the other hand, found 
both lines to consist of only the central component. 

Mrozowski further investigated the structure of the fluores 
cent lines when they were excited by different h.f.s. com 
ponents of the resonance line, together with all the h.f.s. 
components of 4047. He found the rather surprising result that 
only the central component of the triplet lines appeared, no 
matter whether he excited with the - 25-4 mA. component of 
the 2537 line (containing only lines from the isotopes of odd 
atomic weight) or with components containing only lines from 
the isotopes of even atomic weight. He explains this by assum 
ing that metastable mercury atoms of a given isotopic kind 
can excite normal mercury atoms of a different isotopic kind 
to the metastable level by collision of the second kind. He 
further showed that the relative intensity of the triplet lines 
in fluorescence was independent of the h.f.s. components of 
2537 used in the exciting beam. 



54 PHYSICAL AND CHEMICAL EFFECTS 

One should remark at this point, in regard to Collins 's ex 
periments, that changes in the number and relative intensity 
of h.f.s. components of the visible triplet lines seen in stepwise 
fluorescence are to be expected when nitrogen is introduced 
into the tube. The factors governing the change are rather 
complicated, so that no exact theoretical prediction has yet 
been made. As to the result when no nitrogen is present, the 
intensity of the h.f.s. components of a given stepwise line will 
depend on the structure of the 4358 line, whereas, if nitrogen 
is present, ,the structure of the line 4047 will govern the 
excitation. Furthermore, the presence of nitrogen itself adds 
complications. 

le. CADMIUM ASTD ZINC. Since cadmium and zinc show 
similar spectra to mercury, differing only in separation of 
energy levels, Bender [4] thought it worth while to investigate 
the stepwise radiation exhibited by these elements. His 
experimental arrangement consisted of a resonance tube, of 
the usual shape, surrounded by a coil of quartz tubing, through 
which passed a high potential discharge in hydrogen and cad 
mium (or zinc). The resonance tube was temperature controlled 
and the vapour pressure of the cadmium kept constant at 
0-008 mm. The fluorescence was observed end on, and pre 
cautions were taken to avoid scattered light from the quartz 
surfaces of the tube. It was found that an intense bluish-green 
fluorescence was observable when the resonance tube was 
excited by the Cd-H 2 discharge, but that the tube emitted 
no light if cadmium was not present in the discharge. The 
fluorescence, with cadmium vapour alone in the resonance 
tube, contained all the strong lines in the cadmium spectrum 
(see Fig. 16 for spectrum of cadmium) except 2288. 

The effect of the addition of the gases nitrogen and carbon 
monoxide on the stepwise radiation of cadmium was quite 
different from the effects observed with mercury. The addition 
of 0-01 mm. of nitrogen produced an observable increase in the 
intensity of the 3404 line, which attained a maximum of 
intensity at 0-1 mm. nitrogen pressure. At pressures above 
0-1 mm. the ratio of intensity of 3404 to the rest of the spec- 



CONNECTED WITH RESONANCE RADIATION 55 

trum remained constant at 2 to 1 . A similar effect was produced 
on this line by carbon monoxide. There appeared to be no 




Fig. 16. Energy levels of cadmium. 

enhancement of the visible 'triplet (6 3 S a -5 3 P) due to the pre 
sence of nitrogen or carbon monoxide as was the case with 



56 PHYSICAL AND CHEMICAL EFFECTS 

mercury fluorescence, but merely a general quenching of the 
whole spectrum. The enhancement of the 3404 line is probably 
due to the formation of metastable 5 3 P atoms, as in the case 
of mercury. 

There are certain fundamental differences between the 
spectra of cadmium and mercury which are important. In 
the first place the mean life of the 5 3 P 1 state of cadmium is 
about 20 times longer than that of mercury. (Mean life of 
Cd 5^ = 2-5 x 10- 6 , of Hg 6 3?!== 1-08 x 10~ 7 .) This accounts 
for the fact that smaller pressures suffice to give enhancement 
of the 3404 line than are necessary to enhance analogous lines 
in the mercury spectrum. The ratio of the pressures necessary 
is about that of the ratio of the mean lives. Furthermore, the 
energy difference between the 5^ and the 5 3 P states in 
cadmium is only 0-07 volt, whereas in mercury the difference 
is 0*218 volt. The relative kinetic energy of the gas molecules 
at the temperatures used (350 C.) is about 0-08 volt and 
corresponds to the energy difference between 5^ and 5 3 P . 
Thus any S 3 ?! atoms brought to the 5 3 P state by collision 
would have a good chance of being transferred back to the 
5 3 P X state on the next collision. This explains why there is 
little enhancement of the spectrum by the addition of nitrogen 
and carbon monoxide. The main effect of these gases is there 
fore a general quenching of the whole fluorescent spectrum. 

In the case of zinc vapour, stepwise radiation was found, but 
the effect of carbon monoxide and nitrogen was not investi 
gated. 

2. PRODUCTION OF SPECTRA BY COLLISION WITH 
EXCITED ATOMS: SENSITIZED FLUORESCENCE 

2 a. THE PRINCIPLE OF MICROSCOPIC REVERSIBILITY. 
Franck and Hertz discovered in 1913 that electrons, given a 
velocity by acceleration through a potential field, would trans 
fer their kinetic energy into the internal energy of a molecule 
or atom. The atom thus excited might subsequently give up 
this energy as radiation. Such a process, in which a fast electron 
collides with a slow-moving atom and which results in the 



CONNECTED WITH RESONANCE RADIATION 57 

formation of an excited atom and a slow electron, has been 
termed a collision of the first kind. 

In order to preserve thermodynamic equilibrium in a mix 
ture of atoms and electrons it is necessary to assume that some 
kind of reverse process to the one explained above must occur 
in which fast electrons and unexcited atoms result. Not only 
must we assume that at equilibrium the overall rate of forma 
tion of fast electrons and unexcited atoms must be the same as 
the overall rate of formation of excited atoms and slow elec 
trons, but we are forced to make the postulate that : " The total 
number of molecules leaving a given quantum state in unit 
time shall equal the number arriving in that state in unit time, 
and also the number leaving by any one particular path shall 
be equal to the number arriving by the reverse path".* The 
postulate which entails that each microscopic process occurring 
must be accompanied by an inverse process is called the 
Principle of Microscopic Reversibility. 

Klein and E.osseland[35], making use of this type of reason 
ing, therefore postulated that if fast electrons could collide 
with unexcited atoms and produce excited atoms and slow 
electrons, then the reverse process must occur, namely that 
excited atoms may collide with slow electrons and produce 
unexcited atoms and fast electrons. The process must, of 
course, be unaccompanied by radiation. Such a process has 
been called a collision of the second kind. 

26. EFFICIENCY OF COLLISIONS OF THE SECOND KIND 
BETWEEN ATOMS AND ELECTRONS. Klein and Kosseland made 
calculations from which they could make some statements as 
to the efficiency of the processes. In order to carry out the 
calculations, consider an ensemble of atoms and electrons. 
The atoms will be considered to have only two states, a lower 
state 1 of energy E^ and an upper state 2 of energy E 2 . Now 
the number of atoms in each state at equilibrium is given by 

ni =C Pl e-^; n^Cp^ (4), 

* See E. C. Tolman, Proc. Nat. Acad. Sci. 11, 436 (1925), where the above 
statement and a discussion of the Principle of Microscopic Reversibility 
are to be found. 



58 PHYSICAL AND CHEMICAL EFFECTS 

where p i is the statistical weight of the ith state and C is a 
constant independent of E. Now the number of electrons 
having energies between E and E + dE is given by the 
Maxwell-Boltzmann law as 



...... (5), 

where K is again a constant independent of E. Let us define 
S 12 (E) as the probability of a collision of the first kind in such 
a way that the total number of collisions of the first kind taking 

place per second is 

S l2 (E)n I (E l )^(E)dE ...... (6). 

Similarly, for the number of reverse processes per second we 
have 

S 21 (E)n 2 (E 2 )p(E)dE ...... (7). 

Since Franck and Hertz found that for electron energies less 
than E 2 E 1 no excitation is possible, it follows that 

S i2 (E) = for E<E 2 -~E l ...... (8). 

Consider now the equilibrium of electrons in the energy range 
dE between E' and E r + dE when E' < E 2 - E l . Electrons can 
obviously only leave this energy range by collision of the 
second kind, and the number leaving is given by 



The number entering this energy range by collision of the first 
kind must have originally had energies between 

E" = E' + E 2 -Ei and E" + dE. 
The number is given by 



At equilibrium, therefore, we have 

n 2 v,(E')S 2l (E') = n 2 ^(E")S l2 (E") ...... (9). 

Remembering that 

E' f -E f = E 2 -E l ...... (10), 

it follows that 



A similar argument can be considered for the case in which 



CONNECTED WITH RESONANCE RADIATION 59 

E f > E z E! and leads likewise to ( 1 1 ) . One may see from (11) 
that, since 

E"*E' and ^=#2, S^(E')>S^(E ft \ 

which means that a collision of the second kind between a slow 
electron and an excited atom must be very probable. This is to 
be expected for electrons and atoms, at any rate, since a slow 
electron will remain in the neighbourhood of an atom longer 
than a fast one and the probability of energy transfer will 
therefore be greater. Investigations confirming the above 
theory have been made by Smyth [65], LatyschefE and Lei- 
punsky[4i], Kopfermann and Ladenburg[39], and Mohler[5i], 
and will be discussed further in Chap. iv. 

2c. COLLISIONS OF THE SECOND KIND BETWEEN Two 
ATOMS. Franck[24] extended the ideas of Klein and Kosseland 
to include collisions between two atoms or molecules. Thus he 
supposed that an excited atom might collide with a normal 
atom or molecule and give up a quantum of energy (E z jB x ) to 
the unexcited atom; the latter might then take up the energy 
either as translational energy, excitational energy or both, 
there being no loss of energy by radiation during the process. 
Such radiationless transfers of energy Franck also called 
collisions of the second kind. 

Many examples of these processes exist, and a list of them 
will be found in Chap. rv. We are concerned in this chapter with 
the bearing of such collisions on two important phenomena, 
namely, sensitized fluorescence and sensitized chemical 
reactions. 

2d. SENSITIZED FLTJORESCENCE. Consider a mixture of two 
kinds of atoms A and E, which for simplicity we shall suppose 
to have only one excited and one normal state. Let the energy 
state be represented as in Fig. 17, the excited state of A lying 
higher than that of B by an amount ATT. Let this mixture be 
irradiated by light of frequency v. If the number of atoms of 
the kind A is sufficient, there will be a considerable absorption 
of the frequency v and consequently some re-emission of the 
same frequency. If now the number of atoms of the kind B is 
large enough, so that the time between collisions between A 



60 



PHYSICAL AND CHEMICAL EFFECTS 



and B is of the same order of magnitude as the mean life of 
the excited state of A, then, by collision of the second kind 
between excited A atoms and B atoms, energy will be trans 
ferred to the B atoms, and there will be a subsequent emission 
of the frequency v together with the frequency v l . The differ 
ence in energy AW^ will then appear as relative kinetic energy 
of A and -B. Prom the laws of conservation of energy and 
momentum one can calculate what fraction of this kinetic 
energy is carried by A and B. Suppose the temperature is so 



AW 



hv 



Fig. 17. Illustrating sensitized fluorescence. 

low that the energy of thermal agitation is small compared to 
A W. Then from conservation of energy and momentum wehave 

...... (12), 



and 

from which it follows that 



...... (13), 



where V A and V B are the final velocities of A and B respectively. 
From (13) it is easy to see that, if A IF is large, the atom B will 
acquire a considerable velocity from the collision, especially 
if it is light. This fact may be demonstrated by the existence 
of a Doppler effect on the line of frequency v t , which should be 
broadened by an amount Av given by the well-known Doppler 
equation 



v 
- 
c 



...... (14). 

v ' 



CONNECTED WITH RESONANCE RADIATION 61 

These predictions have all been verified by experiment. 
Cario and Franck[i2, 14] tested the theory by experiments on 
mercury and thallium vapours. Their experimental arrange 
ment is shown in Fig. 18. A quartz tube Q, containing thallium 
and mercury vapours, is illuminated by the light of a well- 
cooled quartz mercury arc lamp. A vapour pressure of thallium 
of about 2 mm. is obtained by heating a globule of thallium to 
800 C. in a side tube contained in the oven 2 . Ahigh pressure 
of mercury vapour is also obtained by heating mercury to 
100 C. in the oven 3 . The furnace O x is kept at a temperature 
above 800 C. to keep thallium from condensing in the tube. 
Under these conditions of vapour pressure very bright fluores 
cence takes place in a very small layer close to the front of the 



__ T" '~~ N 

^-'-I_ r -" ~r' 




Tl(Cd) H * 
Fig. 18. Apparatus of Cario and Franck. 

resonance tube*. A spectrogram of the fluorescence shows a 
number of thallium lines in addition to the 2537 line of mer 
cury. In fact the intensity of the green thallium line 5350 is so 
marked that the experiment can be demonstrated before a 
class. When the mercury arc is run without cooling, so that the 
2537 line is reversed, the thallium fluorescence disappears 
completely. On freezing out the mercury vapour in the tube 
a similar disappearance of the fluorescence is noted. 

A list of some of the thallium lines occurring as fluorescence 
is given in Table V together with their classification. 

It will be seen that three of these lines come from energy 
levels which lie higher than 4-9 volts, the excitation energy of 
mercury. The explanation probably lies in the fact that kinetic 

* Such high vapour pressures of mercury obviously do not have to be 
employed to obtain a measurable fluorescence. For example, Mitchell 
(Jwmi. Frankl. Inst. 209, 747 (1930)), was able to obtain sensitized fluores 
cence of cadmium and thallium when the mercury vapour pressure corre 
sponded to that of room temperature. 



62 



PHYSICAL AND CHEMICAL EFFECTS 



energy, obtained through high temperatures, can co-operate 
with excitational energy to excite higher states. However, it 
is difficult to prove this statement conclusively by experiments 
on thallium on account of the low-lying metastable 6 2 P 3/2 
level. The relative intensities of the lines 2768 and 3776 may 
be taken as a test of Eqs. (13) and (14). It was observed that 
these lines did not occur with the same relative intensity with 
which they occur in the arc. For example, the line 3776 was 
very strong whereas 2768 was weak. The reason for this, given 
by the authors, is that the 2768 line comes from the 6 2 D 3/2 
level, lying only 0-4 volt below the excitation voltage of mer 
cury. The emitted line, therefore, is narrow and is absorbed on 
passing through the thallium vapour in the tube. The 3776 

TABLE V 



Line 


Series notation 


Energy 


Line 


Series notation 


Energy 


2580 
2709 


6 2 P 1/2 -8 2 S 1/2 
6P,,-8D 5/i 


4-78 
5-60 


3230 
3519 


6*P 3/2 -8*S 1/2 
6*P, /t -6*D B/1 


4-78 
4-51 


2768 


6*P 12 -6'D 3/2 


4-45 


3530 


6 2 P 3/2 -6*D 3/2 


4-45 


2826 


6 2 P 32 -9 2 s 1/2 


5-36 


3776 


6*P 12 -7*S 1/2 


3-27 


2918 


6P, /r -7D 5/ , 


5-24 


5350 


C 2 P 3/2 -7 2 S 1/2 


3-27 



line, on the other hand, comes from the 7 2 S 1/2 level, lying 1-6 
volts below the 6 3 P X level of mercury, and is consequently 
broadened by Doppler effect and is not weakened by absorp 
tion. 

A quantitative confirmation of this effect was obtained by 
Rasetti[6i], who investigated the sensitized fluorescence of 
sodium. The energy excess of excited mercury above that 
necessary to excite the D lines is 2-8 volts which, on applying 
Eq. (11), would give the excited sodium atoms a velocity of 
4-3x 10 5 cm./sec. The distribution of the velocities of the 
excited sodium atoms is uniform as regards direction in space, 
but is not a Maxwellian one, since all the molecules have the 
same velocity. The emission line should be broadened by the 

amount AA=- , and the intensity distribution should be 
c 

uniform. Taking v as 4-3 x 10 5 , AA is equal to 0-17 A. Using 
a 40-plate echelon grating Rasetti measured the breadth of 



CONNECTED WITH RESONANCE RADIATION 63 

both D! and D 2 . A mean of six observations gave AA 0- 16 A. 
in remarkable agreement with theory. The reader should note, 
however, a further discussion of these results in 2/. 

In order to make an unambiguous test as to whether trans- 
lational energy and excitational energy can co-operate to 
excite higher quantum states, the sensitized fluorescence of 
cadmium was studied. The advantage of cadmium (see Fig. 16) 
lies in the fact that it has no low-lying metastable states which 
might be excited by collision of the first kind with other normal 
atoms having thermal velocities. The experiment was per 
formed with the resonance tube at 800 C., and it was found 
that not only did the line 3261 appear but also the visible 
triplet from the level 6 ^ , having an excitational energy of 6- 3 
volts. When the experiment was repeated with the resonance 
tube at 400 C., the visible triplet did not appear. In order to 
be sure that this effect was not a result of stepwise radiation 
in mercury, the experiments were repeated using a mono 
chromatic illuminator passing only the line 2537, with the 
same results. It is therefore clear that in order to excite the 
6 3 S 1 state of cadmium, excitational energy of mercury (4-9 
volts) must co-operate with translational energy from tem 
perature motion. 

A similar experiment on a mixture of zinc and mercury 
vapour was carried out by Winans [74], who found still other 
effects than those reported by Cario and Franck. The experi 
ments were made in a sealed-off quartz tube containing mer 
cury vapour at 0-28 mm. and zinc vapour at 16 mm. pressure. 
The tube was kept at 720 C. Light filters were used to give 
excitation by various combinations of mercury lines. It was 
found that when the mixture was irradiated by the full spec 
trum of the water-cooled mercury arc (1849-7000 A.) the 
lines given hi Table VI appeared. 

It will be noted that the lines coming from states with 
energies as high as 7-74 volts appeared. When the mixture was 
excited by wave-lengths from 3200-7000 A., no zinc lines 
appeared, which shows that lines in the region below 3200 A. 
are necessary. With incident radiation of from 2300-7000 A. 
all lines appeared except 2138, the intensity of the sharp 



64 



PHYSICAL AND CHEMICAL EFFECTS 



triplet being much reduced, however, by the omission of the 
wave-lengths between 1849 and 2300. When the exciting light 
consisted of only 2537 and 4358 no lines except 3075 appeared. 
If the exciting light contained all wave-lengths from 1849 to 
7000 without the core of 2537, only the sharp triplet appeared. 
The same was true when the exciting light contained wave 
lengths from 1849-2000 with light from the mercury arc 
(either hot or cold) or from the aluminium spark. Finally, with 
wave-lengths between 1950 and 2000 no sensitized fluorescence 
occurred. 

The results are to be explained as follows. Since the sharp 
triplet only appeared brightly when the exciting light con- 

TABLE VI 



Wave 
length 


Series notation 


Energy necessary 
to excite 


4810 
4722 
4680 


4 3 P 2 -5 3 S 1 ) 
4 3 P 1 -5 3 S 1 

4 3 P -5 3 Sj 


G-62 


3344 


4 3 P 2 -4 3 D 3 ) 




3302 
3282 


4 3 P 1 -4 3 B 1 l 
4 3 P -4 3 Dj 


7-74 


3075 
2138 


4%-4 3 P 1 


4-0 1/ Resonance 
5-76 \ lines 



tained wave-lengths near 1849, it is certain that the G 1 ?! state 
of mercury must have been excited. In general, however, 1849 
is highly reversed in a mercury arc. Since the 6 l P l state of 
mercury was excited by a hot arc and aluminium spark it is to 
be inferred that the absorption line at 1849 was highly broad 
ened due to pressure, or perhaps even molecule formation. 
The fact that the diffuse zinc triplet did not appear when only 
2537 and 4358 were in the exciting light shows that these lines 
are probably brought about by collision with some higher 
excited state of mercury formed by step wise radiation. A small 
percentage of the intensity of the sharp triplet is also probably 
due to collision with mercury atoms in higher states due to 
stepwise radiation. 

The results of this experiment are not to be taken as in dis 
agreement with those of Cario and Franck on cadmium, since 



CONNECTED WITH RESONANCE RADIATION 65 



the amount of energy necessary to reach the S^ state of zinc 
is greater than that necessary in cadmium, and the tempera 
tures employed here were not so high. 

The sensitized fluorescence of many other metals has been 
investigated as an aid to finding their energy levels. The fol 
lowing metals have been studied: thallium [12], silver [12], cad 
mium [14], sodium [7], lead, bismuth [38], zinc [74], indium, arsenic 
and antimony [21] (the two last giving negative results). 

2e. EFFECT OF METASTABLE ATOMS. In view of the fact 
that Wood and Cario had shown that the addition of a foreign 
gas quenched mercury resonance radiation, Donat[2i], and 
later Loria [43], made investigations of the effect of added gases 
on the sensitized fluorescence of thallium. The gases argon, 
nitrogen and hydrogen were used. It was to be expected that 
since these gases were known to remove mercury atoms from 
the 6 3 P X state (quenching), the sensitized fluorescence would 
also be quenched as a result. However, on performing the ex 
periment with argon or nitrogen, the intensity of the thallium 
lines was found to increase. This experiment can be explained 
in the following way. Mercury atoms are raised to the 6^ 
state by absorption of 2537; collision with argon or nitrogen 
then brings them to the metastable 6 3 P . These atoms have a 
long mean life, and also appear to be able to survive many 
collisions with nitrogen molecules and argon atoms without 
losing their activation. They are therefore able to remain 
activated until they make a collision with a thallium atom. 
This causes a corresponding increase in the intensity of the 
sensitized fluorescence, since, without nitrogen or argon, a 
considerable fraction of the normal mercury atoms would lose 
their energy by radiation before collision. These experiments, 
therefore, are in agreement with and supplement those of Wood 
on stepwise radiation. Donat measured the change of intensity 
of the mercury 2537 line and the thallium lines as a function of 
nitrogen and argon pressure. He found qualitatively that the 
intensity of 2537 which was lost owing to quenching was gained 
by the thallium lines. Loria and Donat found that there was a 
certain pressure of nitrogen or argon which gave the greatest 



66 PHYSICAL AND CHEMICAL EFFECTS 

increase in intensity of the thallium lines, the optimum pres 
sure for argon being greater than that for nitrogen, as one 
would expect from quenching data. It will be seen that the 
existence of an optimum pressure for sensitized fluorescence is 
in agreement with experiments on stepwise radiation. Hydro 
gen, on the other hand, showed a quenching effect both on 
the 2537 line and on the thallium lines. This shows that colli 
sions with hydrogen always result in the formation of mercury 
atoms in the normal state. Sensitized fluorescence may there 
fore be used as a criterion for telling whether a given gas 
quenches excited mercury atoms to the normal (6 1 S ) or 
metastable (6 3 P ) state. 

Orthmann andPringsheim [59] showed that collisions between 
excited and normal mercury atoms lead to the production of 
metastable atoms. They repeated the Cario and Franck experi 
ment keeping the thallium pressure at 2 x 10~ 2 mm. (610 C.), 
whereas the mercury vapour pressure was gradually increased. 
They noticed that, as the pressure increased up to one atmo 
sphere, the thallium lines lost none of their original intensity, 
whereas the mercury radiation was completely quenched. 

2/. EFFICIENCY OF COLLISIONS OF THE SECOND KIND 
BETWEEN ATOMS. We have mentioned that a collision of the 
second kind between one atom and one electron is most efficient 
when the electron has a small velocity. When a collision of the 
second kind between two atoms occurs, a similar relation holds ; 
viz. the collision will be most efficient when the least energy 
is converted into kinetic energy [23]. That this effect is to be 
expected theoretically was shown by JSTordheim[54] and by 
Carelli [ii]. Later developments of the wave mechanics [34] have 
shown that if two atoms have energy levels lying near to 
gether, a "quantum mechanical resonance" effect takes place 
between them. As an illustration consider an atom A which is 
in an excited state having an energy of 5 volts, say. This atom 
makes a collision, while still excited, with an unexcited atom 
B which has two energy levels, one at 4-9 volts, the other at 
4-0. The quantum theory says that a very strong interaction 
(resonance) will take place between the atom A and the 4-9 



CONNECTED WITH RESONANCE RADIATION 67 

volt energy level of B, which will lead to a very great proba 
bility of the 4-9 volt level of B being excited. The probability 
of the 4-0 volt level being excited is, on the other hand, much 
smaller. 

Several attempts have been made to test these theories ex 
perimentally, but most of the earlier ones led to no definite 
conclusions, due to various complicating factors. Beutler and 
Josephy[7], however, succeeded in showing this effect very 
beautifully by experiments on the sensitized fluorescence of 

TABLE VII 



Na 
term 


Emission 
line (A.) 


Energy 
(volts) 


Energy difference 
(volts) 


Hg 
term 


6'P t 


6*P 


4 2 D 
5 2 P 


5688 5683 
2853 


4-259 
4-322 


-0-601 
-0-538 


-0-383 
-0-320 




6 2 S 


5154 5149 


4-485 


-0-375 


-0-157 




5 2 D 


4983 4979 


4-567 


-0-293 


-0-075 




6 2 P 


2680 


4-599 


-0-261 


-0-043 






(2656) 


(4-642) 


(-0-218) 




6 3 P 


7 2 S 


4752 4748 


4-687 


-0-173 


+ 0-045 




6 2 D 


4669 4665 


4-734 


-0-126 


+ 0-092 




72 p 


2594 


4-751 


-0-109 


+ 0-109 




8 2 S 


4545 4543 


4-805 


-0-055 


+ 0-163 




7 2 D 


4497 4494 


4-834 


-0-026 


+ 0-192 




8 2 P 


2544 


4-846 


-0-014 


+ 0-204 






(2537) 


(4-860) 




(+0-218) 


6 3 P t 


9 2 S 


4223 4420 


4-880 


+ 0-020 


+ 0-238 




8 2 D 


4393 4390 


4-899 


+ 0-039 


+ 0*257 




9 2 P 


2512 


4-907 


+ 0-047 


+ 0-265 




10 2 S 


4345 4341 


4-930 


+ 0-070 


+ 0-288 




9 2 D 


4320 4316 


4-943 


+ 0-083 


+ 0-301 





sodium vapour. Sodium has many energy levels lying between 
and 5*0 volts, several of which lie very close to 4-860 volts 
(G 3 ?! state of Hg) and 4-642 volts (6 3 P state), as is shown in 
Table VII. By exciting with 2537, they observed the intensities 
of various sodium series appearing in sensitized fluorescence. 
One would expect, if the series were excited in the usual way, 
that the intensity of the higher numbers of the series (lines 
coming from states with large n) would decrease monotonically 
with n. On the contrary, Beutler and Josephy found that 
within the series 3 2 P~ft 2 S the line 3 2 P-9 2 S was by far the 



68 



PHYSICAL AND CHEMICAL EFFECTS 



strongest line observed. The state from which this line comes 
lies within 0-020 volt of the 6^ state of mercury. The state 
8 2 P lies even closer (0-014 volt), but this could not be observed 
as it gives rise to the line 2544, which lies too close to the strong 
mercury line 2537 to allow of intensity comparison. Fig. 19 
shows the result of the measurements. In constructing this 
figure the intensity of the various lines was corrected for sensi 
tivity of the plate, divided by v (the frequency) and g (the 



JL 



50 



40 



30 



20 



10 - 




4-1 



4-3 



4*5 



4-7 
75 



95 



5-0 Volts 



Fig. 19. Intensity relations in sensitized fluorescence of sodium. 
(Beutler and Josephy.) 

statistical weight of the upper state) to place them on an equal 
footing for comparison. The ordinates give the probability of 
excitation of a given state and the abscissae the energy of the 
states. It will be seen at once that the 9 2 S state, lying close 
to 6 3 P 15 shows an extremely high probability of excitation. 
A small maximum also occurs at the 7 2 S state, lying close to 
the metastable 6 3 P level. Since the experiments were per 
formed at rather high mercury pressures some metastable 
atoms were present. One should remark that since the lines 
3 2 P-?i 2 S are not resonance lines the results are wtiolly free 



CONNECTED WITH RESONANCE RADIATION 69 

from complications arising from absorption. A similar result 
was obtained by Webb and Wang [73] by mixing sodium vapour 
with excited atoms from the arc stream of a mercury arc. The 
results are in general agreement with those of Beutler and 
Josephy, although the experimental conditions were not as 
clean cut as theirs. 

A remark about Rasetti's experiments (p. 62) is now neces 
sary. He observed that the D lines excited by sensitized 
fluorescence were very broad, but did not concern himself with 
the higher series lines emitted. Since D lines will be emitted 
as a result of excitation of the higher series members as well 
as by direct excitation of the 3 2 P states of sodium, not 
much weight can be attached to the quantitative results of 
Rasetti. 

2g. CONSERVATION OF SPIN ANGULAR MOMENTUM IN COL 
LISIONS OF THE SECOND KIND. The new quantum mechanics* 
predicts another effect which has a bearing on the efficiency of 
collisions of the second kind. This effect depends on the electron 
configurations of two atoms undergoing a collision. Let us 
consider the particular case of atoms having an even number 
of electrons. Each electron in the atom may be considered as 
spinning, and the resultant spin, s, of all the electrons in a 
given state determines the multiplicity of this state (multi 
plicity = 25-1-1). If two electrons spin with their spin vectors 
antiparallel to each other they may be said to be paired, and 
the resultant spin is zero. A state in which all of the electrons 
are paired will have zero resultant spin. If, on the other hand, 
two electrons spin with their spin vectors parallel, they are not 
paired. A state in which two of the electrons are unpaired will 
have a resultant spin of one. If two atoms are about to make 
a collision of the second kind, Wigner's theorem states that, of 
all the possible transfers of energy, that one will be most likely 
to occur in which the total resultant spin, considered for the two 
atoms together, remains unchanged. Consider now the case of 
a krypton atom in the metastable [4p 5 ( 2 P 3/2 ) 5s] state (to be 
denoted by 3 P 2 ) which may make a collision with a mercury 

* E. Wigner, Gott. Nachr. 375 (1927). 



70 PHYSICAL AND CHEMICAL EFFECTS 

atom in the normal state (6 X S ). We may write the electron 
configuration for the two atoms as 

Kr(*P 2 ) + Hg(6%) (a) 

5=1 5 = 8=1 

where s is the resultant spin for each atom and S for the con 
figuration of two atoms. We may suppose the result of the 
collision to be either 

Kr(%) + H g (8iD 2 ) (6) 

5 = 5=0 S=0 

or KrPSoHHg^DJ (c) 

5=0 5=1 5=1 

Of the two end states the theorem states that (c) would be the 
most probable, since the total resultant spin is unchanged. 

Beutler and Eisenschimmel[5] investigated spectroscopi- 
cally the light from a discharge tube containing mercury, 
krypton and helium. Mercury has two states of nearly the 
same energy lying close to the 3 P 2 state of krypton. These are 
&*D n and 8*D 2 . They first measured the intensity of the lines 
emanating from these two states in the mercury-helium dis 
charge containing no krypton. They then added a small 
amount of krypton to the discharge and measured the intensity 
of the same lines under these conditions. The results showed 
that while the intensity of the lines coming from both states 
increased, that of the line coming from 8 3 D n increased con 
siderably more than that from 8 1 D 2 in accordance with (c). 
This experiment would seem to substantiate the theory that 
"electron spin is conserved" on collision. 

Sensitized band spectra of several molecules have also been 
observed. The explanation of the processes involved in the 
production of such spectra involves a discussion of certain 
chemical reactions taking place in the excited gases. The pro 
duction of these bands will therefore be discussed in the next 
section on the chemical effects of resonance radiation. 



CONNECTED WITH RESONANCE RADIATION 71 

3. INTERACTION OF EXCITED ATOMS WITH MOLE 
CULES. CHEMICAL REACTIONS TAKING PLACE IN THE 
PRESENCE OP OPTICALLY EXCITED ATOMS; SENSI 
TIZED BAND FLUORESCENCE 

3 a. INTRODUCTION. It has long been known that certain 
chemical reactions which will not proceed under the influence 
of a given frequency of light can be stimulated by adding a 
substance which is sensitive to this light frequency. After the 
reactionhasrun its course, it is found that the added substance 
is unchanged in composition or physical properties. Such a 
reaction is said to be " photosensitized" to the frequency v by 
the addition of a "sensitizer". As examples of this process we 
may cite the sensitization of photographic emulsions to green 
and red light by addition of certain dyestuff s, and also the sen 
sitization of ozone decomposition to certain light frequencies 
by the addition of chlorine.* 

Two problems arise when one studies photosensitized re 
actions: (1) the action of the sensitizer and (2) the subsequent 
steps of the chemical reactions occurring as a result of the 
action of the sensitizer. The first problem has been practically 
solved through the combined efforts of physicists and chemists, 
and is intimately connected with the study of resonance radia 
tion. The second problem, however, being of a more compli 
cated nature, is still fraught with difficulties, and many con 
tradictions are to be found in the literature concerning it. We 
shall be more concerned in this chapter with the primary 
chemical processes occurring as the result of the absorption of 
resonance radiation by atoms ; the more complicated chemical 
reactions occurring thereafter will be treated with only so much 
detail as will serve to give a picture of this field of research. 

36. REACTIONS TAKING PLACE IN THE PRESENCE OF 
EXCITED MERCURY ATOMS. That atoms excited by resonance 
radiation may give over their energy to other molecules and 
cause them to react chemically was first shown by Cario and 
Franck[i3]. They found that hydrogen, activated by collision 
with excited mercury atoms, could be made to react with 

* F. Weigert, Ann. der Phys. 24, 243 (1907). 



72 PHYSICAL AND CHEMICAL EFFECTS 

metallic oxides, whereas, under similar temperature conditions 
and without the presence of activated mercury vapour, no 
reaction would occur. 

The apparatus consisted of a quartz tube containing a drop 
of mercury and some metallic oxide (CuO or W0 3 ). The quartz 
tube was connected to a vacuum system through which pure 
hydrogen, obtained by heating a palladium tube, could be 
admitted at low pressures. The pressure of hydrogen could be 
measured throughout the course of the reaction by means of 
suitable manometers. Any condensable matter, formed as a 
result of the reaction, could be frozen out in a liquid-air trap. 
The temperature of the reaction vessel was maintained at 
45 C. during the course of the experiments. 

If the reaction tube contained a small amount of hydrogen 
(a few tenths to 20 mm. pressure) and was illuminated by light 
from a cooled mercury arc, a decrease in the pressure of hydro 
gen was observed, whereas, if the mercury arc was allowed 
to run hot so that the resonance line was reversed, no change 
in pressure was noted. Furthermore, no reaction was found 
to occur when mercury vapour was absent. Experiments with 
the yellow oxide of tungsten (W0 3 ) showed that it was reduced 
to the blue oxide in those experiments in which a decrease in 
the hydrogen pressure occurred. The fact that no reaction 
occurred unless the incident radiation contained the un- 
reversed 2537 line of mercury showed at once that the first step in 
the process was the absorption of the resonance line, resulting 
in the formation of excited (6^) mercury atoms (hydrogen 
shows no absorption in this region of the spectrum). The fact 
that the oxides were reduced when hydrogen was in the 
presence of excited mercury atoms, whereas no reaction oc 
curred in their absence, led the authors to suppose that atomic 
hydrogen was formed as a result of a collision between an 
excited mercury atom and a hydrogen molecule. This line of 
reasoning follows from well-known chemical experiments, 
which show that ordinary molecular hydrogen will not react 
with CuO or W0 3 at the temperatures employed in the experi 
ment, but that atomic hydrogen, formed in a discharge tube, 
will reduce these oxides. Cario and Franck suggested, there- 



CONNECTED WITH RESONANCE RADIATION 73 

fore, that the second step of the process was the dissociation of 
$ hydrogen molecule into two atoms as a result of the collision 
with an excited mercury atom. This process is energetically 
possible, since the energy of an excited mercury atom is 4-9 
volts and that needed to dissociate hydrogen is only 4-46 volts. 
The remainder of the energy (about 0*4 volt) was supposed to 
be taken up as relative kinetic energy of the three atoms after 
collision. The mechanism suggested by Cario and Franck for 
this step in the process, while energetically possible, is not the 
only simple mechanism which might be suggested, as we shall 
show later. It is sufficient for our present purpose simply to 
state that hydrogen is " activated " by collision of the second 
kind with excited mercury atoms, thereby being enabled to 
react with the metallic oxides. 

Soon after this experiment was performed other reactions 
sensitized with mercury vapour and involving the reaction of 
hydrogen with other chemical elements were studied. Thus 
Dickinson [18] showed that hydrogen would react with oxygen 
at low temperatures when a mixture of these gases with mer 
cury vapour was radiated with the unreversed resonance line 
of mercury. A further study of this reaction was carried out by 
Mitchell [48], Taylor [67], Marshall [44, 45, 46], and many others. 
Hydrogen was also found to react with ethylene [44] and with 
many other substances under the influence of excited mercury 
vapour. Finally, other substances such as ammonia [19, 69], 
hydrazine[22] and water [63] were found to decompose in the 
presence of excited mercury atoms. 

It will be of more interest to forgo a chronological discussion 
of these reactions and establish a few important facts. The fact 
that none of these sensitized reactions will proceed unless 
mercury vapour is present and the mixture illuminated with 
the unreversed resonance line of mercury shows that mercury 
atoms in the 6 3 P X state are necessary for the process. It does 
not show, however, that atoms in still higher quantum states, 
brought there by stepwise excitation, are not involved in the 
process. That mercury atoms in higher quantum states than 
the 6 3 P X are not involved to any appreciable extent in the 
activating process has been shown by many experiments. 



74 PHYSICAL AND CHEMICAL EFFECTS 

Marshall [44] showed that the introduction of a chlorine- 
bromine filter, absorbing all radiation between 2900 and 
5000 A., had no effect on the hydrogen-oxygen reaction. 
Marshall [46] and Frankenburger[25] found that the hydrogen- 
oxygen and the hydrogen-carbon monoxide reactions are 
directly proportional to the intensity of the 2537 line in the 
exciting source. Mitchell and Dickinson [49] observed no in 
crease in the rate of ammonia decomposition when the mixture 
was radiated with the light from an uncooled mercury arc 
(emitting radiation longer than 2300) in addition to that from 
a cooled mercury arc. Finally, Elgin and Taylor [22], by inter 
posing screens of known transmission between the light source 
and the reaction vessel, showed that the rate of decomposition 
of hydrazine, in the presence of excited mercury vapour, was 
proportional to the first power of the light intensity. 

That metastable (6 3 P ) mercury atoms may also activate 
hydrogen was shown by Meyer [47], who added nitrogen, at 
about 10 mm. pressure, to a mixture of hydrogen and mercury 
vapour. He found that the addition of nitrogen increased the 
rate of reaction between hydrogen and metallic oxides, especi 
ally at low hydrogen pressures. The explanation of this effect 
is analogous to that of the experiments of Donat and Loria on 
the sensitized fluorescence of thallium. Collisions between 
nitrogen and 6 3 P a mercury atoms lead to the formation of 
6 3 P mercury atoms. The production of the metastable atoms 
increases the rate of the reaction since, owing to their long life, 
they have a greater chance of colliding with hydrogen mole 
cules while still excited than have G 3 ?! atoms, and many of 
the latter lose their energy by radiation before collision with 
hydrogen. 

Cario and Franck[i3] investigated the effect of hydrogen 
pressure on the rate of the hydrogen-copper oxide reaction. 
They found that the rate increased as the pressure increased 
up to a limiting value, above which no increase in rate occurred. 
The explanation is that at the higher pressures the excited 
mercury atom loses its activational energy to hydrogen before 
it has time to radiate. At the lower pressures, however, a 
certain number of mercury atoms will radiate their energy 



CONNECTED WITH RESONANCE RADIATION 75 

before colliding, resulting in a falling off in the rate of reaction. 
A quantitative treatment of this idea was given by Turner [71], 
which enabled him to obtain a rough estimate of the mean life 
of a mercury atom in the 6 3 P 1 state from the data of Cario and 
Franck. Since considerations of this type are fundamental to 
the elucidation of the mechanism of all sensitized reactions, we 
give the following simple derivation. 

Mercury atoms are excited by absorption of radiation from 
the arc . ( 1 ) The number excited is proportional to the intensity 
of light, /, of wave-length 2537 in the arc and to the concentra 
tion of mercury vapour in the tube, [Hg]. Excited mercury 
atoms either (2) radiate or (3) collide with a hydrogen molecule 
and activate it. We shall assume that every hydrogen molecule 
struck eventually leaves the gas phase due to reaction with 
the oxide. The rate of formation of excited mercury atoms is 
given by* 

|[Hg'] = M[Hg] ...... (15), 

and the rate at which they leave the excited state by 

-| [Hg'] = ft, [Hg'] + & 3 [Hg'] [HJ ...... (16). 

The rate of activation of hydrogen is given by 



...... (17). 

When a steady state has been reached the rates of formation 
and destruction of excited mercury atoms will become equal 
and we may equate (15) and (16), whereby we may solve for 
the unknown [Hg']. Eq. (17) will then become 



_ 2 __ 
01 ~' + ...... (1 '' 



From Eq. (19) it will be seen that a plot of l/B against 
should give a straight line, the ratio of whose slope to intercept 

* As is customary in chemical reaction theory we designate the concen 
tration of any substance by [ ]. The partial pressure of any constituent 
will be proportional to the concentration. 



76 PHYSICAL AND CHEMICAL EFFECTS 

should be k 2 /k 3} the constants k iy I, [Hg] thereby being elimi 
nated. Turner found that a plotof IjE against l/p^ from Cario 
and Franck's data did actually give a straight line in agree 
ment with theory. Since & 2 * s ^ e chance that a G^j mercury 
atom will emit a light quantum, it is obviously equal to I/T, 
where r is the mean life of the excited state. Similarly, & 3 is the 
chance of collision between an excited mercury atom and a 
hydrogen molecule, which may be calculated from kinetic 
theory. The ratio & 2 /& 3 , determined from this experiment, 
therefore gives a measure of r. Turner's calculation gives a 
value for r in fair agreement with values obtained by other 
methods. 

It should be emphasized at this point that since the mechan 
ism postulated here does not take account of the imprisonment 
or diffusion of resonance radiation or the broadening of the 
absorption line due to pressure, the calculation should only be 
applied when pressure of the mercury vapour and of the 
hydrogen is small. Other experiments, which we shall note 
later, were performed at atmospheric pressure of reacting gases 
and high mercury vapour pressure, so that such simple con 
siderations do not apply. In order to obtain any real insight 
into the mechanism of reactions occurring through the agency 
of resonance radiation, all pressures should be kept as low as 
possible. 

3c. THE MECHANISM OF THE ACTIVATION OF HYDROGEN BY 
EXCITED MERCURY ATOMS. The question of the mechanism 
of the activation of hydrogen by excited mercury atoms, which 
we have so far left open, is one which has interested physicists, 
and chemists for a number of years. Originally three separate 
mechanisms were proposed: (1) Cario and Franck supposed 
that a 6^ mercury atom collides with a hydrogen molecule 
and dissociates it in an elementary act into two hydrogen 
atoms: 

Hg (6 spj + H 2 = Hg (6 iS ) + H + H. 

(2) Mitchell[48] postulated that the result of the collision was a 
hydrogen molecule in a high state of oscillation and rotation: 



CONNECTED WITH RESONANCE RADIATION 77 

(3) Compton and Turner [IT] assumed that the result of the 
collision was a HgH molecule and a hydrogen atom : 



All of the above mechanisms are energetically possible. 

That some atomic hydrogen is formed as a result of collisions 
between excited mercury atoms and hydrogen molecules has 
been shown by Senftleben and his collaborators^, 64]. They 
illuminated a quartz vessel containing hydrogen and mercury 
vapour with light from a water-cooled mercury arc, and ar 
ranged to measure the changes in heat conductivity of the 
hydrogen by a hot-wire method. They found an increase in the 
heat conductivity when the mixture was illuminated, but on 
interposing an absorbing layer of mercury vapour between the 
light source and the conductivity vessel a much smaller in 
crease in the conductivity was observed, showing that the 
effect was caused by the production of excited mercury atoms. 
From the increase in heat conductivity they inferred that 
hydrogen atoms are produced. The experiment is, however, 
not entirely free from objections, and hence cannot be con 
sidered as conclusive proof of the production of hydrogen 
atoms. 

As evidence for the formation of HgH as the mechanism of 
the collision, Compton and Turner observed that HgH bands 
were formed in a low voltage arc in hydrogen and mercury. 
The HgH bands occurred with greatest intensity in those 
places in the discharge which were shown, by absorption 
measurements, to contain a large number of G 3 ?! mercury 
atoms. More recently Gaviola and Wood [29], investigating 
sensitized band fluorescence, observed that HgH bands 
appeared when mixtures of hydrogen, nitrogen and mercury 
were radiated with light from a mercury arc. 

On the theoretical side Compton and Turner have pointed 
out that the reverse process to (1) would be a very improbable 
occurrence, since it would involve a simultaneous collision 
between two hydrogen atoms and one mercury atom. By 
applying the principle of microscopic reversibility, they con 
cluded that mechanism (1) must likewise be improbable. 



78 PHYSICAL AND CHEMICAL EFFECTS 

Beutler and Rabinowitsch [8] have made a more complete 
theoretical analysis of the problem. They assume that when an 
excited atom A' gives over its energy to a molecule BC, not 
only energy but also linear and angular momentum must be 
conserved during the process. Before the collision the molecule 
BC will have a certain amount of rotational energy (E^ ot -) and 
the atom A' will have some kinetic energy relative to the centre 
of gravity ofBC. If the collision takes place in such a way that 
relative motion of the two particles is not along the line joining 
the centre of A' with the centre of gravity of BC, A and EG 
may be considered to be momentarily rotating about their 
common centre of gravity, giving rise to an amount of angular 
momentum M x . Of course, before the collision the molecule 
BC has some angular momentum (Jf 1 rot -). As a result of the 
collision the particles must go apart in such a way as to con 
serve energy and angular momentum. Beutler and Rabino 
witsch have shown that if the mass of A is large compared to 
B or C, the reaction 



will occur in which (AB)*" denotes that the molecule AB will 
possess a large amount of rotational energy. If the reaction is 
exothermic, they showed that AB would possess more rota 
tional energy than if it were slightly endothermic. 

Beutler and Rabinowitsch have found confirmation of these 
ideas in the experiments of G-a viola and Wood [29]. They found 
that HgH bands appeared when mercury, nitrogen and a 
small amount of hydrogen were radiated with the resonance 
line of mercury. The bands also appeared when mercury and 
water vapour were similarly illuminated. In the first case lines 
from the higher rotational states of the HgH molecule were 
very intense, whereas in the second case (H 2 0) the lower 
rotational states were predominant. In both cases the in 
tensity of the bands was proportional to the square of the 
incident light intensity, showing that two excited mercury 
atoms are involved in the process. Since nitrogen or water 
vapour was present in either case, it may be assumed that 
metastable mercury atoms were responsible for the fluorescence . 



CONNECTED WITH RESONANCE RADIATION 79 

The mechanism of production of the bands, as well as the 
energy relations, may be written as follows. Taking the heat of 
dissociation of H 2 as 4-46 volts, of H 2 into OH and H as 5-1 
volts, and that of HgH as 0-37 volt, we have 

Hg(6 3 P ) + H 2 = HgH + H + 0-62volt (a), 

Hg (6 3 P ) + H 2 - HgH + OH - 0- 1 volt (6), 

(c), 
(d). 

That (6) occurs is shown by the presence of OH bands in the 
fluorescence. Since reaction (a) is exothermic HgH molecules 
in high rotational states should be produced, if the theory is 
correct. Since (6) is slightly endothermic HgH molecules in 
low rotational states should be produced. If it be assumed that 
the second collision between Hg' and HgH does not appreci 
ably alter the rotational energy of the molecule, it will be seen 
that the experimental results are in accord with the theory. 

Still more evidence to the effect that mercury hydride 
and hydrogen are formed as a result of the collision between 
hydrogen and excited mercury may be drawn from the be 
haviour of the analogous metals, cadmium and zinc. Bender [4] 
radiated a mixture of hydrogen and cadmium vapour with 
light from a hydrogen and cadmium discharge tube emitting 
the full cadmium spectrum, together with that of hydrogen 
and cadmium hydride. He noticed that the fluorescent light 
from the resonance tube contained not only some of the cad 
mium lines but also CdH bands. Experiment showed that 
CdH was formed by collision with excited (5*Pi) cadmium 
atoms, and that the subsequent emission of the CdH bands 
was due to optical excitation by light from the discharge tube. 
Furthermore, if the cadmium metal used in the tube contained 
some oxides, a chemical reaction took place between the 
atomic hydrogen, formed as a result of the process, and the 
oxides in the tube. This was shown by the decrease in the 
hydrogen pressure and by the freezing out of water vapour in 
a liquid-air trap. If the cadmium metal was distilled free from 
oxides, the pressure drop was greatly decreased and no water 
was formed. In this case the formation of two hydrogen atoms 



80 PHYSICAL AND CHEMICAL EFFECTS 

as a result of the collision is definitely impossible, since the 
energy of the 5 3 Pj state of cadmium is only 3-78 volts. The 
reaction 



is energetically possible, since the heat of dissociation of CdH 
is 0-67 volt. The sum of the excitation energy of Cd (5^) and 
the heat of dissociation of CdH (3-78 + 0-67 = 4-45) is practi 
cally equal to the dissociation energy of hydrogen (4*46 volts), 
so that no energy goes into translational energy. A similar 
reaction takes place when a 4 3 P X zinc atom collides with a 
hydrogen molecule forming ZnH and a hydrogen atom. The 
reaction 



as written, goes with the emission of 0-5 volt energy. Bender 
pointed out that this 0-5 volt may be taken up as vibrational 
energy of the ZnH molecules. 

That the more highly excited n^-P^ zinc or cadmium atoms 
did not enter into the process was shown by the fact that 
fluorescent lines coming from the n l ~P state were not quenched 
by the addition of hydrogen. That this state, having an energy 
considerably in excess of that necessary to dissociate a hydro 
gen molecule, is not quenched by hydrogen is further evidence 
supporting the theory that collisions of the second kind are 
improbable when a large amount of energy goes into trans 
lational motion. 

Recently, Calvert [10] has succeeded in dissociating hydrogen 
molecules by impact with optically excited xenon atoms. 
A reaction vessel, fitted with fluorite windows, containing 
hydrogen and xenon at low pressures and a small amount of 
tungsten oxide, W0 3 , was irradiated with light from a He-Xe 
discharge tube. The exciting source gave a very strong xenon 
spectrum, including the resonance line 1469 ( 1 S~ 3 P 1 ), or in new 
notation [(5jp 6 ) ^-(Sp 6 . 6s) 1]. The xenon atoms in the tube 
absorbed the resonance line and reached the 3 P X state (energy 
8-5 volts), as was shown by the fact that resonance radiation 
was emitted from the reaction vessel when it contained only 
xenon. When hydrogen was admitted to the vessel and W0 3 



CONNECTED WITH RESONANCE RADIATION 81 

was present, a decrease in the pressure of hydrogen occurred 
on illumination. The yellow oxide of tungsten was also dis 
coloured, showing that it had been reduced. Since hydrogen 
itself can absorb no light in the spectral region emitted by the 
exciting source, it follows that the active form of hydrogen 
must have been produced by collision with excited xenon atoms . 
Since there appears to be no possibility of molecule formation, 
due to the inert nature of xenon, Calvert concludes that the 
excited xenon atoms must have dissociated the hydrogen 
molecules, an amount of energy corresponding to 2-6 volts 
going into relative kinetic energy of the reacting particles. 
He furthermore supposes that the mechanism of the dissocia 
tion of hydrogen by excited mercury atoms is similar to that by 
excited xenon atoms, in support of the early considerations of 
Cario and Franck. 

3d. REACTIONS INVOLVING HYDROGEN. The reaction be 
tween hydrogen and oxygen in the presence of excited mercury 
atoms has been studied by many investigators. It was 
at first believed that the primary product of the reaction 
was water. Later studies by Marshall [44, 45, 46], Hirst and 
Rideal[3i, 32], Bonhoeffer and Loeb[9], Frankenburger and 
Klinkhardt[26, 36] showed that hydrogen peroxide (H 2 2 ) was 
formed in great quantities during the reaction. The greatest 
yields of H 2 O 2 were obtained when the experiment was per 
formed by flowing the gases through the illuminated reaction 
zone. Taylor postulated a chain mechanism for the reaction 
between H 2 and 2 . Marshall, by measuring the number of 
molecules of H 2 2 formed per quantum of 2537 absorbed, 
obtained a yield of about four molecules per quantum of 
resonance radiation absorbed. This result was believed to con 
firm the chain mechanism of the reaction. Later measure 
ments of the efficiency of this reaction by Frankenburger and 
Klinkhardt gave a yield of about 1-2 molecules of H 2 2 per 
quantum absorbed at 60 C. These authors believe their 
experiments to show that no chain mechanism is involved. 
Recent experiments of Bates and Salley [i] appear to confirm 
the earlier results of Taylor and Marshall. 



82 PH^YSICAL AND CHEMICAL EFFECTS 

The sensitized reaction between hydrogen and ethylene 
(C 2 H 4 ) appears to be quite complicated. Apart from the 
polymerization of ethylene into solid products, ethane (C 2 H 6 ), 
acetylene (C 2 H 2 ) and many other hydrocarbons have been 
found as products of the reaction [2 , 15 , 58 , 67]. Taylor andHill [70], 
in a critical presentation of their data and those of other experi 
menters, appear to believe that the reaction is too complicated 
to be amenable to theoretical treatment. 

The reaction between H 2 and CO, in the presence of excited 
mercury vapour, is somewhat simpler. Taylor and Marshall 
found formaldehyde (HCHO) as a product. More recently 
Frankenburger[25] has found, by taking absorption spectra of 
the products of the reaction, that both formaldehyde and 
glyoxal (CHO.CHO) are formed. No unstable intermediate 
products were found in the spectroscopic analysis. Both 
Marshall and Frankenburger have measured the photo 
chemical efficiency of the reaction. The former found a yield of 
more than five molecules of HCHO per quantum absorbed, 
while the latter, using an improved form of apparatus, found 
a yield of about one molecule per quantum. Both observers 
agree, however, that H 2 and CO disappear in about a 1 : 1 ratio. 

Taylor and Marshall have shown that the reaction between 
H 2 and N 2 proceeds rapidly in the presence of excited mercury 
atoms, whereas that between H 2 and C0 2 does not. Most 
observers agree that no reaction between H 2 and N 2 occurs 
under the action of excited mercury atoms. Hirst and Rideal, 
and Noyes [55], on the other hand, have found a reaction to 
occur, but their experiments were not carried out under cir 
cumstances from which one could conclude with certainty that 
excited mercury atoms were the activating agent. 

3e. THE SENSITIZED FORMATION OF OZONE. Of those 
sensitized reactions not involving hydrogen the first to be 
studied was the formation of ozone. Dickinson and Sherrill[20] 
allowed oxygen at atmospheric pressure to become saturated 
with mercury vapour at 20 C. and to flow through a chamber 
illuminated with the light of a water-cooled quartz mercury 
arc. To eliminate the direct photochemical formation of ozone, 



CONNECTED WITH RESONANCE RADIATION 83 

which occurs under the influence of radiation in the region 
below 2000 A., a tartaric acid filter was used to absorb this 
radiation from the arc. Their results showed that ozone was 
formed in the presence of excited mercury atoms. The reaction 
is also complicated by the formation of HgO. They showed, 
however, that the reaction 



could not be the first step in the process, since at least seven 
molecules of ozone were formed per mercury atom used. Their 
mechanism assumes that an excited oxygen molecule is formed 
as a result of the collision between excited mercury and normal 
oxygen, and that the formation of ozone proceeds by the 
following mechanism: 



It is possible, however, that the first step in the reaction is 



since the latest value for the heat of dissociation of the oxygen 
molecule into two normal atoms is 5-09 volts. The excess 
energy required for dissociation above that supplied by the 
excited mercury atom might be derived from the relative 
kinetic energy of the mercury atom and oxygen molecule. The 
formation of HgO is probably the result of the action of ozone 
on normal mercury atoms. Leipunsky and Sagulin [42] believed 
that HgO was formed as a primary product. They used no 
light filter, however, and certainly had some photochemical 
formation of ozone as a result of short- wave-length ultra- violet 
light. The work of Noyes [56], performed at low pressures and 
with the help of filters, would appear to substantiate that of 
Dickinson and Sherrill in most respects. 

3/. THE SENSITIZED DECOMPOSITION OF AMMONIA. Another 
very interesting reaction is the mercury-sensitized decom 
position of ammonia. This reaction has been studied exten 
sively by Dickinson and Mitchell [49, 50], and by Bates and 
Taylor [2, 69]. Dickinson and Mitchell studied the reaction at 



84 PHYSICAL AND CHEMICAL EFFECTS 

low pressures (0-1 to 3 mm.) and used an acetic acid filter to 
eliminate the direct photochemical decomposition of ammonia 
which takes place under the influence of radiation of wave 
length shorter than 2300. They showed by the usual methods 
that decomposition occurs in the presence of excited mercury 
atoms. Analysis of the decomposition products was made, after 
freezing out undecomposed ammonia, by the use of a quartz- 
fibre manometer and McLeod gauge. The combined use of 
such apparatus enables one to measure the average molecular 
weight of the decomposition products at low pressures. The 
result of the analysis showed 70 per cent, hydrogen and 30 per 
cent, nitrogen, or practically a stoichiometric ratio (75:25).* 

Mitchell and Dickinson investigated further the effect of 
nitrogen, argon and hydrogen on the rate of decomposition. 
Argon and nitrogen at pressures up to 0-4 mm. had no effect 
on the rate, as would be expected from the fact that at these 
pressures they do not quench mercury resonance radiation 
appreciably. Hydrogen, on the other hand, had a decided 
quenching effect on the rate of decomposition, even a greater 
effect than one would be led to expect from its known quench 
ing ability. The authors inferred from this that excited am 
monia molecules must be involved in the reaction, and further 
more, that hydrogen may take excitation energy from them 
as well as from excited mercury atoms. An analysis of their 
experimental data by methods similar to those already 
described in this chapter appears to substantiate this view. 

Evidence for the existence of excited ammonia molecules is 
given by the discovery of Dickinson and Mitchell that mixtures 
of ammonia and mercury exhibited a fluorescence when radi 
ated with the light of a cooled mercury arc . Mitchell [50] showed 
that the fluorescence consisted of a diffuse band stretching 
from about 2600 up into the green, with a maximum at about 
3400 A. Gaviola and Wood further investigated the fluores 
cence and showed that the intensity of the band was propor- 

* Bates and Taylor, using a flow system and no light filter, found a 
larger percentage of hydrogen in their products, indicating the formation 
of hydrazine and hydrogen. More recent work of Elgin and Taylor [22] 
(see Table III, p. 2069) would appear to substantiate the results of Dickinson 
and Mitchell. 



CONNECTED WITH RESONANCE RADIATION 85 

tional to the first power of the intensity of the exciting light, 
demonstrating that only one excited mercury atom is involved 
in its production. Mitchell further showed that the intensity 
of the maximum of the band increased with increasing am 
monia pressure in an analogous way to which the rate of 
decomposition increased with ammonia pressure. Similarly, 
at constant ammonia pressure, the intensity of the maximum 
of the band decreased with hydrogen pressure in the same way 
as did the rate of decomposition under like circumstances. 
These results show that the decomposition is intimately con 
nected with the fluorescence. 

30. OTHER DECOMPOSITIONS SENSITIZED BY EXCITED 
MERCURY ATOMS. The decomposition of a great number of 
substances has been investigated by Bates and Taylor [2, 69], a 
compendium of whose results is shown in Table VIII. Of all 

TABLE VIII 





Ratio of 








photosensi 
tized to 


Analysis of gaseous 


Analysis of gaseous 


Substance 


non-photo 
sensitized 


products of the non- 
photosensitized 


products of the 
photosensitized 




rate of 


reaction 


reaction 




reaction 






H 2 








73%H 2 ;27%0 2 


NH 3 


200: 1 


96%H 2 ;4%N 2 


89%H 2 ;11%N 2 


C 2 H 4 







88 % H 2 ; 12 % CH 4 , etc. -i 


CH 3 OH 


600:1 





58%H 2 ;42%CH 4 + CO 


C 2 H 5 OH 


50: 1 





46%H 2 ;50%CO+-CH 4 


C 6 H 14 


1000 : 1 





96%H 2 ;4%CH 4 


C 6 H 6 


30: 1 





60 % H 2 ; 40 % CH 4 


(CH 3 ) 2 CO 


2:1 


100%CO+CH 4 


100%CO + CH 4 


HCOOH 


400:1 





76% CO; 24%H 2 


C 2 H 5 NH 2 


60: 1 


96 % H 2 ; 4 % N 2 


96 % H 2 ; 3-7 % CH 4 ; 








0-3 %N 2 



the substances investigated, none failed to decompose in the 
presence of excited mercury atoms. The analysis of the gaseous 
decomposition products is shown in column 4 of the table. 
The decomposition of water was investigated earlier by Senft- 
leben and Rehren[63], who found, however, no oxygen in their 



86 PHYSICAL AND CHEMICAL EFFECTS 

decomposition products. It is quite probable that OH is a 
product of the elementary process according to the mechanism 



or 

since OH bands have been found in sensitized fluorescence in 

the presence of mercury and water vapour. 

Finally, Elgin and Taylor have investigated the photo 
sensitized decomposition of hydrazine (N 2 H 4 ) and found N 2 , 
H 2 and NH 3 as decomposition products. They also showed that 
the addition of 200 mm. of hydrogen (initial pressure of hydra 
zine 10 mm.) made no change in the rate of the reaction. Since 
this effect is not to be expected on account of the known 
quenching power of hydrogen for mercury resonance radiation, 
they were able to give no explanation of it. Nitrogen and 
ammonia also showed no marked effect on the rate. It would 
be of interest to investigate this reaction at low pressures 
where broadening of the absorption line does not occur. 

3 Ti. REACTIONS SENSITIZED BY OTHEB METALLIC VAPOURS 

ACTIVATED BY THE ABSORPTION OF RESONANCE RADIATION. 

We have already mentioned that Bender showed that the 
reaction between hydrogen and metallic oxides occurs in the 
presence of excited zinc or cadmium atoms. Bates and 
Taylor [3] found no reaction to occur between hydrogen and 
ethylene in the presence of excited cadmium atoms. He also 
could observe no ammonia decomposition under like circum 
stances. The investigation of reactions sensitized by cadmium 
and zinc resonance radiation is difficult, since it was not easy to 
get a very intense source of the resonance radiation of these 
metals, and since, furthermore, at the temperatures necessary 
to obtain a sufficient vapour pressure of these elements many 
reactions proceed thermally. 

As further evidence of the fact that a collision of the second 
kind is most effective where least energy goes into kinetic 
energy, Beutler and Eisenschimmel[6] showed that excited 
neon atoms (from a discharge tube) would dissociate hydrogen 
into a normal and an excited atom according to the scheme 

-13 volt. 



CONNECTED WITH RESONANCE RADIATION 87 

As evidence of this reaction they showed that the H a line of 
hydrogen (2 2 S-3 2 P) appeared with high intensity in the dis 
charge tube containing neon and hydrogen. 

4. BANDS CONNECTED WITH RESONANCE LINES 

There are two types of band fluorescence which appear to be 
intimately connected with processes giving rise to resonance 
radiation: (a) bands which lie close to the resonance line and 
appear in fluorescence when a mixture of mercury vapour and 
certain rare gases is illuminated by the unreversed 2537 line; 
and (b) diffuse bands, or continua stretching throughout a large 
region of the spectrum, which occur when mercury vapour 
at high temperature and pressure is optically excited. In 
addition to these two classes, there are bands which may be 
definitely ascribed to the molecules Hg 2 , Cd 23 Zn 2 , a descrip 
tion of which may be found in the literature on band spectra. 

4a. MERCURY-RARE GAS BANDS. Oldenberg[57] made an 
investigation on mixtures of mercury vapour with the rare 
gases helium, neon, argon, krypton and xenon. A mixture of 
mercury with one of the rare gases (at high pressure) was 
jil.nTnma.tftd by a cooled mercury arc. The fluorescence con 
sisted of the resonance line, together with certain continua and 
bands lying in the neighbourhood of 2537. That the fluores 
cence is connected with the production of excited mercury 
atoms was shown by the fact that no fluorescence occurred 
when the core of the resonance line was absent (exciting lamp 
operated without cooling). 

Oldenberg's experiments were made to test the following 
idea: Suppose an excited mercury atom collides with a foreign 
gas atom and radiates at the moment of collision. Can the ex 
citation energy of the mercury atom co-operate in such a way 
with the relative translational energy of the two atoms that a 
line of wave-length different from 2537 will be radiated? The 
process would correspond to the following equation: 

Energy of excited mercury Translational energy 

= hv (radiated). 

Since the translational energy is, in general, not definite, one 



88 PHYSICAL AND CHEMICAL EFFECTS 

would expect to find a continuous band of radiation extending 
a short distance to either side of the 2537 line. Oldenberg 
actually found that such continua did occur when mixtures of 
Hg + Ne, Hg + He and Hg -f Xe were examined. The maximum 
extension of the continuum toward the short wave-length side 
from the 2537 line was found to be greatest for the lightest 
gases, in agreement with predictions made from kinetic theory. 

In addition to the continuous spectra observed, Oldenberg 
found discrete bands lying to the long wave-length side of 2537, 
when mixtures of Hg + A or Hg + Kr were optically excited. 
There were from five to seven bands observed and their posi 
tion was found to depend on whether argon or krypton was 
present. From an intensive study of the subject, the author 
came to the conclusion that these bands are due to the unstable 
molecules HgA and HgKr respectively. Since it is known that 
mercury and the rare gases do not combine to a measurable 
extent when both are unexcited, Oldenberg supposed that an 
excited mercury atom might form a loosely bound molecule, 
due to polarization forces, with an argon or krypton atom. 
Since the binding energy of the combinations is small, the light 
radiated will have a frequency quite near to that of the mercury 
resonance line. 

In some cases, notably argon, krypton and xenon, Oldenberg 
found that the continuum to the short wave-length side of 2537 
consisted of two broad diffuse maxima, the distance between 
the maxima depending on the rare gas used. The explanation 
of this effect, due to Kuhn and Oldenberg [40], is that collision 
between an excited mercury atom and a normal rare gas atom 
results in the formation of quasi-molecules which may be in 
either of two vibrational states, depending on the direction of 
the relative momenta at the time of collision. From each of 
these vibrational states a band may be radiated when the 
molecule returns to the normal state, thus explaining the two 
maxima observed. The fact that two maxima occur is evidence 
in favour of space quantization upon impact. 

46, CONTINUA APPARENTLY ASSOCIATED WITH RESONANCE 
RADIATION. In addition to the bands discussed in the fore- 



CONNECTED WITH RESONANCE RADIATION 89 

going section, continua, or structureless diffuse bands, have 
been observed when the vapours of mercury, cadmium and 
zinc are optically excited. Since the fluorescence shows no 
structure, it has been exceedingly difficult to find a mechanism 
which will explain its production. A large number of experi 
ments have been performed for the purpose of explaining the 
phenomena involved, but none appears to have given a com 
pletely satisfactory explanation. We shall content ourselves 
here, therefore, with giving a short description of the pheno 
mena. 

If mercury vapour, at high pressure, be excited by a high 
frequency discharge, or by light of a wave-length near to the 
resonance line, three sets of continua appear, viz. (1) a con 
tinuum, extending a short distance to the long wave-length 
side of 2537; (2) a broad continuum having a maximum at 
3300; and finally, (3) a continuum with a maximum at about 
4850. Experiments of van der Lingen and Wood [72] indicate 
that the bands only appear in distilling vapour, but other ob 
servers do not substantiate this result. If the bands are 
optically excited by the 2537 line, their intensity is propor 
tional to the first power of the intensity of the exciting light [60]. 
The general belief is that the bands are due to loosely bound 
mercury molecules. In support of this theory, Houtermans [33] 
obtained evidence showing that the bands are connected with 
mercury atoms in the 6 3 Pj and 6 3 P states. 

Similar diffuse bands appear in the spectra of the elements 
cadmium, zinc, thallium and magnesium. A compendium of 
the results of various researches on the subject is given by 
Mrozowski[52] and by Hamada[30]. As in the case of mercury, 
the bands appear to be due to loosely bound molecules and 
are associated with the various excited states of the atoms 
forming the molecule. 

REFERENCES TO CHAPTER II 

[1] Bates, J. R. and Salley, D. J., Journ. Amer. Chem. Soc. 55, 110 (1933). 

[2] Bates, J. R. and Taylor, H. S., ibid. 49, 2438 (1927). 

[3] ibid. 50, 771 (1928). 

[4] Bender, P., Phys. Rev. 36, 1535, 1543 (1930). 



90 PHYSICAL AND CHEMICAL EFFECTS 

[5] Beutler, H. and Eisenschimmel, W., Z.f. Phys. Chem. B 10, 89 (1930). 

[ 6 ] z. f. Elektrochem. 37, 582 (1931). 

[7] Beutler, H. and Josephy, B., Z. f. Phys. 53, 747 (1929). 

[8] Beutler, H. and Rabinowitsch, E., Z. f. Phys. Chem. B 8, 231, 403 

(1930). 

[9] Bonhoeffer, K. F. and Loeb, S., ibid. 119, 474 (1926). 
[10] Calvert, H. R., Z.f. Phys. 78, 479 (1932). 
[11] Carelli, A., ibid. 53, 210 (1929). 
[12] Carlo, G., ibid. 10, 185 (1922). 
[13] Carlo, G. and Franck, J., ibid. 11, 161 (1922). 

[14] ibid. 17, 202 (1923). 

[15] Clemenc, A. and Patat, F., Z.f. Phys. Chem. B 3, 289 (1929). 

[16] Collins, E. H., Phys. Rev. 32, 753 (1928). 

[17] Compton, K. T. and Turner, L. A., Phil. Mag. 48, 360 (1924). 

[18] Dickinson, R. G., Proc. Nat. Acad. Sri. 10, 409 (1924). 

[19] Dickinson, R. G. and Mitchell, A, C. G., ibid. 12, 692 (1926). 

[20] Dickinson, R. G. and Sherrill, M. S., ibid. 12, 175 (1926). 

[21] Donat, K., Z.f. Phys. 29, 345 (1924). 

[22] Elgin, J. C. and Taylor, H. S., Journ. Amer. Chem. Soc. 51, 2059 

(1929). 
[23] Franck, J. and Jordan, P., Anregung von Quantensprungen durch 

Stosse, J. Springer, Berlin, pp. 226-228. 
[24] Franck, 3., Z.f. Phys. 9, 259(1922). 
[25] Frankenburger, W., Z.f. Elektrochem. 36, 757 (1930). 
[26] Frankenburger, W. and Klinkhardt, H., Z. f. Phys. Chem. B 15, 421 

(1931). 

[27] Fiichtbauer, C., Phys. Z. 21, 635 (1920). 
[28] Gaviola, E., Phil. Mag. 6, 1154, 1167 (1928). 
[29] Gaviola, E. and Wood, R. W., ibid. 6, 1191 (1928). 
[30] Hamada, H., Nature, 127, 554 (1931). 

[31] Hirst, H. S. and Rideal, E. K., ibid. 116, 899 (1925); 117, 449 (1926). 
[32] Hirst, H. S., Proc. Camb. Phil. Soc. 23, 162 (1926). 
[33] Houtennans, F. G., Z.f. Phys. 41, 140 (1927). 
[34] Kallmann, H. and London, F., Z. f. Phys. Chem. B 2, 207 (1929). 
[35] Klein, O. and Rosseland, S., Z. f. Phys. 4, 46 (1921). 
[36] Klinkhardt, H. and Frankenburger, W., Z. /. Phys. Chem. B 8, 138 

(1930). 

[37] Klumb, H. and Pringsheim, P., Z.f. Phys. 52, 610 (1928). 
[38] Kopfermann, H^ ibid. 21, 316 (1924). 
[39] Kopfermann, H. and Ladenburg, R., ibid. 48, 15, 26, 51, 192 (1928); 

65, 167 (1930). 

[40] Kuhn, H. and Oldenberg, O., Phys. Eev. 41, 72 (1932). 
[41] Latyscheff, G. D. and Leipunsky, A. L, Z.f. Phys. 65, 111 (1930). 
[42] Leipunsky, A. and Sagulin, A., Z.f. Phys. Chem. B 1, 362 (1928). 
[43] Loria, S., Phys. Eev. 26, 573 (1925). 
[44] Marshall, A. L., Journ. Phys. Chem. 30, 34 (1926). 

[45] ibid. 30, 1078 (1926). 

[46] Journ. Amer. Chem. Soc. 49, 2763 (1927). 

[47] Meyer, E., Z.f. Phys. 37, 639 (1926). 



CONNECTED WITH RESONANCE RADIATION 91 

[48] Mitchell, A. C. G., Proc. Nat. Acad. Sci. 11, 458 (1925). 

[49] Mitchell, A. C. G. and Dickinson, R. G., Journ. Amer. Chem. Soc. 49, 

1478 (1927). 

[50] Mitchell, A. C. G., ibid. 49, 2699 (1927); Journ. Frankl. Inst. 212, 341 

(1931). 

[51] Mohler, F. L., Bur. Stand. Journ. Res. 9, 493 (1932). 

[52] Mrozowski, S., Z.f. Phys. 62, 314 (1930). 

[53] MM. 78, 826 (1932). 

[54] Nordheim, L., ibid. 36, 496 (1926). 

[55] Noyes, W. A., Jr., Journ. Amer. Chem. Soc. 47, 1003 (1925). 

[56] ibid. 49, 3100 (1927); Z. f. Phys. Chem. B 2, 445 (1929). 

[57] Oldenberg, O., Z.f. Phys. 47, 184 (1928); 51, 605 (1928); 55, 1 (1929). 

[58] Olson, A. R. and Meyers, C. H., Journ. Amer. Chem. Soc. 48, 389 

(1926); 49, 3131(1927). 

[59] Orthmann, W. and Pringsheim, P., Z. f. Phys. 35, 626 (1926). 

[60] Pringsheim, P. and Terenin, A., ibid. 47, 330 (1928). 

[61] Rasetti, F., Nature, 118, 47 (1926). 

[62] Senftleben, H., Z. f. Phys. 32, 922 (1925); 33, 871 (1925). 

[63] Senftleben, H. and Rehren, I., ibid. 37, 529 (1926). 

[64] Senftleben, H. and Riechemeier, 0., Ann. d. Phys. 6, 105 (1930). 

[65] Smyth, H. D., Proc. Nat. Acad. Sci. 11 ; 679 (1925); Phys. Eev. 27, 

108 (1926). 

[66] Terenin, A., Z. f. Phys. 37, 98 (1926). 

[67] Taylor, H. S. and Marshall, A. L., Journ. Phys. Chem. 29, 1140 (1925). 

[68] Taylor, H. S., Trans. Farad. Soc. 21, 560 (1925). 

[69] Taylor, H. S. and Bates, J. R., Proc. Nat. Acad. Sci. 12, 714 (1926). 

[70] Taylor, H. S. and Hill, D. G., Journ. Amer. Chem. Soc. 51, 2922 (1929). 

[71] Turner, L. A., Phys. Rev. 23, 466 (1924). 

[72] Van der Lingen, J. S. and Wood, R. W., Astrophys. J. 54, 149 (1921). 

[73] Webb, H. W. and Wang, S. C., Phys. Rev. 33, 329 (1929). 

[74] Winans, J. G., Hid. 30, 1 (1927). 

[75] Wood, R. W., Proc. Roy. Soc. 106, 679 (1924); Phil. Mag. 50, 775 

(1925); 4, 466(1927). 

[76] Wood, R. W. and Gaviola, E., Phil. Mag. 6, 271, 352 (1928). 



CHAPTER III 

ABSORPTION LINES AND MEASUREMENTS OF 
THE LIFETIME OF THE RESONANCE STATE 

1. GENERAL PROPERTIES OF ABSORPTION LINES 

Chapters i and n contained, for the most part, descriptions 
and interpretations of qualitative experiments on resonance 
radiation and resonance lines. It is the purpose of this chapter 
to introduce and perfect the physical and mathematical tools 
which allow a quantitative interpretation of another group of 
experiments on resonance radiation which, either directly or 
indirectly, are connected with the formation of absorption 
lines. 




Frequency v in sec. 1 
Fig. 20. An absorption line. 

1 a. THE NOTION OF AN ABSORPTION LINE. If parallel light 
from a source emitting a continuous spectrum be sent through 
an absorption cell containing a monatomic gas, the intensity 
of the transmitted light, I v , may show a frequency distribution 
similar to that depicted in Fig. 20. When this is the case, the 
gas is said to possess an absorption line at the frequency V Q , 
where v is the frequency at the centre of the line in sec." 1 . The 
absorption coefficient k v of the gas is defined by the equation 

(20), 



ABSORPTION LINES 



93 



where x is the thickness of the absorbing layer. When x is 
measured in cm., Jc v is expressed in cm." 1 . From Fig. 20 and 
Eq. (20) we may obtain k v as a function of frequency, and when 
this is done we have a curve such as that shown in Fig. 21 . The 
total breadth of this curve at the place where k v has fallen to one- 
half of its maximum value, & ma x. , is called the half breadth of 
the absorption line and is denoted by Av. In general the absorp 
tion coefficient of a gas is given by an expression involving a 
function of v and a definite value of &max. and Av, all of which 
may depend on the nature of the molecules of the gas, their 




Frequency v in sec." 1 

Fig. 21 . Variation of absorption coefficient with frequency 
in an absorption line. 

motion, and their interaction either with one another or with 
foreign molecules. 

16. THE EINSTEIN THEORY OF RADIATION. Consider an 
enclosure containing isotropic radiation of frequency between 
v and v + dv, intensity I v and atoms capable of being raised by 
absorption of the radiation from the normal state 1 to the 
excited state 2. Following Milne's [47] treatment of the Einstein 
theory of radiation, we define the following probability 
coefficients: 

-B-^2 / = probability per second that the atom in state 1, 
exposed to isotropic radiation of frequency between v and 
v + dv and intensity 7 V , will absorb a quantum Tiv and pass to 
the state 2. 



94 ABSORPTION LINES AND ME ASFREMENTS 

.4 2^! = probability per second that the atom in the state 2 
will spontaneously emit, in a random direction, a quantum Tiv 
and pass to the state 1. 

J5 2 _ >1 l v = probability per second that the atom will undergo 
the transition from 2 to 1 when it is exposed to isotropic radia 
tion of frequency between v and v + dv and intensity I v , 
emitting thereby a quantum in the same direction as the 
stimulating quantum. 

By considering the thermodynamic equilibrium between the 
radiation and the atoms, Einstein showed that 

ft 



.and ^ ...... (22) ' 



where c is the velocity of light and ft and g% are the statistical 
weights of the normal and excited states respectively. Further 
more, it is clear from the definition of the coefficient -4 2 



+1 
(23), 

where r is the lifetime of the atom in the resonance state in the 
sense in which it was used in Chap. I. 

It should be emphasized at this point that the jB coefficients 
have been defined in terms of intensity of isotropic radiation, 
whereas the original Einstein B coefficients were defined in 
terms of radiation density. The relation between the two kinds 
of J5's is 

B (density) = ^-B (intensity). 

The Einstein theory of radiation lends itself very naturally 
to calculations concerning the absorption of light by atoms and 
molecules, that is, to calculations involving absorption lines. 
In 1920 Fiichtbauer [io] derived a relation between the integral 
of the absorption coefficient of a line (the area under the curve 
in Fig. 21) and a probability coefficient connected with the 
Einstein- A coefficient. In 1921 Ladenburg [37] gave a more 
precise relation between this integral and the Einstein A 



OF THE RESONANCE STATE 95 

coefficient. In 1924 Tolman[74] and Milne [47] derived the 
relation independently. In the following paragraph a deriva 
tion of the formula is given which follows the notation of 
Milne. 

Consider a parallel beam of light of frequency between v and 
v + dv and intensity I v travelling, in the positive x direction, 
through a layer of atoms bounded by the planes at x and 
x + dx. Suppose there are N normal atoms per c.c. of which 
8N V are capable of absorbing the frequency range between v 
and v 4- dv, and N' excited atoms of which 8N V ' are capable of 
emitting this frequency range. Neglecting the effect of spon 
taneous re-emission in view of the fact that it takes place in all 
directions, the decrease in energy of the beam is given by 



where I v \^n is the intensity of the equivalent isotropic radia 
tion for which B l _^ 2 and 5 2 -i are defined. Rewriting Eq. (24), 
we obtain 



Recognizing that the left-hand member is k v 8v as defined by 
Eq. (20), Eq. (25) becomes 



and integrating over the whole absorption line, neglecting the 
slight variation in v throughout the line, 



where v is the frequency at the centre of the line. Making use 
of Eqs. (21), (22) and (23), we have finally 



f M v-*&*(l-* 

J v 8*9i r \ g z 



(27). 

In gases electrically excited at high current densities, the 
number of excited atoms may become an appreciable fraction 
of the number of normal atoms, in which case the quantity 



96 ABSORPTION LINES AND MEASUREMENTS 

Q N' 

.-=r= cannot be neglected. If, however, the only agency re 
sponsible for the formation of excited atoms is the absorption 
of the beam of light itself, the ratio N'/N is exceedingly small, 
of the order of 10~ 4 or less, and consequently Eq. (27) may be 
written 






Eq. (28) is of fundamental importance. It expresses the fact 
that whatever physical processes are responsible for the formation 
of the absorption line, the integral of the absorption coefficient 
remains constant when N is constant. 

Ic. THE RELATION BETWEEN /-VALUE AND LIFETIME. On 
the basis of the classical electron theory of dispersion, the 
optical behaviour of N atoms per c.c. was represented by the 
behaviour of Sft quasi-elastically bound electrons (the so- 
called " dispersion electrons "). The ratio 31/N was found to be 
constant for a particular spectral line and was denoted by /. 
The /-value associated with a spectral line emitted by an atom 
can be regarded as a measure of the degree to which the ability 
of the atom to absorb and emit this line resembles such an 
ability on the part of a classical oscillating electron. In all 
classical formulas of normal and anomalous dispersion, mag 
neto-rotation and absorption, the quantity/ appears. On the 
basis of the quantum theory, the /-value has a very simple 
interpretation: it is proportional to the Einstein A coefficient, 
or, in the case of a resonance line, it is inversely proportional to 
the lifetime of the resonance level. This is most easily shown 
by the classical formula, developed long before the Einstein 
theory, namely 

J AQ me me 

in which n is the index of refraction and UK the electron theory 
absorption coefficient which is connected with the usual 
absorption coefficient by the relation 

^L(vktf\ lf (w\ 

\ \'*iC) K v .(O\J). 



OF THE RESONANCE STATE 97 

From Eqs. (28) and (29) we have Ladenburg's formula p7] 
stating the connection between the /-value of a resonance line 
and the lifetime of the resonance level: 

7re_ 2 Vft N 

me " 



87T0! ' r 



or 



Eq. (31) enables us to calculate the lifetime once the /-value 
has been measured, or vice versa. In Table IX are given values 
of fr for those resonance lines that are most often studied 

to-day. 

TABLE IX 



Element 


Resonance 
line 


ffz/Si 


A in 
A. units 


xlO 


Li 
Na 
K 

Pa 


2 2 S 1/2 -2*P 1/2 
2 2 S 12 -2 2 P 3/2 
3 2 S 12 -3*P 12 
3 2 S 12 -3 2 P 3/2 
4 2 S 12 -fc 2 P 1/2 
4 2 S 1 ' /2 -4 2 P 8/2 


I 
2 
I 
2 
1 
2 
1 


6708 
6708 
5896 
5890 
7699 
7665 
8944 


6-80 
13-6 
5-24 
10-46 
8-94 
17-8 
12-1 


\JO 

Mg 


e^/'-e 2 ?^ 

3% -3 3 P! 
3% -3 1 ?! 


2 
3 
3 


8521 
4571 
2852 


21-9 
9-48 
3-68 


J> 

Ca 


4% -4 3 ?i 


3 
3 


6573 
4227 


19-5 
8*09 


j> 

Zn 


4% -4 3 Pi 


3 
3 


3076 
2139 


4-28 
2-07 


Sr 


S^o -5 3 P' 


3 


6893 


21-5 


nj 


5% -5^ 


3 
3 


4608 
3261 


4-80 


l^CL 


- iq , eip 1 


3 


2288 


2-37 


"Rn 


61 g .gsp 1 


3 


7911 


28-3 


JL>ct 


gig _6ip 


3 


5536 


13-9 


Hg 


V kJQ V J. ! 

6% -6 3 Pi 

6ig o -e 1 ?! 


3 
3 


2537 
1850 


2-91 
1-55 


Tl 


6 2 Pi/ 2 -7 2 S 1/2 


1 


3776 


//JL=2-15 




6 2 P 1/2 -6 2 D 3/2 

ft 2 "D n 2 Q 
v *-3/2* ^^/2 


2 


2768 
5350 


}{l:5S 



2. THE ABSORPTION COEFFICIENT OF A GAS 
2 a. EXPRESSION FOE THE ABSORPTION COEFFICIENT. There 
are in general five processes that contribute to the formation 
of an absorption line of a gas. Each process can be regarded as 



98 ABSORPTION LINES AND MEASUREMENTS 

an agent for broadening the absorption line. The five types of 
broadening are as follows: 

(1) Natural broadening due to the finite lifetime of the 
excited state. 

(2) Doppler effect broadening due to the motions of the 
atoms. 

(3) Lorentz broadening due to collisions with foreign gases. 

(4) Holtsmark broadening due to collisions with other 
absorbing atoms of the same kind. 

(5) Stark effect broadening due to collisions with electrons 
and ions. 

Both Lorentz and Holtsmark types of broadening are often 
referred to as " pressure-broadening " (" Druckverbreiterung "), 
since the first depends on. the pressure of the foreign gas, and 
the second on the pressure of the absorbing gas. Although the 
recent work of Weisskopf [83] seems to indicate that the two 
kinds of broadening are identical, this point is still in sufficient 
doubt to make it desirable to retain the old nomenclature and 
to distinguish between the two phenomena. 

Fortunately it is possible in many cases to choose experi 
mental conditions in such a manner that all but one or all but 
two broadening processes are either completely absent or 
negligibly small. For example, the absorption line produced 
in a continuous spectrum which passes through an attenuated 
beam of atoms moving perpendicular to the path of light would 
(if it could be spectroscopically resolved) be determined en 
tirely by natural broadening. In a gas or vapour that is not 
electrically excited, and whose pressure is kept below 0-01 mm., 
Stark-effect broadening and Holtsmark broadening may be ig 
nored. Lorentz broadening, that due to collisions with foreign 
gas molecules, however, cannot be disposed of so easily. In 
many experiments on resonance radiation one cannot get along 
without the use of foreign gases. In such cases, if the foreign 
gas pressure is kept below about 5 mm., the contribution to the 
absorption line due to Lorentz broadening is small in com 
parison with the Doppler effect. Lorentz broadening as a 
phenomenon in itself will be discussed later on in the book. 



OF THE RESONANCE STATE 99 

Most of the experiments leading to values of / or r are per 
formed under conditions in which only natural broadening and 
Doppler broadening are present. To interpret such experi 
ments it is necessary to have a mathematical expression for 
the absorption coefficient of a gas under these conditions. 

Such an expression was developed in 1912 by Voigt [75], and 
a little later independently by Reiche [60], on the basis of the 
classical electron theory. Voigt's formula is very general, in 
volving the Doppler effect, natural damping, and any other 
damping process that can be represented by a function of the 
velocity of the absorbing atoms. When only the first two pro 
cesses are considered Voigt's formula becomes identical with 
a formula which will be developed in the next few pages with 
out the necessity of going through the long and somewhat 
complicated calculation of the dispersion theory. A fuller 
discussion of Voigt's and Reiche 's formulas will be found in 
the Appendix. 

It is a well-known result that, when natural damping is 
neglected, and only the heat motions of the atoms are taken 
into account, the absorption coefficient of a gas is given by 

rC v = KQ e *- D (o-^), 

where Av^ is the Doppler breadth, depending only on the 
absolute temperature T and the molecular weight M according 

to the formula 

2V2RI&2 FT 

A VJ> = P JM ^ )' 

and & is the purely ideal quantity, the maximum absorption co 
efficient when Doppler broadening alone is present. k can be 
calculated as follows: Integrating Eq. (32), one obtains the 
formula 




(34), 

HI & 

whereas Eqs. (28) and (29) yield 



; 



100 ABSORPTION LINES AND MEASUREMENTS 

2 /In 2 A n 2 <7o N 



v^V TT '877^' r 
Consequently &0 i , _ ...... (35). 




When, on the other hand, the Doppler effect is neglected, and 
only natural damping is taken into account, the absorption 
coefficient is proportional to 

1 



where Av^ is the natural breadth, which according to Dirac's 
theory of radiation [25, 82] is equal to the Einstein A coefficient 
divided by STT or, in the case of a resonance line, 



Now the Doppler effect and natural damping are entirely 
independent broadening processes. Consequently the com 
bined absorption coefficient of a gas (i.e. when both processes 
are present) may be calculated by considering either every 
infinitesimal frequency band of the pure Doppler curve to be 
broadened by natural damping, or every infinitesimal fre 
quency band of the natural damping curve to be broadened 
by the Doppler effect. Suppose we pick some frequency band 
at a distance v v from the centre of a line showing only 
natural broadening. To represent the Doppler broadening of 
this frequency band, a variable distance 8 from the point 
v VQ is chosen. The integration is then taken over 8. The 
absorption coefficient is therefore given by 

f . .-KvErfr 

=(? - _ - -dS ...... (37), 



where C is a constant determined by the condition [Eq. (28)] 
that 



r 

J o 



Or THE RESONANCE STATE 



101 



Integrating Eq. (37) with respect to v, and using Eqs. (28) and 
(35), is found to be 



The Doppler breadth of an absorption line offers itself as a 
convenient natural unit with which to describe an absorption 
line. Considerable simplification is therefore attained if the 
following two quantities are introduced: 



Vln2 



(38), 



Letting y~-r VETS!, Eq. (37) becomes 



(39). 



(40), 



TABLE X 











1 


I J 




Atom 


Line 


X 


r sec. 


27TT 


1/5-716x10 ^o^j^ 


a- - V 1 * 2 










sec.- 1 


sec.' 1 


VD 


Hg 


6% -6'?! 


2537 


1-1 x 10~ 7 


14 x 10 6 


1-0 x 10 9 (20 C.) 


0012 


Na 




5896 


1-6 x 10~ 8 


1-0 x 10 7 


l-6xl0 9 (160C.) 


0052 


Cd 


5% -5 1 ?! 


2288 


2-0 x 10~ 9 


0-8 x 10 8 


l-9xl0 9 {200C,) 


035 



which is identical with Voigt's expression (see Appendix). The 
quantity a will be called hereafter the "natural damping 
ratio". Since it is a constant for a particular absorption line 
of a gas at constant temperature, the integral in Eq. (40) is 
therefore a function of u. Values of the natural damping ratio, 
a, for three important resonance lines are given in Table X. 
It is seen that a is always small, in the neighbourhood of 0-01. 
It is therefore of value to study the characteristics of an 
absorption line with a small natural damping ratio. 

2 b. CHARACTERISTICS OF AN ABSORPTION LINE WITH SMALL 
NATURAL DAMPING RATIO. It is shown in the Appendix that, 



102 ABSORPTION LINES AND MEASUREMENTS 

when a is of the order of 0-01, Eq. (40) can be put in the 
form 

^ = er"~[l-2<F(a>)] ...... (41), 



where 



F (o>) = e~" 2 f " e^ dy ...... (42). 

J o 



A table of values of jF(o>) and of 1 2o> F(a>) is given in the 
Appendix. With the aid of this table, the ratio k v jk Q can be 
evaluated for any desired value of co, that is, at any part of an 
absorption line whose natural damping ratio is known. In 
Table XI are given values of k v /k Q from the centre of a line 
(co = 0) to a distance about eight times the Doppler breadth 
(w = 16) for an absorption line whose natural damping ratio 



is 0-01 = 0-00886, a value within the range of most reso- 

2t 

nance lines. It is of advantage to study this table in two parts : 
the " central region of the line", | o> | < 2; and the " edges of 
the line", |o>|>6. 

2c. THE CENTRAL BEGION OF THE LINE. The fraction of the 
incident light of frequency v that passes through an absorbing 

k 
layer of thickness Z is equal to e~V. Since k v l~j~.kQl, it is 

KQ 

necessary to know the product k Q l in order to calculate how 
much light is transmitted at some particular part of an absorp 
tion line. From Eq. (35) it is evident that k Q depends upon N 9 
or more simply upon the pressure of the absorbing gas. If the 
pressure of the absorbing gas and the thickness of the absorbing 
layer are chosen low enough, k Q I can be made small, say about 3. 
(This is usually achieved at pressures from 10~ 7 to 10~ 4 mm., 
and with thicknesses from 0-1 to 3 cm.) In this case it is seen 
from Table XI that k v l has a value large enough to produce 
measurable absorption only within the central region of the 
line, being negligibly small for the values of | co | greater than 
two. Moreover, it can be seen that the values of k v /k Q in this 
part of the line differ from the values of e->* by only a few per 
cent, at most. With an error well within that of experiment the 
statement can be made: when the pressure of the absorbing gas 



103 



OF THE RESONANCE STATE 

and the thickness of the absorbing layer are chosen small enough to 
make k Q l about 3, the edges of the absorption line may be neglected 
and the whole line may be regarded as a pure Doppler line with 



TABLE XI 











k 1-1 " 


^-3000 






. 2o)F(a)) 


ky/k 


o 






W 2 


from 


from 




. 




k I 






Appendix 


Eq. (41) 


M 


e v 


W 


e 



.2 


1-0000 
9608 


1-0000 
9221 


9900 
9516 


2-970 
2-855 


0513 
0576 


.1 
o S3 






.A 


8521 


7121 


8450 


2-535 


0793 


173 '1 





6 


6977 


4303 


6934 


2-080 


1249 


2 g 





8 
1-0 
1-2 
1-4 
1-6 
1-8 
2-0 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 


5273 
3679 
2369 
1409 
07730 
03916 
01832 
-0001234 















. 


1487 
-07616 
-2175 
-2782 
- -2797 
-2485 
- -2052 
- -06962 
- -03480 
- -02134 
- -01451 
- -01053 
- -008000 
- -006290 
-005076 
- -004183 
- -003510 
-002958 
- -002551 
-002222 
-001953 


5258 
3687 
2391 
1437 
08010 
04165 
02037 
0008196 
0003480 
0002134 
0001451 
0001053 
00008000 
00006290 
-00005076 
00004183 
00003510 
00002958 
00002551 
00002222 
00001953 
_ 


1-577 
1-106 
717 
431 
240 
124 
061 

|| 
ii 

o & 


2066 
3309 
4882 
-6499 
-7866 
8834 
9408 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 


3l 

c3 & 

"o 3 

o 

HI 

2-459 
1-044 
6402 
4353 
3159 
2400 
1887 
1523 
1255 
1053 
-08874 
07653 
-06667 
05859 









0855 
3520 
5273 
6473 
7291 
7866 
8278 
8590 
8816 
9003 
9148 
9259 
9352 
9427 





2d THE EDGES OF THE LINE. If the pressure of the 
absorbing gas is from about 10~* to about 10- mm. (not high 
enough to produce Holtsmark broadening of the absorption 
line!) and the thickness of the absorbing layer is from 10 to 
50 cm, W may be made very large, say about 3000. It is seen 
from the table in this case that Tc v l in the central region of the 
line is so large that, in any experiment, this region would be 
completely absorbed. Only in the edges of the line would a 
measurable amount of light be transmitted, that is, the form 
of the line wovM be determined entirely by the edges. At the edges 



104 ABSORPTION LINES AND MEASUREMENTS 

of the line Eq. (41) assumes a very simple form. It is shown in 
the Appendix that, for large values of o>, 



whence, for values of | o> greater than 6, Eq. (41) becomes 



Introducing the values of co and a given by Eqs. (38) and (39), 
Eq. (45) becomes 



and, by virtue of Eq. (34), Eq. (46) assumes the form 



which expresses the very interesting result that the extreme 
edges of the line are due entirely to natural damping. 

The results of these calculations may be summed up as 
follows: When there is weak absorption the central region of 
the line plays the main role and the absorption coefficient is 
determined by the Doppler effect; whereas when there is very 
strong absorption, the edges of the line are important and the 
absorption coefficient is determined by damping. This is 
shown graphically in Figs. 22 and 23, in which the numbers in 
Table XI are plotted. 

A very important distinction between the two cases arises 
when we consider the problem of hyperfine structure. The 
whole discussion up to now has been concerned with a simple 
line. When a line* shows hyperfine structure, it may be re 
garded as being composed of a number of simple lines that are 
either completely separated (resolved) or overlap one another. 
All the formulas that have been written, therefore, must be 
applied to each hyperfine structure component. It is obvious 
then, that, in the case of weak absorption where the central 
region of each hyperfine structure component plays the main 
role, it is necessary to know the number of components, their 
separation, and their respective intensities, in order to give 



OF THE BESONANOE STATE 



105 



an exact expression for the absorption coefficient. In the case 
of strong absorption, however, where one is interested in the 



AA Weak absorption /% Z =3 
BB Strong absorption V 




-16 -14 -12 HO -8 -6 -4 -2 



2 4 6 8 10 12 14 16 
Doppler Breadth 

Fig. 22. Narrow and broad absorption lines. 



AA Weak absorption k 
BB Strong absorption 




-16 -14 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 14 16 

s y 

** Doppler Breadth 

Fig. 23. Variation of absorption coefficient with, frequency 
in narrow and broad absorption lines. 

extreme edges of a line, at a distance from the centre of gravity 
of the hyperfine structure components of a line that is much 



106 ABSORPTION LIKES AND MEASUREMENTS 

larger than the average separation of the components, the 
situation is much simpler, for if this distance be large enough, 
the absorption coefficient will be practically the same as if all 
the hyperfine structure components coincided at their common 
centre of gravity. In other words, in order to interpret experi 
ments performed on the extreme edges of a line that has a com 
plicated hyperfine structure it is a sufficiently accurate procedure 
to use equations that refer to a simple line. 

3. EMISSION AND DIFFUSION OF 
RESONANCE RADIATION 

3 a. EMISSION CHARACTERISTICS OF A RESONANCE LAMP. 
In an ideal resonance lamp there are just enough absorbing 
atoms present to absorb an extremely small portion of the 
exciting radiation, but not enough to absorb the re-emitted 
radiation on its way out of the lamp. In such a lamp there 
would be a uniform distribution of excited atoms in the direct 
path of the exciting radiation and no excited atoms anywhere 
else, and the emitted resonance radiation would be due to only 
one absorption and emission process on the part of each atom. 
Such resonance radiation is known as primary resonance 
radiation. It is obvious that the requirements of an ideal 
resonance lamp can never be completely satisfied in practice. 
If there are enough atoms present to absorb an appreciable 
amount of the exciting radiation, then the re-emitted radia 
tion will also be absorbed, not only on its way out of the exit 
window but also in all parts of the lamp . The primary resonance 
radiation thus absorbed will be re-emitted (secondary reso 
nance radiation), and this, in turn, will give rise to tertiary 
resonance radiation, and so on. In other words the radiation 
will be diffused or^ imprisoned. On the basis of the Einstein 
theory, this situation can be described by saying that light 
quanta perform rapid transits from atom to atom alternating 
with periods of imprisonment of average duration r, the time 
r being large compared with the time of transit. It was first 
pointed out by K. T. Compton[2, 3] that the propagation of 
resonance radiation in an absorbing gas was analogous to the 
process of diffusion, and, on the basis of this analogy, he was 



OF THE RESONANCE STATE 107 

able to explain some phenomena in connection with the be 
haviour of low voltage arcs. A rigorous treatment of the pro 
blem was given later by E. A. Milne [48], who showed that the 
differential equations giving the concentration of excited atoms 
and the intensity of resonance radiation as a function of dis 
tance and time were similar to the ordinary diffusion equation 
except for a third order term that arose from the finite lifetime 
of the excited state. Milne's theory is of value in considering 
the one-dimensional flow of resonance radiation of very narrow 



Exciting 



Radiation 



/v. 



Exit--' 
Window 



JLL 



Resonance 
Radiation 



Fig. 24. Characteristics of an ideal resonance lamp. 

spectral width, but leads to mathematical difficulties when 
applied to the more complicated conditions that are present in 
connection with an actual resonance lamp. The use of Milne's 
theory in interpreting experiments on the quenching of reso 
nance radiation will be discussed in Chap. iv. At present an 
approximate treatment of the emission characteristics of a 
resonance lamp will be given in which the conditions of gas 
pressure and geometry are such that radiation diffusion may 
be neglected as a first approximation. 

Let us consider the resonance lamp shown diagrammatically 
in Fig. 24. The exciting radiation I v passes down the lamp 
grazing the exit window, so that there is practically no layer of 



108 ABSORPTION LINES AND MEASUREMENTS 

unexcited atoms through, which the resonance radiation must 
pass on its way out. The aperture in the exit diaphragm is 
chosen small, and a lens is imagined at sufficient distance from 
the exit window to receive only a parallel beam of resonance 
radiation E v emerging perpendicularly from the exit window. 
Furthermore, the pressure of the absorbing gas in the reso 
nance lamp is considered small enough, so that secondary and 
tertiary resonance radiation can be neglected as a first approxi 
mation. If these requirements are satisfied, then the following 
approximate statements will hold well enough for practical 
purposes: 

(a) The resonance radiation, E v , is due only to the emission 
by excited atoms within the boundaries indicated by the 
shaded portion in Fig. 24. 

(6) The concentration of excited atoms within these boun 
daries is uniform; i.e. the emission of all infinitesimal layers, 
such as dx, is the same. 

(c) The primary radiation emitted by a layer such as dx is 
absorbed on its way out, but only a negligible fraction of this 
absorbed energy is re-emitted in the original direction; i.e. 
E v consists entirely of primary resonance radiation. 

An approximate expression for E v may now be obtained. 
Let the absorption coefficient of the gas in the resonance lamp 
be k v f . Then the total energy absorbed from the exciting beam 
by the layer of atoms in the shaded area will be equal to 

. const. J/ v e~V'''i v 'd v (48). 

Some of this energy is re-emitted at right angles to the direc 
tion of the exciting beam. The experiments of Orthmann and 
Pringsheim [55] and of Rump [63] have shown that the form or 
frequency distribution of resonance radiation emitted at right 
angles to the direction of the exciting beam is independent of 
the form of the exciting line, and depends only on the form of 
the absorption coefficient. Therefore the radiation in a unit 
frequency band at the frequency v emitted at right angles by 
the infinitesimal layer dx is proportional to 

[const. $I v e~ k v l "k v 'dv].k v 'dx = Ck v 'dx (49), 

in which C will be constant, when the exciting lamp and the 



OF THE RESONANCE STATE 109 

resonance lamp are run under constant conditions of tempera 
ture, pressure, etc. The radiation emitted by dx is absorbed on 
its way out, so that the amount emerging is 



The emerging radiation from the whole layer of emitting atoms 
is therefore 



' f 
J o 



or E v =C(l-e- k v' 1 ') ...... (50). 

This is then the expression for the frequency distribution of 
the radiation emitted by a resonance lamp approximating ideal 
conditions, and was first used by Ladenburg and Eeiche[35] in 
connection with the emission characteristics of sodium flames. 
It is rigorously true only for an emitting layer of vanishingly 
small cross-section, that is, for a filament of length Z', but can 
be expected to give a satisfactory description of the radiation 
from any resonance lamp in which the gas pressure is low enough 
to render the amount of secondary and tertiary resonance 
radiation small in comparison with the primary resonance 
radiation. 

Other expressions have been used with varying degrees of 
success to represent the radiation emitted by a resonance lamp. 
Kunze [33] used a resonance lamp in which the distance I' was 
so small that Eq. (50) reduced to 

E v = const. k v ' 9 

and then corrected this expression to take account of a small 
amount of absorption by a layer of unexcited atoms lying next 
to the exit window. Schein[65] and Zemansky[89] recognized 
that a line emitted by a resonance lamp is broader than the 
absorption line; and, in working with mercury resonance 
radiation under conditions in which k v ' = k^e"^, used for the 
form of the emitted line an expression of the type e^^^ 2 which, 
with a > 1, has a breadth greater than the curve e^ 2 . Although 
this is not as good an approximation as Eq. (50), it is still 
serviceable in many cases, particularly those in which there 
may be some doubt as to the applicability of Eq. (50). 



110 ABSORPTION LINES AND MEASUREMENTS 

36. METHODS or MEASURING LIFETIME. It is obvious that, 
for a resonance lamp which justifies the use of Eq. (50), a 
measurement of the total emitted radiation, $E v dv, is an in 
dication of the number of excited atoms in the emitting layer. 
(This is strictly true only when E v is primary resonance radia 
tion. If radiation diffusion plays a role, Milne showed that not 
only the number of excited atoms but also their gradient must 
be taken into account.) If such a resonance lamp be excited 
for a while, and the excitation then cut off, the decay of the 
re-emitted radiation, $E v dv, is a measure of the decay of the 
excited atoms. From the definition of the Einstein A coefficient 
the number of excited atoms n present at a time t after the 
cut-off of the excitation is given by 

n = n Q e-Ai-i-i* = n e~' /T (51), 

provided 

(a) the excited state is the resonance state, 

(b) there is no further rate of formation of excited atoms due 
to radiation imprisonment, or to transitions from higher levels 
down to the resonance level. 

If the above conditions are satisfied, an experimental curve 
of $E v dv against the time should be exponential, with an ex 
ponential constant equal to 1/r. In order to use Eq. (51) to 
measure r, one must have a device for producing excited atoms 
that can be cut off suddenly, and a receiving device for 
measuring the radiation emitted after the cut-off. Several 
methods have been used, as follows: 

3c. RESONANCE LAMP WITH ELECTRICAL CUT-OFF. In a 
tube first described by Webb [78] there is a filament-grid system, 
the gas to be investigated, and a grid-photoelectric plate 
system. An alternating potential between the filament and the 
grid produces an intermittent stream of electrons with suffi 
cient energy to excite the atoms to the resonance state, and an 
alternating potential of the same frequency between the photo 
electric plate and grid enables the resulting radiation to be 
measured during the proper half-cycle. By varying the fre 
quency, the time between excitation and reception of the 



OF THE RESONANCE STATE 111 

emitted radiation is varied, and from a curve of photoelectric 
current against frequency, the lifetime of the radiation 
may be calculated. In this way, Webb and Messenger [79] 
measured the lifetime of the resonance radiation of Hg, 2537, 
at low vapour pressure and found the limiting value to be 
about 10~ 7 sec. ; and Slack [69] found the lifetime of the hydrogen 
resonance line, 1216, to be 1-2 x 10~ 8 sec. With an improved 
apparatus of this type, in which the photoelectric system 
occupied a separate tube, Garrett[i2] made a very careful in 
vestigation of the lifetime of mercury resonance radiation at 
very low vapour pressures and obtained for r, 1-08 x 10~ 7 sec., 
which is one of the most reliable values up to date. 

3d. RESONANCE LAMP WITH OPTICAL CUT-OFF. The electro- 
optical phosphoroscope was first described by Abraham and 
Lemoine[i] and later used by Pringsheim to measure the 
velocity of light. In the modified form, due to Gaviola[i3, 143, 
in which it can be used to measure the after-glow of radiation, 
it consists essentially of the following parts: (1) a beam of 
exciting light that is rendered intermittent by passing through 
a Kerr cell which is placed between crossed Nicols and across 
which is established an alternating potential; (2) a resonance 
lamp containing the gas to be studied; (3) another Kerr cell 
between crossed Nicols which allows the re-emitted resonance 
radiation to pass through intermittently because of the alter 
nating potential on the Kerr cell. The use of this apparatus in 
order to measure the lifetime of the resonance radiation 
emitted by the gas in the resonance lamp is rather complicated, 
and for these details the reader is referred to the paper of 
Gaviola quoted above, and to a recent paper by Duschinsky [5a]. 
With this device Hupfield[27] measured the lifetime of Na 
resonance radiation consisting of both D lines. The Na vapour 
was at a pressure corresponding to a temperature between 
190 C. and 200 C. at which some imprisonment of resonance 
radiation must have taken place. Unfortunately, the effect of 
vapour pressure on lifetime was not studied. The value ob 
tained, however, 1-5 x 10~ 8 sec., is in excellent agreement with 
those obtained by other methods to be described later. A 



112 ABSORPTION LINES AND MEASUREMENTS 

f 

repetition of this experiment, with substantially the same 
apparatus, was made by Duschinsky [5] in 1932 with startling 
results. First, the lifetime of the sodium resonance states was 
found to be 8-2 3 x 10~ 9 sec., almost one-half of Hupfield's 
value. Second, radiation imprisonment was found to begin at 
a temperature of 170 C., indicating that Hupfield's result 
(obtained at 190C.) concerned the lifetime of the radiation 
caused by repeated emissions and absorptions, rather than the 
lifetime of the atom. Third, the presence of nitrogen shortened 
the lifetime, whereas the presence of helium did not. The life 
time 8-2 x 10~ 9 sec. corresponds to an /-value for both D lines 
of 1-9, whereas, according to the / sum rule, the sum of the 
/-values for all the lines of the principal series of an alkali 
atom should be equal to about 1. Moreover, measurements of 
magneto-rotation of polarized light at the edges of the reso 
nance lines of Na, K and Cs yield /-values in good agreement 
with the theory. Duschinsky 's result is therefore in very serious 
disagreement with both theory and experiment. It is further 
to be noted that, although there is no doubt that radiation 
imprisonment takes place in sodium vapour at a temperature 
higher than 170C. (unpublished measurements of Zehden 
confirm this), there is still no assurance that the lifetime of the 
radiation measured under these conditions should be twice as 
large as the lifetime of the atom. 

The dependence of the lifetime on the foreign gas pressure 
brings up the possibility of a new kind of collision process, 
namely, one in which an excited atom is stimulated by an 
impact with a foreign gas molecule to radiate sooner than it 
ordinarily would. If such a collision process takes place, it is 
hard to understand why a nitrogen molecule should be effec 
tive and a helium atom should not. In fact, one would expect 
the opposite to be the case, inasmuch as nitrogen is known to 
quench sodium resonance radiation, thereby taking the ex 
citation energy of the excited sodium atom away and not 
allowing it to radiate, whereas helium does not quench sodium 
resonance radiation. An experiment on sodium resonance 
radiation was performed by von Hamos [20] to discover whether 
such a process takes place, and it was found that the results 



OF THE RESONANCE STATE 113 

could be explained quite adequately in terms of collision 
broadening of the absorption line by the foreign gas molecules. 
This experiment, however (which is discussed more in detail 
in Chap, rv under "Lorentz Broadening"), does not prove 
conclusively that no such process exists. Moreover, other 
experiments seem to indicate the possibility of a 4 "collision- 
stimulated" emission of an excited atom. It is therefore 
worth while, at this point, to consider the consequences of such 
a process in the light of thermodynamic equilibrium, to see if it 
is theoretically sound. 

First of all, if there is to be thermodynamic equilibrium 
in an enclosure containing radiation, absorbing atoms and 
foreign gas molecules, a "collision-stimulated" spontaneous 
emission cannot be assumed without also assuming "collision- 
stimulated" absorption and "collision-stimulated" induced 
emission. That is, corresponding to the three Einstein coeffi 
cients defined early in this chapter (in capital letters), there 
must be three more, say, fe-^g ; #2-^1 an( i ^a->i with the same 
definitions as the Einstein coefficients except that, instead of 
being atomic constants, they are all proportional to the foreign 
gas pressure. It can easily be shown that, upon introducing 
these three new coefficients, Planck's law can be derived. 

Now, if the " collision-stimulated " absorption and "colli 
sion-stimulated" induced emission be added to the Einstein 
absorption and induced emission in the derivation in 16, 
Eq. (28) becomes 



which shows that, if the number of atoms in the normal state, 
N, remain constant, and the ratio N'/N (fraction of excited 
atoms) is small, the integral of the absorption coefficient should 
increase with the foreign gas pressure, since a 2 ^. 1 is propor 
tional to the pressure. The integral $lc v dv over the mercury 
resonance line 2537 was measured by Fiichtbauer, Joos and 
Dinkelacker [ii J in the presence of foreign gases at pressures 
from 10 to 50 atmospheres and, instead of finding an increase, 
they noted a decrease of at most about 20 per cent. If one could 



114 ABSORPTION LINES AND MEASUREMENTS 

be certain that the factor N\l-~-^=\ remained constant 

during the experiment, one might conclude from this that the 
presence of a ^collision-stimulated" emission on the part of an 
excited atom was disproved. No such conclusion, however, 

can be made, because there is a possibility that N\l -^=\ 

\ fft-N J 

became smaller as the foreign gas pressure increased, thereby 
masking any increase due to a 2 _^ . The possibility of a decrease 



in N 1 1 -=r=r I arises from the fact that the metastable 6 3 P 

level of mercury lies so close to the radiating state 6 3 P X . If 
metastable atoms are formed by collision and are prevented 
from diffusing to the walls by the tremendous foreign gas 
pressure, they will then be raised again to the 6 3 P X state, and 
mercury atoms will continually be oscillating between, the two 
states. This will result in a high population of the 6 3 P state 
and a consequent reduction in N. This is given only as a 
possible explanation of Fiichtbauer's results, in order to show 
that they do not completely preclude the possibility of a 
collision-stimulated emission. The whole question must, at 
this time, be left open until further experimental work is 
done. 

3e. ATOMIC BAY OPTICALLY EXCITED. Perhaps the most 
direct measurement of the lifetime of a resonance state con 
sists in the measurement of the light emitted by a beam of 
atoms moving perpendicularly through a narrow beam of ex 
citing radiation [4]. The distance along the beam measured from 
the point where it is illuminated by the exciting radiation is a 
measure of the time after excitation, and the intensity of the 
radiation emitted at some point on the atomic beam is pro 
portional to the number of excited atoms at the point. The 
curve obtained by plotting intensity of radiation against time 
after excitation is exponential, with an exponential constant 
equal to 1/r in the case of resonance radiation. This method is 
applicable only to an atom whose lifetime is of the order of 
10~ 6 sec. or more, because the maximum thermal velocity 



OF THE RESONANCE STATE 115 

obtainable in experiments of this sort is of the order of 
10 5 cm. /sec. Koenig and Ellett [30] used this method to measure 
the lifetime of the 5 3 P 1 state of the cadmium atom by sending 
a beam of cadmium atoms perpendicularly through a narrow 
beam of radiation of wave-length 3261 (5 1 S ~5 3 P 1 ), and found 
r to be 2-5 x 10~ 6 sec. A qualitative experiment of the same sort 
was performed by Soleillet[Ti] on the same cadmium line, con 
firming Koenig and Ellett's result. 

3/. CANAL RAY. In order to measure somewhat shorter 
lifetimes than 10~ 6 sec., a beam of ions (canal ray) accelerated 
by an electric field to any desired velocity may be used. As the 
ions recombine and emit light, the intensity along the beam 
can be used to show the decay of the number of resonance 
atoms, provided sufficient time has elapsed for transitions 
from higher levels to the resonance level to take place. This 
method then leads to accurate results only when the lifetime 
of the resonance state is longer than that of higher states. 
Wien[84], Kerschbaum[28, 29] and Rupp[64] have used this 
method extensively with Hg, Na, H, Li, K, Ca and Sr, but only 
with moderate success. Wien's value of r for the G 3 ?! state of 
mercury, 0-98 x 10~ 7 sec., agrees well with other measurements, 
but all other values are much too large a result that is due 
undoubtedly to the presence of transitions from higher atomic 
levels. It is an important point that, in all cases, the decay 
curves appeared to be exponential, although, on account of 
transitions from higher levels, the curves would have to be 
represented by a sum of exponentials each with different ex 
ponential constants. That such a series can appear exponential, 
and yet yield a value of the exponential constant far from the 
actual value, is a danger that must be guarded against in all 
work in which the lifetime of a particular level is to be inferred 
from the decay of a spectral line. 

3*7. ABSOLUTE INTENSITY OF A RESONANCE LINE. If a gas 
is in thermal equilibrium at the temperature T, then the 
number of excited atoms per c.c., n, will be given by 



116 ABSORPTION LINES ANB MEASUREMENTS 

where N is the number of normal atoms per c.c., g^ and <7 2 are 
the statistical weights of the normal and the excited states 
respectively, and e the energy difference between the normal 
and excited states. If the excited state be the resonance state, 
the total energy E emitted by the excited atoms will be 

(53). 

r r 2 

A measurement, therefore, of the absolute intensity of a 
resonance line, E, enables one to measure r. The first measure 
ments of this kind were made by Gouy [16, 17, 18] and by Zahn [86] 
on the sodium D lines , and were used by Ladenburg [36] to obtain 
an estimate of the lifetime of the resonance states. An early 
measurement of the emission of a sodium flame by Ornstein 
and van der Held [52] yielded the value 5x 10~ 8 sec. for the 
lifetime of the 3 2 P states, which is more than three times as 
large as the accepted value. This discrepancy was explained 
by Ladenburg and Minkowski [40] as due to an error in estimat 
ing N from the degree of dissociation of the salt (Na 2 C0 3 ) which 
was used in the flame. A repetition of this experiment by 
van der Held and Ornstein [23] in 1932 yielded the value 
T= 1-63 x 10~ 8 sec., in good agreement with other results, and 
also showed that the discrepancy present in the earlier deter 
mination was due in part to the slow vaporization of the water 
droplets present in the Na 2 C0 3 solution that was sprayed into 
the flame. 

4. ABSORPTION WITHIN AND AT THE EDGES OP 
A RESONANCE LINE 

4 a. AREA UNDER THE ABSORPTION COEFFICIENT. It was 
proved in 2 of this chapter that, whatever physical properties 
are responsible for the formation of a resonance absorption 
line, the following equation, Eq. (28), remains valid: 



If a continuous spectrum be passed through a gas, and the 



OF THE RESONANCE STATE 117 

transmitted light be measured as a function of the frequency, 
the absorption coefficient may be calculated and plotted 
against the frequency. By graphical integration, then, the 
integral fk v dv may be obtained, and from a knowledge of N, 
r of the resonance state may be calculated. The outstanding 
difficulty c6nnected with this method of measuring r is the 
narrowness of most resonance lines. It is obvious that, if the 
monochromatic image of the slit of a spectrograph on the 
photographic plate cover a frequency range larger than the 
spectral width of the absorption line, the distribution of 
blackening on the plate will give no indication whatever of the 
true form of the absorption line. It is therefore necessary to 
work only with very broad absorption lines if the spectrograph 
is to have the usual working slit- width. This may be done by 
introducing a foreign gas at a very high pressure and making 
use of Lorentz broadening to such an extent that the absorp 
tion line has a much larger width than the monochromatic 
image of the spectrograph slit on the photographic plate. 

Using several foreign gases at pressures ranging from 1 to 50 
atmospheres, Fiichtbauer, Joos and Dinkelacker[ii] measured 
$k v dv for the mercury resonance line 2537 when the mercury 
vapour pressure corresponded to a temperature of 18 C., and 
found that the value of the integral decreased with increasing 
foreign gas pressure. Extrapolating to zero foreign gas pres 
sure, Tolman [74] showed that the integral yielded a value of r 
equal to 1-0 x 10~ 7 sec. The decrease in $k v dv with foreign gas 
pressure has already been commented on, and a possible 
explanation in terms of metastable atoms has been suggested. 
There remains to be pointed out only the fact that the extra 
polation to zero foreign gas pressure is decidedly necessary in 
order to obtain a good value of r, and that this extrapolation 
constitutes the main error in this method which otherwise is 
fairly simple and direct. 

46. ABSORPTION COEFFICIENT AT THE CENTRE OF A RE 
SONANCE LINE. If resonance radiation from a resonance 
lamp be passed through a narrow absorption cell containing 
the same gas that is in the resonance lamp, and the ratio of 



118 ABSORPTION LINES AND MEASUREMENTS 

the transmitted to the incident radiation be measured, the 
"absorption" A can be calculated as follows: 
. , Transmitted radiation 

A=l r =-i 7 =F P 

Incident radiation 

If the frequency distribution of the incident radiation (the 
radiation emitted by the resonance lamp) is denoted by E v and 
the absorption coefficient of the gas in the absorption cell by 
k v , and the thickness of the absorption cell by I, the absorption 
is given by 



-- ...... <> 

There are two important applications of the above equation, 
as follows: 

4c. METHOD OF LADENBTJRG AND E.EICHE. Suppose that 
the source of resonance radiation is a resonance lamp of the 
type shown in Pig. 24, containing a gas whose absorption 
coefficient is k v ' and with an emitting layer of thickness V. 
Then from Eq. (50) E V =C (l-e-W). If the radiation from 
this lamp is sent through an absorption cell of thickness Z, 
containing a gas whose absorption coefficient is k v , then from 
Eq. (55) the absorption is given by 



Ladenburg and Reiche [35] considered an experimental situa 
tion in which the emitting layer of the resonance lamp and the 
absorbing layer in the absorption cell were identical in every 
respect, i.e. in temperature, vapour pressure and thickness. 
This provides that Jc v 'l' = k v l, whence, calling the absorption 
A L in this case, 

--M 

...... (57)> 



The quantity A L has been called by Ladenburg and Reiche 
the "line-absorption" ("Linienabsorption"). Measurements 
of line-absorption are practicable only when the vapour pres- 



OF THE RESONANCE STATE 119 

sure in both the resonance lamp and the absorption cell is 
low. If, in addition to this, the natural damping ratio of the 
absorption line is of the order of 0*01 or smaller (which has 
been shown to be the case with most resonance lines), then 
the absorption coefficient k v can be expressed by Eq. (43), 
namely 



and A L becomes finally 

r (l- 



Jo 



)da> 



Eq. (58) has been evaluated by Kopfermann and Tietze[3i], 
and also by Ladenburg and Levy [42]. A table of values of A L 
for various values of k l is given in the Appendix, and A L is 
plotted against k Q l in Fig. 25. It is evident from this curve 
that one can obtain the value of k Q l that corresponds to any 
experimentally observed value of A L . From Eq. (35), r or/ 
is given by 

1 Ayp / 77 877*7! ^o 
r~""~2~ \ ln2'A 2 <7 2 '-Ar 

/ 77 me k n 



which enable one to calculate r or /from a knowledge ofk Q ,N 
and Av0 . The usual procedure is to measure A L for various 
values of N, and to plot the resulting values of k Q l against Nl- 
The slope of the resulting straight line yields k^N, which is 
then used to calculate r or/. 

Measuring k$l for various values of Nl by the method of 
Ladenburg and Reiche involves varying the conditions in both 
theresonancelampandtheabsorptioneell at the same time and 
in exactly the same way. This is not always convenient. From 
an experimental standpoint it may be desirable to keep the 
resonance lamp under strictly constant conditions of tempera 
ture, pressure and thickness of emitting layer (optimum con- 



120 ABSORPTION LINES AND MEASUREMENTS 

ditions), and to vary the temperature, pressure and thickness 
of the absorption cell only. If the variations in temperature of 
the gas in the absorption cell are not large enough to cause the 
Doppler breadth to differ from that in the resonance lamp by 
more than a few per cent, (which is usually the case, since 
Doppler breadth varies as the square root of the absolute tem- 




"012345 
Mg. 25. Line absorption of Ladenburg and Reiche. 

perature), the absorption coefficients of the gas in the absorp 
tion cell and in the resonance lamp may be written, respectively, 



2(v it,.) , 

where co= - ^Vln2 and^Ai^ is the constant Doppler 



OB 1 THE RESONANCE STATE 121 

breadth of the gas in the resonance lamp. Calling the absorp 
tion in this case A'^.p, Eq. (56) becomes 

f (l-e-Ve-" 2 ) (l-e-V'-'V"' 
^=^"75 - ...(59). 
(l-e-*'r<-*)da> 

J 00 

Now, as the pressure of the absorbing gas in the cell is varied, 
there will, in general, be one value of Nl in the absorption cell 
which is identical with that in the resonance lamp. At this 
value of Nl, k Q l will be practically equal to & T (neglecting 
again the slight difference between the two Doppler breadths), 
and this value of & ' I' may be found by measuring the absorp 
tion at this value of Nl and using the Ladenburg-Reiche 
curve in Fig. 25. Substituting this value of k 'l' in Eq. (59) 
there is obtained a relation between the absorption and k l 
from which the value of k l corresponding to any experiment 
ally observed absorption (at any value ofNl) may be obtained. 
Eq. (59) has been evaluated for several values of & T and k l 
and a table of values of A'^ v is given in the Appendix. 



4tf. METHOD IN WHICH E v Ce-^ l0 ^. In order to employ 
the method of Ladenburg and Reiche it is necessary to 
have a resonance lamp which satisfies the conditions given on 
p. 108 and which is constructed according to Fig. 24. This is 
not always feasible. It is often necessary to interpret experi 
ments on the absorption of light from a source excited by 
electron bombardment, or from a resonance lamp in which 
either the vapour pressure or the thickness of the emitting 
layer or both are not accurately known. In such cases it is 
convenient to use for the frequency distribution of the emitted 
radiation an empirical expression which represents roughly 
the line broadening resulting from the vapour pressure and 
temperature conditions within the lamp. A convenient expres 
sion for this purpose is 

...... (60), 



where co = ~ vln2 and A^ is the Doppler breadth of 



122 ABSORPTION LINES AND MEASUREMENTS 

the absorption line. It is evident in this expression that 

_ Emission line breadth 
Absorption line breadth' 

so that a value of oc equal to unity implies a line of the same 
shape and breadth as that of the absorption coefficient of the 
gas in the absorption cell. A value of a greater than unity 
represents a line of the same shape but of greater breadth than 
that of the absorbing gas. In the case of a lamp with a very 
thin emitting layer, the expression E v Ce~ ((D ' K ^ represents 
rigorously the emitted radiation, and a is given by the square 
root of the ratio of the absolute temperatures of the emitting 
gas and the absorbing gas. 

Setting Jc v equal to fe^-^ 2 as before, and calling the absorp 
tion in this case J. a , Eq. (55) becomes 



...... (61), 



7 

J 



which has been evaluated by Malinowski[45], Orthmann[54] ? 
Kunze[33], de Groot[i9] and Zemansky [89]. A table of values 
of A & for various values of <x and of & Z is given in the 
Appendix. To find oc in any experiment in which the operating 
conditions of the lamp remain constant, one can proceed as 
follows: Choose any value of a, and use the resulting curve of 
A a against k l to give the values of Jc Q l corresponding to 
experimentally measured values of the absorption. Plot these 
values of Jc Q l against Nl. According to Eq. (35), this should be 
a straight line. If it is not, choose another oc until one is found 
that yields a straight line between k Q l and Nl. This value of a 
can then be used to describe approximately the radiation of 
the lamp in question in any further work that is done with the 
same lamp under the same operating conditions. 

Although the three methods just described refer to an 
absorption line whose structure is simple, it is obvious that 
they may, with equal validity, be applied to an absorption line 
which consists of any number of equal, completely separate, 
simple lines. 



OS 1 THE BESONANCE STATE 123 

4e. MEASUREMENTS ON SIMPLE LINES. The absorption of 
the mercury resonance line 2537 from a resonance lamp by a 
column of mercury vapour was first investigated in 1914 
by Malinowski[45] who assumed that the radiation emitted 
by the resonance lamp had a pure Doppler form; i.e. he used 
Eq. (61) with oc=l. Later measurements of Orthmann[54], 
Goos and Meyer [15], Hughes and Thomas [26], Thomas [73] and 
Schein[65] gave rather discordant results, partly because of 
insufficient control of experimental conditions and partly be 
cause of the inapplicability of the absorption formulas that 
were used. In recent years a number of new measurements of 
the absorption coefficient of the mercury resonance line have 
agreed well among themselves and have shown themselves to 
be consistent with a value of r very close to 10~ 7 sec. In all of 
these experiments, the assumption was made that the line 
consists of five equal, completely separate lines, enabling the 
absorption formulas for a simple line to be used. It will be 
shown later that this is by no means a bad approximation. 

Using the method of Ladenburg and Reiche, Kopfermann 
and Tietze [31] measured the absorption of mercury vapour and 
found the maximum absorption coefficient (i.e. the average 
absorption coefficient at the centre of the five components) to 
vary with the number of absorbing atoms, N, very nearly 
linearly for small values of N according to the law 



corresponding to a value of r equal to 1-05 x 10~ 7 sec. Kunze [33] 
used a resonance lamp with a very thin emitting layer lying 
behind a thin non-emitting layer and used Eq. (61) with oc = 1 
and with a correction term to take account of the absorption of 
the non-luminous vapour. He found that for small values of 
N, k varied very nearly linearly with N such that 



corresponding to r=l-04x!0- 7 sec. Using Eq. (61) with 
a =1-21, Zemansky's measurements [89] of the absorption of 
mercury resonance radiation yielded the result that 



which is consistent with a value of r equal to 1-0 x lO" 7 sec. 



124 ABSORPTION LINES AND MEASUREMENTS 

The absorption of the cadmium resonance line, 2288, was 
measured by Zemansky[90], using the modified method of 
Ladenburg and Reiche [Eq. (59)]. Since the line emitted from 
his resonance lamp showed practically no hyperfine structure, 
the absorption formula for a simple line could be used with 
confidence. The results obtained were: Jc Q = 1-64 x lO" 11 ^ and 
T = 2-Ox 10~ 9 sec. 

4/. ABSORPTION OF A NUMBER OF SEPARATE SIMPLE LINES 
OF DIFFERENT INTENSITIES. If we denote the separate hyper- 
fine-structure components by superscripts, the absorption A 
is given by the formula analogous to Eq. (55), as follows: 



j... 

$EWdv+$EWdv + ... '" ( '' 

Using the method of Ladenburg and Reiche, with k^ = & (i) e~ 
r (l-e-V l <-"')* do>+ f" (l-e- 

T __ J oo J 00 



T __ 



f" (l-e-* ul <-**)da>+ ^ (l-e- k * 

J 00 J 00 

which is analogous to Eq. (58). If we write 



then, from Eq. (58), 

r a- 

J CO 

and A L becomes 

ZL = 



Both S and A L are functions of k l, and are tabulated in the 
Appendix for many values of k l. In order, therefore, to 
calculate A L , it is merely necessary to know the respective 
& Z's for all the hyperfine-structure components. These are 
determined as follows: If there are n hyperfine-structure com 
ponents, then experimental or theoretical determinations of 
the intensities of the components yield the n- 1 equations: 



OF THE HESOlSTAlSrCE STATE 125 

where a, 6, etc. are the intensities. The one more equation 
needed to compute all the k Q Vs is supplied by Eq. (28), which 
becomes in this case: 



me 



The above equation is a result of an assumption that is justified 
theoretically, namely, that all hyperfine levels of a resonance 
level have the same lifetime. Knowing Av^ and either r or/, 
all the & Z's are determined as functions of NL A L may then be 
calculated for a number of convenient values of NL 

On the basis of Schiller and Keyston's analysis of the hyper- 
fine structure of the mercury 2537 line (see Chap, i), Zehden 
and Zemansky [87] calculated by the above method the absorp 
tion A L as a function of NL The resulting theoretical curve 
agreed exceedingly well with the experimental curve of 
Kopfermann and Tietze[3i], provided r was taken to be 
1-08 x 10~ 7 sec. in agreement with Garrett's[i2] value. On the 
basis of the simple picture of the hyperfine structure, i.e. five 
approximately equal components, the agreement between 
theory and experiment is fairly satisfactory (within 5 per cent. ) , 
so that this simple picture is still useful in cases where the 
consideration of the accurate hyperfine structure leads to too 
great a complication in calculating, and where the magnitude 
of the experimental error does not warrant refinements in 
calculation. 

Using a mercury lamp with a very thin emitting layer ex 
cited by electron bombardment and operating under constant 
conditions, Garrett [12] measured the absorption of the mercury 
resonance line, 1 849, 6 1 S -6 ^ , by a column of mercury vapour 
contained in an absorption cell. From Schiller and Keyston's 
analysis of the mercury line, 4916, 6 1 P 1 ~7 1 S , Garrett was 
able to deduce the fine structure of the 1849 line, and by the 
methods described above was able to interpret his experiments 
in terms of the absorption of five completely separate simple 
lines of different intensity. Since the lamp in this experiment 



126 ABSORPTION LINES AND MEASUREMENTS 

had a very thin emitting layer, and since the square root of the 
ratio of the absolute temperature of the emitting gas to that 
of the absorbing gas was 1-2, Garrett used for each hyperfine- 
structure component of the emission line an expression of the 

-( V 
type E v (i) = & (l) I e \ 1-2 / . The absorption formula used to inter 

pret the experiments was as follows: 



with <x= 1*2. The experimental results were found to be con 
sistent with a value for the lifetime of the 6 1 P 1 state of the 
mercury atom equal to 0-3 x 10~ 9 sec., the smallest value of r 
that has yet been measured. 

4g. ABSORPTION OF A LINE WITH OVERLAPPING COM 
PONENTS. When the hyperfine-structure components of aline 
overlap, the absorption must be calculated by graphical in 
tegration. Using the method of Ladenburg and Reiche, 
Eq. (57) can be evaluated graphically as soon as a graph of k v l as 
a function of frequency can be drawn. This is done as follows: 
First, the various k Q Vs are calculated as in the preceding 
section. A number of Gauss error curves are then drawn side 
by side so that each curve has a maximum height equal to one 
of the & o rs and a breadth equal to Av^. The separations be 
tween the curves are made equal to the measured hyperfine- 
structure separations. The curves are then added, and the 
resulting curve represents k v l. The curves of (1 e~ k v l ) and 
( 1 er V) 2 are then plotted against frequency and, by graphical 
integration, A L is obtained. 

The only case in which this procedure has been carried out 
carefully is that of the sodium resonance lines. The absorption 
of the sodium D lines emitted by a resonance lamp of the type 
shown in Fig. 24 was measured very accurately by Zehden[88] 
for various values of the sodium vapour pressure in the 
absorption cell. The experiment was performed by the method 
of Ladenburg and Reiche and the results were expressed as 
curves of absorption against NL In order to calculate the 
absorption A L according to the method just outlined, it was 



OF THE RESONANCE STATE 127 

necessary first to know the intensity ratios of the hyperfine- 
structure components of both the D lines. According to 
Schiller each line is a doublet with a separation of 0-060 cm.- 1 , 
owing to the splitting up of the 2 S 1/2 state, the splitting of the 
2 P 1/2 and 2 P 3/2 states being too small to produce any effect. 
Since the nuclear moment of the sodium atom was not known 
at the time, and since there existed no reliable measurements 
of the intensity ratio of the components, it was necessary for 
Zehden to try several values for the nuclear spin. Assuming 
the spin to be J, and the lifetime of the 2 P states to be 
1-6 x 10~ 8 sec., a theoretical curve of A against Nl was obtained 
which did not agree satisfactorily with the experimental curve. 
Recent measurements of the separation of the hyperfine- 
structure components of each D line by Van Atta and 
Granath[74&], and of the nuclear spin (3/2) by Rabi and 
Cohen [59 a], will enable Zehden' s measurements to be re-inter 
preted when they are published. 

4 h. ABSORPTION OF A GAS IN A MAGNETIC FIELD. In order 
to obtain an expression for the absorption of resonance radia 
tion by a gas in a magnetic field it is necessary merely to use 
for the absorption coefficient the sum of a number of Gauss 
error curves, with wave-length separations determined by the 
-Zeeman effect, as was first shown by Malinowski[45]. The 
details of such a calculation are given in a paper by Schein[65], 
who derived the absorption formula applicable to the absorp 
tion of mercury resonance radiation by mercury vapour placed 
in a magnetic field. The calculations agreed approximately with 
the experimentally observed decrease of the absorption as the 
magnetic field was varied from to 1000 gauss. The complete 
experimental curve of absorption against magnetic field up to 
13>000 gauss showed five maxima. 

By placing an absorption cell containing mercury vapour 
between the poles of an electromagnet, Mrozowski[5i] was able 
to show that, at certain values of the field strength, only one or 
two hyperfine-structure components of the mercury 2537 line 
were transmitted. In this way he was able to investigate one 
component by itself and the other four components in com- 



128 ABSORPTION LINES AND MEASUREMENTS 

binations of two. By measuring the magnetic depolarization 
of the resonance radiation (see Chap, v) excited in mercury 
vapour by one or two hyperfine-structure components of the 
2537 line, Mrozowski arrived at a value of r for each kind of 
radiation. The three values of r so obtained differed from one 
another, in disagreement with the ideas of Schiller and Key- 
ston, whose analysis of the hyperfine structure of the mercury 
2537 line indicates that the lifetimes of all the hyperfine levels 
are the same. A re-evaluation of Mrozowski's results by 
Mitchell (see Chap, v) indicates the same lifetime for all 
hyperfine levels, but that the absolute value of this lifetime is 
larger than the usually accepted value. There is a possibility, 
in spite of the author's assertion to the contrary, that the dis 
crepancy is within the limits of experimental error. 

4i. ABSORPTION COEFFICIENT AT THE EDGES OF A RESO 
NANCE LINE. It was shown in Sect. 2 d that the extreme edges 
of an absorption line are due entirely to natural damping and 
that the absorption coefficient very far from the centre of the 
line is given by Eq. (47), namely, 



[icdv=!f^.- 

J 8770! T 



Since icdv=.- and Ai^=--, 

277T 



and ifk v ,N and (v - v ) are measured, r may be calculated from 
the above formula. This is not, however, the procedure that 
has been adopted in the past, for the reason that it has not 
always been possible to measure N either because of a lack of 
knowledge of the vapour pressure curve, or because non- 
uniform temperature conditions of the absorption tube pro 
hibited the use of any vapour pressure data. To avoid the 
necessity of knowing N, it has been customary to perform 
two different experiments with the same apparatus, and to 
eliminate N between them. In order to explain the way this is 
done it is convenient to put Eq. (47) into the classical form in 
which it has most often been used. 



OF THE RESONANCE STATE 129 

Using the classical result 



me 



Eq. (47) becomes ^ . A 
H v ; v J 2 -v 2 




me 



which, in the classical notation, becomes 

...... (64) > 



where P* 8 1 ( 65 )> 

(66), 

(67), 

(68). 

It is clear from Eq. (64) that if pi/ is determined by measuring 
(UK) and ^c, and if p is determined at the same time by some other 
experiment, v' can be finally calculated. 

Minkowski [49] passed a continuous spectrum through a long 
column of sodium vapour at various vapour pressures and 
photographed the D lines in absorption. Plotting the absorp 
tion coefficient against the frequency he was able to show that, 
in the vapour pressure region from 0-0053 mm. to 0*0087 mm., 
the absorption coefficient obeyed Eq. (64); whereas at lower 
vapour pressures, the absorption line was too narrow to be 
resolved properly by the slit of the spectrograph, and at higher 
vapour pressures Holtsmark coupling broadening made the 
line so broad that Eq. (64) was invalidated. In the region of 
vapour pressure in which Eq.(64) is valid, Minkowski measured 
UK and jit 2 and calculated therefrom pv' at a number of vapour 
pressures. From experiments on magneto-rotation, which will 
be described later, he obtained p at these vapour pressures, and 
combining the results, obtained v and consequently r. 



130 ABSORPTION LINES AND MEASUREMENTS 

4J. TOTAL ENERGY ABSORBED FROM A CONTINUOUS 
SPECTRUM BY A RESONANCE LINE THAT is NOT COMPLETELY 
RESOLVED. If a continuous spectrum is passed through an 
absorbing column of gas and the intensity of radiation trans 
mitted is plotted against the frequency in the neighbourhood of 
an absorption line, the curve obtained may appear as the heavy 
curve in Eig. 26. Ladenburg and Reiche[35] defined as the 
" Total Absorption" ("Gesamtabsorption"), A Q , 2?r times the 
ratio of the absorbed energy to the incident intensity. If the in- 




shaded area 

G ~ 4 

Fig. 26. Meaning of "total absorption". 

cident intensity is 7 , the absorption coefficient k v , and the 
thickness of the absorbing column I, the absorbed energy is 



whence 



/ O f (1-e-V)*;, 

Jo 

= tor ["(l-e-^W 

Jo 



...... (69), 



which has the units of 2-77 times frequency. If the pressure of 
the absorbing gas and the thickness of the absorbing layer are 
large enough to absorb completely the central region of the 
line but not high enough to produce Holtsmark broadening, 
then the absorption coefficient is given by Eq. (64), namely 

7 ^ P v ' ( \ 

k ^T UK = ^^ ( '* 

A o 



OF THE RESONANCE STATE 131 

In order to evaluate Eq. (69), it is convenient to replace the 
continuous spectrum, of intensity / , by a Gauss error curve 
distribution of intensity I e-^^ y where q is a number which, 
when later allowed to approach zero, will make the distribution 
of intensity continuous. Since ^rrdv = d^ A 6 is then given by 

pv'l 



/* o 

= 

J 



As q approaches zero 



whence, for a continuous spectrum, 



It must be emphasized that the above equation holds only 
when pi (which depends upon the pressure and the thickness of 
the absorbing layer) is large enough to warrant the use of 
Eq. (70). The advantage of using Eq. (71) to calculate pv' is 
that the measurement of the shaded area in Fig. 26 is, within 
limits, independent of the width of the slit of the spectrograph. 
If the absorption line depicted by the heavy curve in Fig. 26 
is not completely resolved, the photometer curve may appear 
as the dotted curve in this figure. Minkowski showed that the 
area above the dotted curve was, for several values of the slit- 
width, equal to the shaded area, within the limits of experi 
mental error. 

This method of measuring v was first employed by Laden- 
burg and Senftleben[34] in connection with a sodium flame at 
atmospheric pressure. The result will be discussed in the next 
chapter under "Lorentz Broadening"* Using pure sodium va 
pour , Minkowski [49 3 measured the total absorption and obtained 
with the aid of Eq. (71) the quantity pv' for the sodium D lines 
at various vapour pressures, and compared these values with 
those obtained by the method of Section 4i. The photometer 



132 ABSORPTION LINES AND MEASUREMENTS 

curves obtained by Minkowski in both methods did not show 
the slightest asymmetry, because the frequency distance from 
the centre of the D lines at which the measurements were made 
was so large in comparison to the hyperfine-structure separa 
tion. 

Since in Eq. (71) v is a constant equal to 1/r, and p contains 
Nf, A G is a convenient measure of Nf, the number of dispersion 




-^Vln 2~]=log [10-6 kf] 

7T&V D J 



Kg. 27. Van der Held's theoretical curves of total absorption 
against number of absorbing atoms. 

electrons associated with the absorption and emission of a 
particular spectral line. The number of dispersion electrons 
associated with the blue caesium doublet, 4593 and 4555, was 
measured by Schiitz[67j, who verified that A Q varies as the 
square root of Nf at high caesium vapour pressures. If the 
general expression for the absorption coefficient given by 
Eq. (40) is substituted in Eq. (69), and A G calculated by 
graphical integration for various values of the parameters, the 
resulting curve enables one to obtain a measure of the number 



OF THE BESONANCE STATE 133 

of dispersion electrons corresponding to any experimentally 
measured value of A a , no matter what the vapour pressure is. 
This was done by Schiitz [68], who, in a summary of the subject 
in the Zeitschrift fur Astrophysik, has given a curve of A G 
against Nfl for three different values of the natural damping 
ratio. A similar group of curves was computed by van der 
Held [22] for four different values of the natural damping ratio. 
These curves are shown in Fig. 27. The natural damping ratio, 
denoted by Schiitz by the symbol a>'/b and by van der Held by 
the symbol a, is exactly twice the quantity a appearing in 
Eq. (40). The values of a shown on the figure are those of van 
der Held. 

A a was measured by van der Held and Ornstein[23] at a 
number of values of the sodium vapour pressure, and the 
experimental curve of A a against Nfl was compared with van 
der Held's theoretical curves. The experiments indicated a 
value of the natural damping ratio equal to 0*005 (within 8 per 
cent.), corresponding to a lifetime of 1*6 x 10~ 8 sec. 

5. MAGNETO -ROTATION AT THE EDGES 
OF A RESONANCE LINE 

5 a. MAGNETO-ROTATION AT THE EDGES OF A RESOLVED 
RESONANCE LINE. If a beam of plane polarized light be 
allowed to traverse longitudinally an absorbing gas placed 
between the poles of a magnet, the plane of polarization of a 
particular frequency in the neighbourhood of an absorption 
line will be rotated by an angle % v . The theory of this pheno 
menon, which is the familiar Faraday effect, was first worked 
out by Voigt[76], and later extended by Kuhn[32]. A simple 
account of Kuhn's theory is given in the Appendix. On the 
basis of this theory, the angle of rotation at a frequency distance 
from the centre of the line, which is large in comparison with the 
separation of the Zeeman components of the line, is given by 

_ <rre*Hlz Nf 

Xv ~ 2m*c*'p* ( )? 

where H is the strength of the magnetic field, I the length of the 
absorbing column of gas, ju, equal to 2?r (v v ), and z is a func- 



134 ABSORPTION LINES AND MEASUREMENTS 

tion of the separations and relative intensities of the Zeeman 
components. When the magnetic field intensity is in the 
neighbourhood of 1000 gauss, z is a constant for a particular 
spectral line. A complete discussion of the quantity z along 
with a table of values for various resonance lines is given in 
the Appendix. 

Introducing the classical quantity p = , Eq. (72) 
becomes 

<*TJ~1 

(73), 



which enables one to compute p from experimental measure 
ments of Xv o V? an <l H. IfN is known, / can be calculated from 
p. If not, the value of p at a particular pressure is combined 
with the value of pv r at the same pressure obtained by the 
methods of Sections 4i or 4J, to yield finally a value of v. It 
must be emphasized that Eq. (73) is valid only when \i is large, 
that is, at great frequency distances from the centre of the line. 
In order that the angle x v shall have a measurable value at the 
extreme edges of the absorption line, the pressure of the absorb 
ing gas and the length of the absorbing column (that is, pi) 
must be made rather large. These are usually chosen so that 
the centre of the line is completely absorbed. It is also neces 
sary that the resolving power of the spectroscope or spectro- 
graph must be large enough to enable one to measure the exact 
value of /z, at which a particular angle of rotation occurs. The 
choice of polarization apparatus depends on the spectral region 
in which one is working. For details as to the measurement of 
X v the reader is referred to the papers of Kuhn[32] and Min- 
kowski[49]. 

The first exact measurements of p by the method of magneto- 
rotation were made by Ladenburg and Minkowski[38], who 
measured the magneto-rotation at the edges of the sodium D 
lines at various vapour pressures. Combining the resulting 
values of p with values of the sodium vapour pressure, / was 
found to be very nearly equal to 1/3 for the D l line and 2/3 
for the D 2 line, or, what amounts to the same thing, assuming 
/ Dl to be 1/3 and f^ 2 to be 2/3, the curve of p against 



OF THE RESONANCE STATE 135 

temperature was shown to be in agreement with the vapour 
pressure curve. 

Minkowski [49] measured the magneto-rotation at the edges 
of the sodium D lines at various vapour pressures and com 
bined the resulting values of p with his own values of pv' 
obtained by the methods of Sections 4i and 4j. The result of 
these three investigations was a value of v for both lines equal 
to 0-62 x 1C 8 , yielding a value for r equal to 1-6 x 10~ 8 sec. In 
the same way, Schiitz measured v for the blue caesium 
doublet. 

From measurements of magneto-rotation and vapour pres 
sure, Minkowski and Miihlenbruch [50] obtained p and N for 
the two caesium resonance lines (6 2 S 1/2 -6 2 P 1/2 , 8944; and 
6 2 S 1/2 -6 2 P 3/2 , 8521), yielding a value of /= 0-32 for the first 
and 0-66 for the second, corresponding to r = 3-8x 10~ 8 sec. 
and 3-3 x 10~ 8 sec. respectively. In the same way Kuhn[32] 
obtained for the two cadmium resonance lines (5 1 S -5 1 P 1 , 
2288; and S^-S^, 3261), /= 1-20 and 0-0019 respectively, 
corresponding to r = 2-0 x 10~ 9 sec. and 2-5 x 10" 6 sec., and for 
the two thallium resonance lines (6 2 P 1/2 -6 2 D 3/2 , 2768; and 
6 2 P 1/2 -7 2 S 1/2 , 3776) 3 /=0-20 and 0-08. Similarly, Weiler[80] 
found for the two potassium resonance lines (4 2 S 1/2 -4 2 P 1/2 , 
7699; and 4 2 S 1/2 -4 2 P 3/2 , 7665), /= 0-33 and 0-67. 

56. MAGNETO-ROTATION AND ABSORPTION OF A RESO 
NANCE LINE THAT is NOT COMPLETELY RESOLVED. If a con 
tinuous spectrum be sent in turn through a polarizing Nicol, 
an absorption tube placed longitudinally between the poles of 
a magnet, an analysing Nicol and a spectroscope which does 
not resolve the absorption line of the gas in the absorption tube, 
the whole field of view will be dark when the two Nicols are 
crossed and when the magnetic field is zero. If the Nicols are 
kept crossed, and the magnetic field is turned on, the amount 
of light of a particular frequency that passes through the 
analysing Nicol will depend upon (1) the angle x v through which 
the plane of polarization of that wave-length has been rotated, 
and (2) the absorption coefficient k v of the gas for that wave 
length. If the pressure of the absorbing gas and the length of 



136 ABSORPTION LINES A1STD MEASUREMENTS 

the absorption tube are great enough to absorb completely the 
central region of the line, but not great enough to produce 
Holtsmark broadening, then, from Eq. (73), 

ezHpl 



and, from Eq. (70), k v = /^- 2 



If the intensity of the continuous spectrum be / , and the 
length of the absorption tube be I, the total intensity of the 
light J passing through the analysing Nicol will be 

J = / r sin 2 Xv e-V^ ...... (74), 

J -co 

J-/./...-^ ...... p.). 

T xx- 
Lettmg 



8mc 2 V 
2m cv r 



U ~^IT' 

Eq. (75) becomes 



_oo^ 2 
and since 



the final result is 



- 

J 4V 2c 

It is apparent from the above equation that a measurement of 
J// and H, along with either a measurement or a calculation 
of p, is sufficient to enable one to calculate v. This method was 
employed by Schiitz[66] to measure v for the two sodium D 
lines. He extended Eq. (78) to include both lines which were 
not separated by his spectroscope, and calculated p from 
Minkowski's measurements of /and from the vapour pressure. 
He obtained the result that v = 0-64 x 10 8 (r = 1-6 x 10~ 8 sec.) 
in the sodium vapour pressure interval from 6-6 x 10~ 4 mm. to 



OF THE RESONANCE STATE 137 

3-7 x 10~ 3 mm., and that v increased at higher vapour pressure 
bf>canse of Holtsmark broadening. Further results of Schutz 
in connection with collision broadening by foreign gases will 
be discussed later on in this book. 

The disadvantage of Schutz 's method of determining v is 
the necessity for knowing p. An extremely ingenious variation 
of Schiitz's method was developed by Weingeroff [81], in which 
a knowledge of/) is not necessary. It will be remembered that 
the method of Schutz involved the measurement of the total 
intensity of light transmitted through the analysing Nicol 
when both Nicols were crossed. Weingeroff noticed that, when 
the magnetic field was at some constant value and the analys 
ing Nicol was rotated in the direction of the magneto-rotation, 
the observed line was first bright on a dark background, then 
it vanished into the background, and then it appeared dark on 
a bright background. A similar series of changes occurred when 
the analysing Nicol was turned in a direction opposite to the 
magneto -rotation. If the angle <j> denote the position of the 
analysing Nicol with reference to the crossed position (when 
Nicols are crossed ^ = 0), then the difference between the 
amount of light due to magneto -rotation plus background and 
the amount due to background alone is given by 



f a 

*././_ 



(79), 



which obviously reduces to Schiitz's expression, Eq. (74), when 
$ = 0. When the central region of the line is completely absorbed, 
X v and Jc v can be expressed as before, and Eq. (79) becomes 



which, upon substituting 

2 _ezHpl ^ 

X "" Smc 2 '~p?' 

2mcv r 

b = ~^H~> 
reduces to 



138 ABSORPTION LINES AND MEASUREMENTS 

Since 




...... (82), 



...... (83). 

The above equation gives the amount of light over and above 
the background that passes through the analysing Nicol when 
the magnetic field is H and the setting of the analysing Nicol is 
(j>. If H is kept constant and <f> varied, there will be a value of <f> 
for which E will vanish, that is, the line will merge with the 
background. Let this value of <f> be denoted by < . Then < is 
given by the equation 



cos 2 

...... (84), 

whose solution was obtained graphically by Weingeroff and is 

shown in Fig. 28 in which < is plotted as abscissa and b mC * 

&z fi 

plotted as ordinate. The experiment consists in measuring the 
angle <f> Q through which the analysing Nicol must be rotated in 
order that the line merge with the background. Prom Fig. 28 



the corresponding value of ~- is read off, whence, knowing 

z and H, v is calculated. The great advantage of this method 
lies in the fact that a knowledge of the vapour pressure (that 
is, p) is not necessary. In this way Weingeroff measured v for 
the sodium D lines at various vapour pressures. Since the two 
D lines were not separated by his spectroscope, Weingeroff 
extended Eq. (83) to include both lines. Furthermore, since it 
was necessary to work at low magnetic field intensities where 



OF THE RESONANCE STATE 



139 



z is not constant but is a function of H, it was necessary to per 
form other experiments to obtain z. The final result was that 
in the vapour pressure range corresponding to temperatures 
from 240 C. to 330 C., v remained constant at 0-62 x 10 8 
(r= 1-6 x 10~ 8 sec.), and beyond 330 C. it increased because of 
Holtsmark broadening. Schiitz found that v began to increase 



3-0 



2-0 



1-0 



2 
Fig. 28. Graph of 



4 6 8 10 12 14 16 18 20 22 
$ in degrees 




at a vapour pressure corresponding to a temperature of 265 C., 
and Minkowski at a temperature of 287 C. Of these three 
results, that of Weingeroff is probably the most accurate. 

6. DISPERSION AT THE EDGES OF 
A RESONANCE LINE 

6a. GENERAL DISPERSION FORMULA. On the basis of 
Kramers' quantum-theoretical dispersion formula, Laden- 



140 ABSORPTION LI3STBS AND MEASUREMENTS 

burg [39] showed that the index of refraction of a gas at a wave 
length A is given by 



- ...... (85) ' 



where k and j refer to any two stationary states (Jc being the 
upper state) whose statistical weights are g k and g j respectively. 
N k and Nj are the numbers of atoms in the two states, X kj the 
wave-length of the radiation emitted in the transition k ->j, 
and f k j is connected with the Einstein A coefficient by the 
formula [see Eq. (31)] 

g k 



It is convenient to consider three special cases of Eq. (85), in 
order to discuss the existing experimental work in this field. 

66. NORMAL DISPERSION OF AN UNEXCITED GAS VERY FAR 
FROM THE ABSORPTION LINES. If the gas is not electrically 
excited and is at a moderate temperature, there will be only a 
negligible number of atoms in excited states other than the 
normal one. Denoting the normal state by j 1, and calling 
Nj*=Ni = N, Eq, (85) can be simplified by neglecting the ratio 
in comparison with unity. There results then 

...... (86) ' 



where X kl (i.e. A 21 , A 31 , A 41 , etc.) are the wave-lengths of the 
absorption lines that influence the dispersion, and f kl are the 
respective / values of these lines. This is the ordinary normal 
dispersion curve first derived classically by Sellmeyer, and 
gives the value of the index of refraction at wave-lengths that 
are hundreds or thousands of Angstroms away from the 
absorption lines. In this region, n is most easily measured by 
the method of Puccianti[59], involving the use of a Jamin 
interferometer. 

It was shown by Herzfeld and Wolf [24] that the existing 
values of n for each inert gas He, Ne, A, Kr and Xe in the visible 
region could be represented by an equation of the type 

const. 



V-* 2 ' 



OF THE RESONANCE STATE 141 

The values of A calculated from the empirical curves, however, 
did not agree with the known ultra-violet resonance lines of the 
noble gases, and were, in fact, in all cases, of shorter wave 
length than the series limit. Upon attempting to use a disper 
sion formula of two terms, one term involving the correct 
ultra-violet resonance frequency, it was found that the wave 
length of the second absorption line did not correspond to any 
known absorption line, being also of much too short a wave 
length. It is therefore apparent that measurements of index 
of refraction at wave-lengths that are too far removed from 
the wave-lengths at which the absorption lines occur are not 
very reliable in giving information concerning the absorption 
lines themselves. 

A very careful measurement of the index of refraction of 
mercury vapour was made by Wolfsohn[85] at wave-lengths 
from 2700 to 7000. He found that the results could be repre 
sented by Eq. (86), using three terms, the first two involving 
the two ultra-violet resonance lines of mercury, 1850 and 2537, 
and the third involving a wave-length somewhere between 
1400 and 1100. Inserting in the formula the accurate /-value 
for 2537 obtained by measurements of anomalous dispersion 
(to be described later), he found that the /-value for 1850 
varied from 0*7 to 1-0 depending upon the wave-length chosen 
for the third term. Choosing the third absorption line to be at 
1 1 90, the limit of the principal series of mercury, he obtained [43] 
for the /-value of the 1850 line 0-96 corresponding to a lifetime 
of the 6 1 ?! state of 1-6 x 10~ 9 sec. 

6c. ANOMALOUS DISPERSION OF AN UNEXCITED GAS AT 
THE EDGES OF A RESONANCE LINE. If, instead of measuring 
n at wave-lengths that are hundreds or thousands of Ang 
stroms from an absorption line, the index is measured from 
0-5 to 1 Angstrom from the centre of the resonance line at A 21 , 
the effect of all the other absorption lines becomes negligible, 
and Eq. (86) may be further simplified by not having to sum 
over k. Denoting A 21 by A and/ 21 by/, Eq. (86) becomes 

71 1 = 



"27rmc 2 'A 2 -A 2 ' 



142 ABSORPTION LINES AND MEASUREMENTS 



or 



_ 
A 



.(87). 



This is the well-known formula of anomalous dispersion, and 
has been used in conjunction with experiment to provide some 
of the best /-values that have as yet been obtained. The most 
accurate experimental method is the "hook-method" of 
Roschdestwensky [61, 62], which will be described in detail. In 
Fig. 29 is shown a schematic diagram of a Jamin interferometer. 




II 




Fig. 29. Jamin interferometer used in Roschdestwensky "hook-method". 

Gas may be admitted into tube I at any known pressure, but 
tube II is kept evacuated. A source of continuous radiation is 
used, and the resulting beam of light is focused on the slit of a 
spectroscope. With both tubes evacuated, and with the com 
pensating plate P removed, the continuous spectrum is crossed 
by horizontal interference fringes. With the compensating 
plate in position, the interference fringes are oblique. If the 
wave-length separation of a convenient number of fringes in 
the immediate neighbourhood of A is measured, an important 
constant of the apparatus K can be calculated as follows: 

-_ , No. of fringes 

Wave-length separation of these fringes * 



OF THE RESONANCE STATE 143 

If a gas with an absorption line at AQ is now introduced into 
tube I, the oblique interference fringes become hook-shaped 
symmetrically on both sides of the absorption line. If A re 
present the wave-length separation of two hooks symmetric 
ally placed with regard to the absorption line, then the theory 
of this method in conjunction with Eq. (87) yields the equation 



- e^wr KA * (88)> 

from which /may be calculated when ^V" and I (the thickness of 
the layer of gas) have been determined. A simple derivation of 
Eq. (88) may be found in a paper by Ladenburg and Wolf- 
sohn[4i]. 

Roschdestwensky[62] used the hook-method to study the 
anomalous dispersion in the neighbourhood of the absorption 
lines of Na, K, Rb and Cs. The measurements led in all cases 
to the ratio of the /-values associated with the principal series 
of doublets. The results are tabulated in Table XII. 

TABLE XII 



Elem ent 


Running numbers 
n, m 


/of7i 2 S 1/2 -m 2 P 3/2 


/of7* 2 S 1/2 -^ 2 P 1/2 


Na 


3,3 


1-98 




K 


4,4 


1-98 







4,5 


2-05 




Rb 


5,5 


2-01 






5,6 


2-57 






5,7 


2-9 




Cs 


6,6 


2-05 






6,7 


4-07 






6,8 


7-4 






6,9 


9-1 





By the same method, Ladenburg and Wolfsohn [41] measured 
the anomalous dispersion of mercury vapour near the reso 
nance line 2537 within a wide range of vapour pressures. Using 
Eq. (88) for low values of the vapour pressure, and the results 
of Wolfsohn's investigation of the normal dispersion of mer 
cury vapour at high vapour pressures, the authors obtained a 
value of/ equal to 0-0255 0-005, corresponding to a lifetime 
of the G 3 ? state of l-14x 10~ 7 sec. With the Jamin inter- 



144 ABSORPTION LINES AND MEASUREMENTS 

ferometer enclosed in an evacuated vessel, Wolfsohn[85aj 
measured the anomalous dispersion of mercury vapour in the 
neighbourhood of the 1849 line (G^Q-G 1 ?!) and obtained for/, 
1-19, corresponding to a lifetime of the 6 1 P 1 state of 1 30 x 1 0~ 9 
sec. 

By means of the Roschdestwensky hook-method, Prokof- 
jew [58] studied the anomalous dispersion of the resonance lines 
of Ca, Sr and Ba under experimental conditions which did not 
allow the accurate measurement of vapour pressure. Calling r x 
the lifetime of the singlet state and r 2 the lifetime of the triplet 
state, Prokof Jew's experiments yielded the ratio rjr^ . For Ca, 
Sr and Ba, this ratio was found to be 1-25 x 10~ 5 , 26-9 x 10~ 5 
and 335 x 10~ 5 respectively. In the same way, Filippov[8] 
found the ratio rjr 2 of Zn and Cd to be 6-76 x 10~ 5 and 
72-5xlO- 5 respectively. Prokofjew and Solowjew[57] found 
the ratio of the /-values of the thallium lines, 5350 and 3776, 
to be 0-95. 

6d. ANOMALOUS DISPERSION OF A STRONGLY EXCITED. 
GAS AT THE EDGES OF THE ABSORPTION LINES X ki . If n is 
measured very close to an absorption line, the effect of the 
other absorption lines may be neglected, but when the excita 
tion is strong enough, the number of atoms in the higher state 
N k may become an appreciable fraction of the number in the 
lower state N f . Eq. (85) then becomes 



nl- 



47TWC 2 A / 



/ N Q \ 
The expression 1 1 - -~ . ^ I is known as the negative dispersion 

\ J \3 K/ 

term and is appreciably different from unity only when the 
excitation of the gas is very strong. By the hook-method of 
Roschdestwensky, Ladenburg, Kopfermann and Levy in 
vestigated the anomalous dispersion of electrically excited 
neon, in the neighbourhood of many absorption lines originat 
ing at the metastable 3 P 2 and 3 P levels. The results of these 
investigations, in conjunction with the results of intensity 
measurements of the neon lines, enabled the authors to give 
relative /-values of all the neon lines studied. It was found that 



OF THE RESONANCE STATE 145 

when the current through the discharge tube was greater than 
200milliamps. the negative dispersion term began to play an 
important role. Similar measurements were made on hydrogen 
by Ladenburg and Carst, and on helium by Levy. For further 
details the reader is referred to the original papers in volumes 
48, 65 and 72 of the Zeitschrift fur Physik. 

7. TABLES OF LIFETIMES 
AND DISCUSSION 

la. SUMMARY OF METHODS OF MEASURING LIFETIME, AND 
TABLES OF LIFETIMES. 

Methods involving the emission of radiation. 

Decay of electrically excited resonance radiation, 3c. 
Decay of optically excited resonance radiation, 3d. 
Decay along an optically excited atomic ray, 3e. 
Decay along a canal ray, 3/. 
Absolute intensity of a resonance line, 3g. 

Methods involving absorption of radiation. 
Total area of absorption coefficient, 4 a. 
Absorption coefficient at the centre of a resonance line, 

46,c,d. 

Absorption coefficient at the edges of a resonance line, 4i. 
Total energy absorbed from a continuous spectrum, 4j. 

Methods involving magneto-rotation of polarized light. 

Magneto-rotation at the edges of a resolved resonance 
line, 5 a. 

Magneto-rotation and absorption of an unresolved reso 
nance line, 56. 

Methods involving dispersion of radiation. 

Normal dispersion very far from a resonance line, 66. 
Anomalous dispersion at the edges of a resonance line, 6 c. 

Methods involving depolarization (see Chap. v). 

Depolarization of resonance radiation by a steady 

magnetic field. 

Measurement of the angle of maximum polarization in 
small steady magnetic fields. 



14:6 ABSORPTION LINES AND MEASUREMENTS 

Depolarization of resonance radiation by an alternating 

magnetic field. 

All the results that have appeared throughout the chapter 
axe coUected in Tables XIII, XIV and XV. 

TABLE XIII 



Atom 


Series notation 
of resonance 
line 


Wave 
length 


T in sees. 


/-value 


Author, reference 
and method 


H 
He 
> 


1 2Q 213 

JL Oj/ 2 ^ Jt 


1216 
584 


1-2 x!0~ 8 
442 x 10- 10 
5-80 x ID" 10 


0-349 
0-266 


Slack [69], 3c 
Vinti[7?a], Theor. 
Wheeler [ssa], 
Theor. 


Li 


2 2 S 1/2 -2 2 P 


6708 


2-7 x!0~ 8 


0-25 and 0-50 


Trumpy [74 a], 
Theor. 


Na 


3 2 S 1/2 -3 2 P 

37 


5896, 5890 


1-5 x!0~ 8 
8-2 xlO~ 9 
1-6 xlO~ 8 





Hupfield[27],3d 
Duschinsky [s],3c? 
v. d. Held and Orn- 








: 


l-48x!0- 8 * 
1-6 x!0~ 8 


0-35 and 0-70 
0-33 and 0-67 


stein [**], 30, 4^ 
Ladenburg and 
Thiele[4a],76 
Minkowski [49], 5a, 
4i 











1-6 x!0~ 8 


0-33 and 0-67 


Minkowski [49], 5a, 


K 

Cs 


6 2 S^-6 2 P 1/2 


7699^7665 
8944 


1-6 x!0~ 8 
1-6 x!0~ 8 
1-6 xlO~ 8 
2-7 x!0~ 8 * 
3-8 xlO~ 8 * 


0-33 and 0-67 
0-33 and 0-67 

0-33 and 0-67 
0-32 


Schiitz[66],56 
Weingeroff [si], 56 
Sugiura [/a], Theor. 
Weiler [so], 5 a 
Minkowski and 
Miihlenbruch [so], 





6 2 S 1/2 -G'P 3/2 


8521 


3-3 xlO~ 8 * 


0-66 






76. DISCUSSION or TABLES. The values off and r listed in 
the tables represent for the most part work done in the last 
eight years. Previous work was concerned mainly with the 
ratio of the /-values of the principal series doublets of the 
alkalis. A convenient summary of such work can be found in 
the Zurich Habilitationsschrift of W. Kuhn and in a paper by 
J, Weiler, Z. f. Phys. 50, 436 (1928). Further information can 
be found in the articles of R. Minkowski and R. Ladenburg in 
the section of Miller-Pouillet's Handbuch der Physik devoted 
to optics, in the article on dispersion and absorption by 
G. JafiEe in the Handbuch der Experimentalphysik, Vol. 19, and 



OF THE BESONANCE STATE 



147 



TABLE XIV 



Atom 


Series notation 
of resonance line 


Wave 
length 


T in sees. 


/-value 


Author, reference 
and method 


Mg 


S^o-S 8 ?! 


4571 


~4 x 10~ 3 





Frayne [9], 76 


Zn 


4 1 S -4 3 P 1 


3076 


-1 x 10~ 5 





Soleillet, chap, v 


it 


,, 





~1 x 10~ 5 





Soleillet [71], 3e 





4 1 S -4 1 P 1 


2139 


<10~ 7 





Soleillet [71], 3e 


Cd 


S^o-S 3 ?! 


3261 


2-5 x 10~ 6 * 





Koenig and Ellett 










2-5 x 10~ 6 * 


0-0019 


Kuhn [32], 5 a 











-2 x 10~ 6 





Soleillet, chap, v 











2-3 x 10- 6 * 





Ellett, chap, v 





5 1 S -5 1 P 1 


2288 


1-98 x 10~ 9 * 


1-20 


Kuhn [32], 5a 











1-99 x 10~ 9 * 





Zemansky [90], 4e 





>} 





~10~ 9 





Soleillet, chap, v 


Tl 


6 2 P 3/2 -7*S 1/2 


5350 


(T of 7 2 S 1/2 \ 


0-076* 


Prokofjew and So 








J state is L 




lo wjew [57], 6c 





6 2 P 1/2 -7*S 1/2 


3776 


(l-4xlO~ 8 j 


0-08* 


Kuhn [32], 5a 





6*P 1/2 -6*D 3/2 


2768 





0-20* 


Kuhn [32], 5a 



TABLE XV 



Atom 


Series 
notation of 
resonance 
line 


Wave 
length 


T in sees. 


/-value 


Author, reference 
and method 


Hg 


e^o-e^ 


2537 


-1 x 10~ 7 





Webb and Messenger [79], 3c 







'> 


1-08 x 10-'* 





Garrett[i2],3c 


>J 


> 


?> 


0-98 x 10~ 7 





Wien [84], 3/ 


ff 


99 


? 


1-0 xlO- 7 





Fiichtbauer, Joos and Dinke- 












lacker, as calculated by Tol- 












man[n, 74], 4a 


99 


t9 





1-08 xlO~ 7 * 


0-0278 


Kopfennann and Tietze, as 












calculated by Zehden and 












Zemansky [si, 87], 4/ 








> 


1-14 x 10~ 7 * 


0-0255 


Ladenburg and Wolfsohn [41], 












6c 








> 


1-13 x 10~ 7 





von Keussler, Chap, v 






> 


1-08 x 10~ 7 * 





Olson, recalculated by Mitchell, 












Chap, v 


It 






~io- 7 





Breit and Ellett, Chap, v 


9 


| 


-10- 7 





Fermi and Basetti, Chap, v 


Hg 


e 1 ^ 1 ?! 


1849 


0-3 xlO~ 9 





Garrett [12], 4/ 










1-6 xlO~ 9 


0-96 


Ladenburg and Wolfsohn [is], 












66 











1-30 x 10~ 9 * 


1-19 


Wolfsohn [ssa], 6c 



148 ABSORPTION LINES AND MEASUREMENTS 

in an article by Korff and Breit in the Reviews of Modern 
Physics, Vol. 4, No. 3. 

The values in the tables which, in the opinion of the authors, 
are the most accurate are starred. The value for the lifetime of 
the 3 2 P states of sodium given by Ladenburg and Thiele, 
1-48 x 10~ 8 sec., is suggested as the best value to date, being 
the result of a critical survey of previous experiments. In the 
case of the lifetime of the 6^ state of mercury, the value of 
1-08 x 10~ 7 sec. (Garrett and Webb) is suggested as the most 
reliable, partly because it is independent of a knowledge of the 
mercury vapour pressure and also because it agrees best with 
the absorption measurements of Kopfermann and Tietze when 
the Schiller and Keyston hyperfine structure is taken into 
account. 

The most accurate value of lifetime is probably that of the 
5 3 P a state of the cadmium atom, 2-5 x 10~ 6 sec., inasmuch as 
precisely this value is obtained by two utterly different 
methods (Kuhn, Koenig and Ellett), and very nearly this 
value, 2-3 x 10~ 6 sec. (Ellett), by still a third method. The 
agreement between Kuhn's and Zemansky's values for the 
lifetime of the 5 1 ?! state of the cadmium atom suggests that 
the value 2-0 x 10~ 9 sec. for this lifetime is quite reliable. 

The lifetime of the 7 ^S^ state of thallium was obtained as 
follows. From Kuhn's measurement of the /-value of the 3776 
line, and from Ladenburg's equation connecting the /-value 
with the Einstein A coefficient, the result was obtained: 

^3776 = 3-7 xlO 7 . 

Vonwiller [77] measured the ratio of the intensity of the 3776 
line to that of the 5350 line and obtained the value 1-56. From 
the relation 

-*3776 _ -^3776 V 3776_.. j.gg 
^5350 -^5350 V 5350 

-^5350 was found to be 3-4 x 10 7 . Prokofjew and Solowjew [57] 
measured the ratio of the /-values of the 5350 and 3776 lines 
and obtained the value 0-95. From the relation 



OF THE RESONANCE STATE 149 

-4 5350 was found to be 3-5 x 10 7 , in good agreement with the 
first value. The sum of the two Einstein A' a is 

3-7 x 10 7 + 3-5 x 10 7 = 7-2 x 10 7 , ' 

and since r== l/S-4, the lifetime of the 7 2 S 1/2 state is 1-4 x 10~ 8 
sec. 

The value of the lifetime of the 3 3 P X level of magnesium 
calculated by Frayne[9] on the basis of Houston's wave- 
mechanical formulas is given in the table, because it is partly 
substantiated by Frayne's experiments on the emission 
characteristics of a magnesium arc. These experiments in 
dicate that the intensity of the 4571 line emitted by magne 
sium vapour in the presence of foreign gases is consistent with 
a value of r equal to 4 x 10~ 3 sec. 

7c. ELECTRON EXCITATION FUNCTIONS. A possible con 
nection between lifetime and electron excitation function was 
found by Hanle[2i], Schaffernicht[64a] and Larch<S[44]. If the 
intensity of a spectral line be plotted against the electron ex 
citation voltage a curve is obtained which starts in the neigh 
bourhood of the excitation potential, rises to a maximum and 
then decreases to zero as the voltage is increased. Such a curve 
is called an excitation curve, and in the case of a resonance line 
there seems to be a relation between the width of the maximum 
and the lifetime. The excitation curves for the intercombina- 
tion lines of Hg, Cd and Zn rise quickly and descend quickly 
with a width that is quite narrow. The curves for the singlet 
resonance lines, however, descend very slowly, making the 
width rather large. The authors conclude that short lifetimes 
are associated with wide excitation curves, and long lifetimes 
with narrow excitation curves. More experimental material, 
however, is needed to express this regularity in a more quanti 
tative form. The excitation curve of the cadmium line 2288 
(5 1 S -5 1 P 1 ) obtained by Larche showed an interesting ano 
maly. It has a slight depression as though it were the sum of 
two curves, one thin and the other thick. On the basis of the 
relation just expressed between lifetime and width of excita 
tion curve, this seems to indicate that the 5 1 ?! level of cad 
mium has two lifetimes, of the order of 10~ 9 sec. and 10~ 6 sec. 



150 ABSORPTION LINES AND MEASUREMENTS 

respectively, which is exactly what was inferred by Soleillet [70] 
from his experimental curves expressing the percentage 
polarization of cadmium resonance radiation 2288 and external 
magnetic field. There seems to be no doubt about the experi 
mental results of Larche and Soleillet, but there is considerable 
objection to supposing that the hyperfine structure levels of 
the 5 1 P 1 state of cadmium, which are known to be extra 
ordinarily close together, should have lifetimes differing by a 
factor of 1000. No other explanation, however, has as yet 
been given. 

In contradiction to the experimental results of Hanle, 
Larch6 and others, Michels[46] obtained narrow excitation 
curves for all lines, whether singlet or intercombination lines. 
It is therefore a possibility that the apparent relation between 
lifetime and width of maximum is illusory. It is impossible to 
decide the question at this time. 

Id. THE PAUU-HotrsTON FORMULA. An interesting re 
lation was derived by Pauli on the basis of the correspondence 
principle and later by Houston on the basis of the wave 
mechanics. 

If T! = lifetime of the first r P l state of a 2 electron atom, 
r 2 = lifetime of the first ^ state of a 2 electron atom, 
A v = frequency separation of 3 P and 3 P 2 , 
8 v = frequency separation of ^ and centre of gravity of 

3 P states (one-third the way from 3 P to 3 P 2 ), 
the Pauli-Houston formula states tha/t 

(90). 



In Table XVI, columns (3) and (5), values of T^ calculated 
by Eq. (90) are compared with the experimental measurements 
of this ratio. It is seen that in all cases the calculated values are 
larger than the experimental ones . In a private communication 
it was pointed out by Houston that the experimental values of 
T i/ T 2 are i n better agreement with a " fourth power of the 
frequency" law than with Eq. (90). Values of the expression 



2 /Ay\ /v t \* 

W w 



OF THE RESONANCE STATE 151 

are listed in column (4) of Table XVI, and are seen to be in 
fairly good agreement with measured values ofr^r^,. No ex 
planation, however, has as yet been given for this agreement. 

TABLE XVI 





(1) 


(2) 


(3) 


() 


(5) 




Atom 


/AzA 


"2 


2/A*f/V 2 y 


2/AiAy* 2 \ 4 


r_ 1= ^ 


Authors 




\$v ) 


V-t 


9 \foj \~J 


9\~8v) \Vi/ 


T 2 A! 








1 






measured 




Mg 


4-63 x 10~ 3 


624 


11-6 xio~ 7 


7-24 x 10- 7 






Ca 


1-87 x 10~ 2 


643 


2-06 x 10~ 5 


1-33 x 10~ 5 


l-25xKT 5 


Prokof jew [w] 


Zn 


4-07 x 10~ 2 


695 


124 x 10~ 5 


8-64 x 10- 5 


6-71 x 10- 8 


Filippov [s] 


Sr 


8-08 x 10~ 2 


668 


4-31 x 10~ 4 


2-88 x 10-* 


2-69 x 10~* 


Prokof jew [SB] 


Cd 


1-32 x 10- 1 


702 


134 x 10~ 4 


940 x 10~ 4 


8-0 x!0~ 4 


Kunn [32] 












7-25 x 10-* 


Filippov [a] 


Ba 


2-32 x 10- 1 


700 


4-12 x 10- 3 


2-88 x 10~ 3 


3-35 x 10~ 3 


Prokof jew [68] 


Hg 


448 x 10" 1 


728 


1-73 x 10-* 


1-26 x 10- 2 


1-2 xlO~ 2 


Grarrett [12] 


o 












Wolfsohn [as a] 



7e. HIGHER SERIES MEMBERS OF THE ALKALIS. In working 
with the resonance radiation of the alkali vapours it is some 
times necessary to know the absorption or emission of the next 
doublet in the same series. In all cases the /-value and the 
transition probability of the next doublet are much smaller 
than those of the resonance lines. This is shown in Table XVII. 

TABLE XVII 



Atom 


Atomic 
number 


/ 2 -*i 


A*->i 


Author and reference 


/3^1 


^ 3 -*i 


Li 

Na 
K 
Rb 
Cs 


3 
11 
19 
37 
55 


136-5 
69-5 
111-5 
70-3 
69-0 


314 
21-8 
30-3 
20-3 
19-2 


A. Filippov [7] 
A. Filippov and W. Prokof jew [e] 
W. Prokof jew and G. Gamow [ce] 
I). Roschdestwensky [62] 
R. Minkowski and W. Miihlenbruch [so] 



REFERENCES TO CHAPTER III 

[1] Abraham, H. and Lemoine, J., Compt. fiend. 129, 206 (1899). 
[2] Compton, K. T., Pliys. Rev. 20, 283 (1922). 

[3] Phil. Mag. 45, 752 (1923). 

[4] Dunoyer, L., Le Rod. 10, 400 (1913). 

[5] Duschinsky, F., Z./. Ptys. 78, 586 (1932). 

[6a ] ibid. 81, 7,23(1933). 



152 ABSORPTION LINES AND MEASUREMENTS 

[6] Filippov, A. and Prokofjew, W., Z. f. Phys. 56, 458 (1929). 

[7] Filippov, A., ibid. 69, 526 (1931). 

[8] Sow. Phys. 1, 289 (1932). 

[9] Frayne, J. G., Phys. Rev. 34, 590 (1929). 

[10] Fiichtbauer, C., Phys. Zeits. 21, 322 (1920). 

[11] Fiichtbauer, C., Joos, G. and Dinkelacker, 0., Ann. d. Phys. 71, 204 

(1923). 

[12] Garrett, P. EL, Phys. Rev. 40, 779 (1932). 

[13] Gaviola, E., Ann. d. Phys. 81, 681 (1926). 

[14] Z. f. Phys. 42, 853 ( 1927). 

[15] Goos, F. and Meyer, H., ibid. 35, 803 (1926). 

[16] Gouy, G. L., Ann. Chim. Phys. 18, 5 (1879). 

[17] Compt. Rend. 88, 420 (1879). 

[18] ibid. 154, 1764 (1912). 

[19] de Groot, W., Physica, 9, 263 (1929). 

[20] v. Hamos, L., Z.f. Phys. 74, 379 (1932). 

[21] Hanle, W., ibid. 56, 94 (1929). 

[22] v, d. Held, E. F. M., ibid. 70, 508 (1931). 

[23] v. d. Held, E. F. M. and Ornstein, S.. ibid. 77, 459 (1932). 

[24] Herzfeld and Wolf, Handb. d. Experimentalphysik, 19, 89. 

[25] Hoyt, F. C., Phys. Rev. 36, 860 (1930). 

[26] Hughes, A. L. and Thomas, A. R., ibid. 30, 466 (1927). 

[27] Hupfield, H., Z. f. Phys. 54, 484 (1929). 

[28] Kerschbaum, H., Ann. d. Phys. 79, 465 (1926). 

[29] ibid. 83, 287 (1927). 

[30] Koenig, H. D. and EUett, A., Phys. Rev. 39, 576 (1932). 

[31] Kopfermann, H. and Tietze, W., Z.f. Phys. 56, 604 (1929). 

[32] Kuhn, Vf.,Danske VidenskabernesSelskab (1926) (Zurich, Habilitations- 

schrift). 

[33] Kuoze, P., Ann. d. Phys. 85, 1013 (1928). 

[34] Ladenburg, R. and Senftleben, H., Naturwiss. 1, 914 (1913). 

[35] Ladenburg, R. and Reiche, F., Ann. d. Phys. 42, 181 (1913). 

[36] Ladenburg, R., Verh. d. D. Phys. Ges. 16, 765 (1914). 

[37] Z. f. Phys. 4, 451 (1921). 

[38] Ladenburg, R. and Minkowski, R., ibid. 6, 153 (1921). 

[39] Ladenburg, R., ibid. 48, 15 (1928). 

[40] Ladenburg, R. and Minkowski, R., Ann. d. Phys. 87, 298 (1928). 

[41] Ladenburg, R. and Wolfsohn, G., Z.f. Phys. 63, 616 (1930). 

[42] Ladenburg, R. and Levy, S., ibid. 65, 189 (1930). 

[43] Ladenburg, R. and Wolfsohn, G., ibid. 65, 207 (1930). 

[43a] Ladenburg, R. and Thiele, E., ibid. 72, 697 (1931). 

[44] Larch6, K., ibid. 67, 440 (1931). 

[45] v. Malinowski, A., Ann. d. Phys. 44, 935 (1914), 

[46] Michels, W. C., Phys. Rev. 38, 712 (1931). 

[47] Milne, E. A., Mon. Not. Roy. Ast. Soc. 85, 117 (1924). 

[48] Journ. Lond. Math. Soc. 1, 1 (1926). 

[49] Minkowski, R., Z. f. Phys. 36, 839 (1926). 

[50] Minkowski, R. and Muhlenbruch, W., ibid. 63, 198 (1930). 

[51] Mrozowski, S., Butt. Acad. Pol p. 464 (1930). 



OF THE RESONANCE STATE 153 

[52] Ornstein, S. and v. d. Held, E. F. M., Ann. d. Phys. 85, 953 (1928). 

[53] z. f. Phys. 77, 459 (1932). 

[54] Orthmann, W., Ann. d. Phys. 78, 601 (1925). 

[55] Orthmann, W. and Pringsheim, P., Z.f. Phys. 43, 9 (1927). 

[56] Prokofjew, W. and Gamow, G., ibid. 44, 887 (1927). 

[57] Prokofjew, W. and Solowjew, W., ibid. 48, 276 (1928). 

[58] Prokofjew, W., ibid. 50, 701 (1928). 

[59] Puccianti, L., Handb. d. Experimentalphysik, 19, 74. 

[59a] Rabi, 1. 1. and Cohen, V., Phys. Rev. 43, 582 (1933). 

[60] Reiche, F., Verh. d. D. Phys. Ges. 15, 3 (1913). 

[61] Roschdestwensky, D., Ann. d. Phys. 39, 307 (1912). 

[62] Trans. Opt. Inst. Len. 2, No. 13 (1921). 

[63] Rump, W., Z. f. Phys. 29, 196 (1924). 

[64] Rupp, E., Ann. d. Phys. 80, 528 (1926). 
[64a] Schaffernicht, W., Z. f. Phys. 62, 106 (1930). 

[65] Schein, M., Helv. Phys. Acta, 2, SuppL 1 (1929). 

[66] Schiitz, W., Z.f. Phys. 45, 30 (1927). 

[67] ibid. 64, 682 (1930). 

[68] Z. f. Astrophys. 1, 300 (1930). 

[69] Slack, F. G., Phys. Rev. 28, 1 (1926). 

[70] Soleillet, P., Compt. Rend. 187, 212 (1928). 

[71] ibid. 194, 783 (1932). 

[72] Sugiura, Y., Phil. Mag. 4, 495 (1927). 

[73] Thomas, A. R., Phys. Rev. 35, 1253 (1930). 

[74] Tolman, R. C., ibid. 23, 693 (1924). 

[74a] Trumpy, B., Z. f. Phys. 66, 720 (1930). 

[746] Van Atta, C. M. and Granath, L. P., Phys. Eev. 44, 60 (1933). 

[75] Voigt, W., Munch. Ber. p. 603 (1912). 

[76] Handb. d. Ekkt. u. Mag. von Graetz, 4, 577 (1920). 

[77] Vonwiller, 0., Phys. Rev. 35, 802 (1930). 

[77a] Vinti, J. P., ibid. 42, 632 (1932). 

[78] Webb, H. W., ibid. 24, 113 (1924). 

[79] Webb, H. W. and Messenger, H. A., ibid. 33, 319 (1929). 

[80] Weiler, J., Ann. d. Phys. 1, 361 (1929). 

[81] Weingeroff, M., Z.f. Phys. 67, 679 (1931). 

[82] Weisskopf, V. and Wigner, E., ibid. 63, 54 (1930). 

[83] Weisskopf, V., Phys. Zeits. 34, 1 (1933). 

[83a] Wheeler, J. A., Phys. Rev. 43, 258 (1933). 

[84] Wien, W., Ann. d. Phys. 73, 483 (1924). 

[85] Wolfsohn, G., Z. f. Phys. 63, 634 (1930). 

[ 8 5a] ibid. 83, 234 (1933). 

[86] Zahn, H., Verh. d. D. Phys. Ges. 15, 1203 (1913). 

[87] Zehden, W. and Zemansky, M. W., Z.f. Phys. 72, 442 (1931). 

[88] Zehden, W., Z. f. Phys. 86 (1933). 

[89] Zemansky, M. W., Phys. Rev. 36, 219 (1930). 

[9 0] z. f. Phys. 72, 587 (1931). 



CHAPTER IV 

COLLISION PROCESSES INVOLVING 
EXCITED ATOMS 

1. TYPES OP COLLISION PROCESSES 

On the basis of classical kinetic theory, a molecule was re 
garded as a rigid sphere with a definite radius, and a collision 
between two molecules was defined as an encounter in which 
the two spheres touched. It is of course no longer possible to 
ascribe a definite radius to a molecule or atom, and when two 
such bodies come together and part again, they do so in a 
manner which cannot be described in detail. It is therefore 
necessary to adopt a point of view which is independent of the 
actual shape and dimensions of the molecules, and which at 
the same time is unambiguous. This has been done with admir 
able clearness by Samson [84], and the following treatment will 
follow that of Samson rather closely. 

la. THE ME ANi^a OF "COLLISION". When any molecule 
passes another at any distance and with any relative velocity, 
a "collision" is said to take place. The best description of a 
particular collision is to give the relative velocity before the 
collision V and the perpendicular distance q between the centre 
of the second molecule and the line of the velocity V through 
the centre of the first. We may call this a (F, q) collision. For a 
(F, q) collision there is a probability J>(V 9 q) that a given pro 
cess, say a transition of energy state, may occur on such a 
collision. We know nothing of the function <j> (F, q) except that 
it must become zero for very large q and probably for very 
large F. In the case of an upward transition we know that 
<f>(V,q) is zero until F reaches a value F at which there is 
sufficient relative kinetic energy to produce the transition. 
There is no definite value of q for which (f>(V,q) suddenly be 
comes zero and which could be called the sum of the radii of 
the two bodies. The values of $ (F, q) must also be expected to 
vary differently with F and q for different transition processes. 



COLLISION PROCESSES 155 

16. THE MEANING OF "EFFECTIVE CROSS-SECTION". For 
statistical purposes we resort to an artifice which gives a con 
venient index number with which to describe the statistical 
average over all values of q. We can calculate easily the total 
number of collisions of relative velocity V within a distance Q 
say, denote it by Z (V, Q 2 ) dV and, by equating this to the total 
number of collisions actually known by experiment to produce 
the given process, evaluate Q 2 and call it " the effective velocity 
cross-section for the given process". (The cross-section area is 
really nQ 2 , but it is convenient to drop the TT and refer simply to 
Q 2 as the cross-section.) It will clearly be a function of velocity 
and of the process considered and may have widely different 
values for different processes. It has no relation whatsoever to 
the gas-kinetic cross-section for the pair of molecules. 

Since actual experiments usually do not differentiate be 
tween velocities but are carried on at a known temperature, it 
is convenient to make a similar definition of an " effective 
temperature cross-section for the given process". If Z (T, a 2 ) 
represents the total number of collisions of all velocities 
within the distance o- at temperature T, then 



)= r } Z(V,Q 2 )dV. 
Jo 



The left-hand member of the above equation can easily be 
calculated on the basis of the Maxwellian distribution of 
velocities along the lines of classical kinetic theory, and the 
result is obtained __ 

+ ...... (91), 



where M I9 M% and N, n are the molecular weights and con 
centrations respectively of the colliding molecules, and R is 
the universal gas constant. "The effective cross-section for the 
process A" is therefore calculated as follows: From the results 
of an experiment in which it is known that collision processes 
of type A occur, the number of such collisions per sec. per c.c. 
is calculated. This number is equated to the right-hand 
member of Eq. (91). The resulting value of a 2 is denoted by 
a A 2 and is called the effective cross-section for the process A. 



156 COLLISION PBOCESSES 

Ic. COLLISIONS OF THE SECOND KIND. Klein and Rosse- 
land[37], in 1921, on the basis of thermodynamical reasoning, 
inferred that, if ionizing and exciting collisions take place in an 
assemblage of atoms and electrons, inverse processes must also 
take place, namely, collisions between excited atoms and 
electrons in which the excitation energy is transferred to the 
electrons in the form of kinetic energy. They called such colli 
sions "collisions of the second kind". The term was extended 
by Franck and others to include collisions between excited 
atoms and normal atoms (or molecules) involving a transfer of 
the excitation energy from one to the other. As more and more 
types of collision processes were discovered the conception 
became broader, until now the expression " collision of the 
second kind" includes all collision processes in which the 
following conditions are fulfilled: 

(1) One of the colliding particles is either an excited atom 
(metastable or otherwise) or an ion. 

(2) The other colliding particle is either an electron, a 
normal atom or a normal molecule. 

(3) During the collision either all or a part of the excitation 
of particle (1) is transferred to (2). 

Typical examples of collisions of the second kind are given 
in Table XVIII. Some of these have been discussed in Chap, n, 
and the others will be considered throughout this chapter. 

Id. PERTURBING COLLISIONS. There are types of collisions 
involving excited atoms in which either no energy or an ex 
tremely small amount of energy is transferred. Such collisions 
involve a perturbation of the excited atom so that its radiation 
or absorption characteristics are altered in some way. If the 
breadth of an absorption line of a gas is measured at high pres 
sure or in the presence of a foreign gas, it is found to be greater 
than usual, indicating the existence of collisions which alter 
the absorbing characteristics of an atom. Such collisions can 
be called broadening collisions. If the percentage polarization 
of the resonance radiation emitted by a gas is measured in the 
presence of a foreign gas, it is found to be smaller than usual, 
indicating the existence of collisions which alter the position 



INVOLVING EXCITED ATOMS 



157 



of the electric vector of the light emitted by an excited atom. 
Such collisions are called depolarizing collisions and will be 
treated in Chap. v. 



TABLE XVHI 



Particle 
No. (1) 


Example of collision 
of second kind 


Methods by which such 
collisions are studied 




Cs( 2 P)+e 

= 08(6^ + 6 


Optical and electrical 
measurements on the 
positive column of a 
gas discharge 




^JS^+H+H 


Quenching of resonance 
radiation. Reduction 






of H 2 pressure as oxide 
is reduced by H atoms 




Hg(6 3 Pi)+Na 


Sensitized fluorescence 


Atom in an 
excited state 
from which 
it can emit 


=Hg(6%)+Na(10*S 1/2 ) 
g =Hg(6*P )+(N,r 


Quenching of resonance 
radiation. Rapidity 
of escape of resonance 
radiation 


resonance ra 
diation 


Na(3*P 8/2 )+A 
=Na(3 2 P 1/2 )+A 


Radiation of D a line 
when excited by D 2 in 
the presence of Argon 




Cs(m 2 P)+Cs 
=(CsCs)+ + e 


Photo-ionization of va 
pour by means of 
6 ^pm 2 P at various 
pressures 




Tl(7 2 S 1/2 )+I 2 


Quenching of Tl line 
5351 when excited Tl 






atoms are produced by 
photo-dissociation of 
Til 


Metastable 
atom 


Hg(6*P ) + H 2 
=(EgE)' + H 

=Hg(6P 1 ) 2 +N 2 


Bands in fluorescence 

Rapidity of escape of 
resonance radiation 


Ion 


=(Cu+)'+Ne 
He++N 2 


Enhancement of spark 
lines in gas discharge 
Absorption of canal 




=Ke + N 2 + 


rays 



Note. A dash means an unspecified excited state. A chemical symbol 
unaccompanied by any other designation refers to the normal state. 



158 COLLISION PROCESSES 

2. CLASSICAL THEORY OF LORENTZ BROADENING 
OF AN ABSORPTION LINE 

2 a. THE PHENOMENON OF LORENTZ BROADENING. The 
interpretation of the broadening of spectral lines as due to 
collisions goes back to Rayleigh and Helmholtz. The first ex 
perimental evidence of the pressure broadening of spectral 
lines was obtained by Michelson[58], who showed that emission 
lines were broadened by an increase of pressure and who 
worked out an expression for the frequency distribution of the 
emitted radiation. Schonrock[85] extended Michelson's theory 
of emission lines and obtained an expression for the half- 
breadth of an emission line in terms of the mean free path and 
the temperature. In view of the complicated conditions that 
are present in a source of light such as an arc or spark discharge, 
no simple expression for the frequency distribution or half- 
breadth of an emission line can hope to take into account all the 
broadening factors. It is therefore much more fruitful to con 
sider the broadening of an absorption line, since the conditions 
inside of an absorption tube can be made relatively simple. 

Lorentz [51] was the first to formulate a simple theory of the 
pressure broadening of absorption lines, and was able to 
calculate both the half-breadth and the frequency distribution 
of an absorption line that was broadened by collisions either 
with other absorbing atoms or with foreign gas molecules. 
Since the time of Lorentz many experiments have been per 
formed on the broadening of an absorption linebyforeigngases, 
and most of these experiments, notably those of Piichtbauer 
and his co-workers, show the following characteristics as the 
foreign gas pressure is increased: 

(1) The absorption line is broadened. 

(2) The maximum of the absorption line is shifted. 

(3) The absorption line becomes asymmetrical. 
These three phenomena are illustrated in Fig. 30. 

The simple theory of Lorentz is capable of giving an inter 
pretation, on the basis of classical theory, of only the first of 
these effects. Both the shift and the asymmetry are apparently 
outside the realm of classical theory and require for their 



INVOLVING EXCITEB ATOMS 



159 



explanation the introduction of quantum ideas. The quantum 
theory of Lorentz broadening along with quantum explana 
tions of shift and asymmetry will be touched upon later. For 
an approximate interpretation of existing experimental data 
the simple Lorentz theory which will be given in the next 
paragraph will be found to be helpful. 



"Without foreign gas 




With foreign gas 



Fig. 30. Lorentz broadening of an absorption line, showing 
broadening, shift and asymmetry. (Exaggerated.) 

2b. THE SIMPLE LORENTZ THEORY. The effect of collisions 
upon the absorbing and emitting characteristics of a classical 
" oscillator-atom" was treated by Lorentz in a manner analo 
gous to that of radiation damping. If an absorbing atom per 
forms Z collisions per second, with the molecules of a foreign 
gas, the resulting effect is equivalent to Z interruptions per 
second in an undamped wave train. The expression for the 



160 COLLISION PROCESSES 

absorption coefficient of a gas under these conditions was found 
by Lorentz to be of the same form as that when natural 
broadening is present, namely 

7, const - (92) 





where Av L is called the Lorentz half-breadth and is given by 
1 /number of broadening collisions per\ 

/\v I I 

L TT \ second per absorbing atom / 
= ^ (93). 

7T 

It is quite apparent that Eq. (92) is a symmetrical curve with a 
maximum at v V Q , and therefore it would seem incapable of 
handling an experiment in which shift and asymmetry are 
present. When, however, a broadened absorption line is 
spectroscopically resolved, both the shift and the asymmetry 
can be corrected for, so that the Lorentz half-breadth may be 
obtained, and from it the number of broadening collisions. In 
other experiments where the line is not resolved, the effect of 
the shift can be eliminated entirely, leaving asymmetry as the 
only error. Eq. (92) therefore is by no means useless, but can 
be used in conjunction with some experiments to yield an 
approximate value for kv L . 

2c. COMBINATION OF LORENTZ, NATURAL AND DOPPLER 
BROADENING. An approximate expression for the absorption 
coefficient of a gas under conditions in which Lorentz, natural, 
and Doppler broadening are present can be obtained by a 
method due to Reiche[8i], in which the interdependence of 
Doppler and Lorentz broadening is ignored, i.e. as if the colli 
sions performed by one absorbing atom with the foreign gas 
molecules did not take place irregularly, but with a certain 
constant time interval equal to l/Z L . With this simplification 
Lorentz broadening can be combined with Doppler broadening 
in exactly the same way that natural broadening was com- 



INVOLVING EXCITED ATOMS 161 

bined with Doppler broadening. The resulting absorption 
coefficient is given by 



r 2 ~|2 

exp- -r Vln2 
* LA^ J 

]2 



where & is the maximum absorption coefficient when only 
Doppler broadening is present, Av^ is the natural half-breadth 
of the line and Av D is the Doppler breadth. It has been men 
tioned before that Voigt [99] calculated on the basis of classical 
theory the absorption coefficient of a gas under conditions in 
which Doppler broadening, natural damping and any other 
damping process were present. This theory is capable of yield 
ing a more accurate expression than Eq. (94), because Lorentz 
broadening can be introduced as a damping term which is not 
constant, but is instead a function of the velocity of the 
absorbing atom. When this is done, an integral is obtained 
which is much more complicated than Eq. (94). It was pointed 
out by Reiche, in a private communication, that Voigt's in 
tegral represents a symmetrical function of v with a maximum 
at i/Q, and therefore, since it does not account for the shift and 
asymmetry, its slight advantage over Eq. (94) hardly warrants* 
its use, in view of the added mathematical difficulties. 

In dealing with the pressure broadening of infra-red absorp 
tion lines, Dennison [13] derived a formula which is substantially 
the same as Voigt's general formula, but which, for purposes of 
calculation, had to be replaced by two simple Lorentz expres 
sions: one for the centre of the line and one for the edges. It is 
doubtful whether Dennison's final formulas are very much 
more accurate than Eq. (94), in that they also do not take into 
account the asymmetry and shift that are present. For a 
simple derivation of Eq. (94) on the basis of classical theory the 
reader is referred to a recent paper by Weisskopf [104], Intro 
ducing the quantities 

...... 05) 



and a' = 2 ...... (96), 



( 97 )- 



162 COLLISION PROCESSES 

and letting y = -r Vln 2, 

^y ' /*00 /) J/* (J1J 

Eq. (94) becomes k v =^k Q ~- , 2 / -r- 2 

^ v y " 77- J _oo a +(^ 2/) 

The above equation will be recognized to be of the same 
form as that representing the absorption coefficient when 
natural and Doppler broadening only are present (see Chap, 
in, 2a). There is, however, an important distinction. The 
quantity a' cannot, in this case, be treated as a small quantity ; 
for, due to the presence of Av^ , it may be made as large as we 
please by increasing the foreign gas pressure. The integral, 
therefore, in Eq. (97) cannot be expressed in a simple form, but 
must be evaluated by series or by numerical integration. 
A table of values of k v jk Q for several values of a! and o> will be 
found in the Appendix. In Fig. 31, Eq. (97) is plotted as a 
function of co for four different values of a'. 

3. EXPERIMENTS ON LORENTZ BROADENING 

3 a. PHOTOGRAPHIC MEASUBEMENTS. A most extensive 
investigation of Lorentz broadening was made by Fiichtbauer, 
Joos and Dinkelacker [22] on the mercury resonance line -2537. 
A beam of light from a source emitting a continuous spectrum 
was sent through an absorption tube containing a mixture of 
mercury vapour at room temperature and a foreign gas. The 
light was then focused on the slit of a spectrograph, and photo 
graphs were taken of the 2537 line in absorption, while the 
mercury vapour pressure remained constant and the foreign 
gas pressure was increased from 10 to 50 atmospheres. So 
much broadening was produced at these "high foreign gas 
pressures that the absorption line was easily resolved by the 
slit of the spectrograph. Under these conditions also, the 
quantity a! in Eq. (97) is so large that the absorption coefficient 
reduces to the simple Lorentz form 

const. 



The experimental curves of absorption coefficient against 



INVOLVING EXCITED ATOMS 163 

frequency, obtained by taking photometer measurements of 
the plates, showed the shift and asymmetry already men 
tioned. The half-breadth of the shifted curve was taken to be 
the Lorentz half -breadth. In this way Av^ was measured with 



-9 -8 -7 -6 -5 -4 -3 -2 - 




Curved, a0 
Curve B, a=0-5 
C-urveC, a- 1-0 
Curve A a= 2-0 



56789 



Fig. 31. Simple Lorentz broadening of a Doppler line. 

various foreign gases at various pressures, and it was found 
that the graph of Av x against p (the foreign gas pressure) was 
a straight line with a different slope for each foreign gas. A few 
of these curves are shown in Fig. 32. The results will be inter 
preted in the light of effective cross-sections later on in this 
chapter. 



164 



COLLISION PROCESSES 



36, MEASUREMENTS INVOLVING MAGNETO-ROTATION. The 
conditions under which Schiitz [87] studied the Lorentz broad 
ening of the sodium resonance lines were the same as those 
described in Chap, m, 56. An absorption tube containing 
sodium vapour and a foreign gas was placed in a longitudinal 






A 



10 20 30 40 50 

Relative density of foreign gas in atmospheres 



60 



Fig. 32. Fiichtbauer, Joos and Dinkelacker's experiments on 
Lorentz broadening of the mercury resonance line. 

magnetic field and between a polarizing and an analysing 
Nicol. A beam of light from a source emitting a continuous 
spectrum was sent through the tube and focused on the slit of 
a spectroscope-photometer arrangement. With zero magnetic 
field and crossed Mcols, no light entered the photometer; but 
with the Nicolskept crossed and the magnetic field established, 
magneto-rotation at the edges of the absorption line caused 



INVOLVING EXCITED ATOMS 165 

light to enter the photometer. It has already been shown that 
the amount of light of a particular frequency passing through 
the analysing Nicol depends upon the absorption coefficient for 
that frequency, the strength of the magnetic field, and certain 
atomic constants dealing with the Zeeman effect. The sodium 
vapour pressure was high enough to absorb completely the 
centre of the line, and the foreign gas pressure was kept very 
low so that a! was kept small. Under these conditions, Eq. (97) 
reduces to 



(98), 



which, when expressed in classical notation, and introduced 
into the equations of Chap, in, 56, leaves them completely 
unaltered in form. Only the quantity v is changed, being now 
the sum of natural and Lorentz damping. Sinc, the final 
equation is a relation between the intensity of light entering 
the photometer and v ', the method of Schiitz allows v to be 
obtained at any foreign gas pressure. The results of Schutz's 
experiments were expressed in the form of a graph between 
v'/V and the foreign gas pressure, where v ' represents the 
natural damping. Some of these curves are shown in Fig. 33, 
and they are seen to be straight lines. Their interpretation will 
be given later. 

3c. EXPERIMENTS ON THE ABSORPTION OF RESONANCE 
RADIATION. It will be remembered that the absorption of a 
beam of resonance radiation in traversing a gas depends upon 
the form (frequency distribution) of the emission and absorp 
tion lines. Orthmann[76] was the first to study the Lorentz 
broadening of the mercury resonance line by measuring the 
absorption of a beam of mercury resonance radiation by a mix 
ture of mercury vapour and hydrogen. Neumann [71] extended 
Orthmann's measurements, using argon, air, helium and 
hydrogen. In later years Kunze[42] and Zemansky [iu] per 
formed the same experiment under conditions which allowed 
the Lorentz half -breadth to be calculated with fair accuracy. 
The theory of the method is very simple. Assuming the mer 
cury resonance line to consist of five equal, completely separate, 



166 



COLLISION PROCESSES 



hyperfine structure components ; and representing the emission 
line from the resonance lamp by the expression E v , and the 
absorption coefficient of the mixture of mercury vapour and 




10 15 20 

Foreign gas pressure in mm. 



25 



30 



Fig. 33. Schiitz's experiments on Lorentz broadening of 
sodium resonance line. 

foreign gas, by Jc v , the absorption A is given by (see Chap, m, 
46) 



(99). 



r 

J o 



In the experiments of Kunze, the foreign gas was admitted 
to the resonance lamp at exactly the same pressure as in the 
absorption cell, thereby eliminating any error due to the 
shift of the absorption line relative to the emission line. 
This necessitated the use of inert gases only, since a gas like 



INVOLVING EXCITED ATOMS 167 

hydrogen or oxygen, if admitted to a resonance lamp, would 
quench the resonance radiation to such a low intensity that it 
could not be measured. Since the resonance lamp employed 
by Kunze satis fied fairly well the conditions laid down in 
Chap, in, 3 a for an ideal resonance lamp, and since the thick 
ness of the emitting layer of the resonance lamp was nearly 
equal to the thickness of the absorption cell, the expression for 
E v becomes [see Eq. (50)] 

E v = const. (1-e-V) (100), 

and A can be written 



J 
/" 



; J^ (101) - 

(1 e *<> )dv 



The conditions of temperature and mercury vapour pressure 
in Kunze's experiment were such that k Q l was 0475. Sub 
stituting this value for Jc l in the above formula, and replacing 
k v /k by the expression given by Eq. (97), a result is obtained 
which can be integrated graphically with the aid of the table 
in the Appendix. (The graphical integration is to be done for 
all five hyperfine structure components.) The result is a 
different value of A for all the different values of a' . Since a! 
contains the ratio Ai/^/Avp, the theoretical curve of A against 
a! can be used to give the value of Av^/Av^ corresponding to 
any experimentally measured value of A at any foreign gas 
pressure. It is to be expected, of course, that the neglect of the 
accurate hyperfine structure of the line and its asymmetry in 
broadening will produce a small error in the final value of A V L . 
In this way, the ratio AvJAv^ was obtained for the three inert 
gases as a function of the gas pressure. A graph of the results is 
shown in Fig. 34. 

In Zemansky's experiments, many gases were used which 
could not be introduced into the resonance lamp because of 
their strong quenching ability, and consequently the emission 
line remained fixed while the absorption line was shifted and 
broadened by the foreign gases. It will be seen later, however, 
that the results agree quite well with those of Fiichtbauer, Joos 



168 



COLLISION PROCESSES 



I 

0-8 
0-6 
0-4 
0-2 



Av, 




c 
I 

2-0 
1-5 
1-0 
0-5 


X^ \ \ i i i i 


) 20 40 60 80 100 120 
Foreign gas pressure in mm. 
Hg. 34. KLunze's experiments on Lorentz broadening of 
mercury resonance line. 


Av L 








Hy , 




Av D 








/ 




A 






/ 


/ 


> 


x 






/ 


s* 


^ 


-He 




/ 




^ 


^ 




, 


& 


^ 













tOO 



50 

Pressure (mm.) 

Fig. 35. Zemansky's experiments on Lorentz broadening of 
mercury resonance line. 



150 



INVOLVING EXCITED ATOMS 169 

and Dinkelacker and with those of Kunze. To obtain a theo 
retical curve between A and a' to be used with Zemansky's 
experimental results, the emission line was represented by the 
expression [see Eq. (60)] 

_f^L\ 2 
E = const. 6 ViW (102), 




Line-F.J.andD. 
o Kunze 
B -Zemansky 



_L 



J_ 



20 



100 120 



40 60 80 
Argon pressure in mm. 
Fig. 36. Lorentz broadening of mercury resonance line by argon. 

and the absorption became 



/CO 

J -o 



(103). 



da) 



In his experiments, k Q l was 4-44 and, upon introducing Eq. (97) 
for JcJk Q and integrating graphically, A was calculated as a 
function of a!. The results for a few foreign gases are shown in 
Fig. 35; and in Fig. 36, a comparison of the results of Fiicht- 



170 COLLISION PROCESSES 

bauer, Joos and Dinkelacker, Kunze, and Zemansky is shown 
for the case of argon. 

3d. EVALUATION OF EFFECTIVE CROSS-SECTIONS FOR 
LORENTZ BROADENING. It is seen from Figs. 33, 34, 35 and 36, 
that all experiments on Lorentz broadening provide linear 
relations between the Lorentz half -breadth and the foreign gas 
pressure. This is in agreement with the Lorentz formula for 
AI/J given by Eqs. (93) and (91), namely 



where o-^ 2 is the effective cross-section for Lorentz broadening 
and N is the number of foreign gas molecules per c.c. If p is the 

9740 
foreign gas pressure in mm., then N = =- .p x 10 15 , and 

Eq. (104) becomes 



which shows how the effective cross-section o-^ 2 may be ob 
tained from the slope of any curve in Figs. 33 to 36. 

Table XIX contains all the values of a L 2 obtained in this way. 

3e. LORENTZ BROADENING IN A SODIUM FLAME. The 
increase in intensity of a sodium flame, as the thickness of the 
flame or the sodium concentration, or both, were increased, was 
first measured by Gouy[25] in 1879. Since then, similar ex 
periments have been made by Senftleben [90], Wilson [106], 
Locher[48], Child [ii] and Bonner[iO], who, with the exception 
of Child, showed that the intensity of the light emitted by the 
flame was a function of the product of flame thickness and the 
concentration of the sodium salt that is sprayed into the flame. 

When the partial pressure of the sodium vapour in the flame 
is small, the flame can be treated in exactly the same manner as 
the emitting layer of an ideal resonance lamp (see Chap, in, 
3 a). If /! denotes the intensity of light (comprised entirely of 
the D lines) emitted by a flame of thickness Z, then we have 

/! = const. J(l-e-V)dv (106), 



INVOLVING EXCITED ATOMS 



171 



where k v depends on the amount of sodium vapour present, and 
the absorption line form, which is obviously determined by 
natural and Lorentz damping and the Doppler effect. (Hyper- 
fine structure is practically wiped out by Lorentz broadening.) 
A convenient way of representing the experimental results is 
to plot the ratio of the intensity from a flame of thickness 

TABLE XIX 







a,, 2 x 10 16 












Fucht- 








Absorb 
ing gas 


Foreign 
gas 


bauer, 
Joos and 


of x 10 16 
Zemansky 


a L * x 10 16 
Kunze 


a L x 10 16 
Schiitz 






Dinke- 












lacker 








Hg 


He 





15-0 


21-4 







H 2 


27-8 


24-5 










Ne 





* 


35-7 







CO 





44-5 










N 2 


64-8 


51-0 










2 


65-1 











, 


CH 4 





42-8 








9 


H 2 


68-5 













A 


88-9 


61-5 


62-0 







C0 2 


125 













NH 3 





71-2 











C 3 H 8 





73-5 








Na 


He 








' 


31-4 




Ne 











37-8 




H 2 











33-6 


" 


^2 










68-9 





A' 











81-0 



21 (/ 2 ) to that from a flame of thickness I (IJ against I I . This 
ratio can be written 



(107), 



')dv 



and can be evaluated for various values of k Q l (and therefore 
of I x ) once kJk Q is known as a function of v. In Fig. 37 are 
shown the experimental results of Gouy and Bonner, with the 
ratio /a//! plotted against I. The abscissa scales are chosen 
to make the two sets of results coincide with each other as much 



172 COLLISION PROCESSES 

as possible. It is quite clear that 7 2 / 7 X first attains a minimum 
value of about 1-35 and then rises slowly. 

Schiitz [88] was the first to obtain a curve of this shape theo 
retically. He introduced into Eq. (107) an expression for Jc v /k Q 



2-0 
1-9 
1-8 
1-7 



x o 

l'6h 



1-5 

1-4 
1-3 
1-2 



1-0 



OBonner 
X Gouy 



XD 
X 






_x__._ x ___VT 



x x 



-I 1 1 1 1 1 I L 



20 40 60 80 100 120 140 160 180 
Z x in arbitrary units 

Fig. 37. Experiments of Gouy and Bonner on the emission of sodium flames. 

equivalent to our Eq. (97), representing the absorption coeffi 
cient when natural and Lorentz damping and Doppler effect 
are present. With a! equal to any arbitrarily chosen value, 
Schiitz was able to show that 1^1^ first attained a minimum 
and then rose slowly to the value V 2 - He estimated that, to 
agree with Gouy and Senftleben's results, a! would have to be 



INVOLVING EXCITED ATOMS 173 

about 0-5. From this we can estimate the effective cross- 
section associated with sodium and air. 



Since 



0-35- 




4 O20- 



10 20 30 40 50 

Relative density of foreign gas in atmospheres 

Fig. 38. Fiichtbauer, Joos and Dinkelacker's measurements of the 
shift of the mercury resonance line. 

then, since Av^/Avp is very small, Av i /A^ = 0-6. Replacing 
Av^ by Z L lT and Z L by its gas kinetic expression, and calculat 
ing Av^ , o^ 2 is found to be roughly 15 x 10" 16 cm. 2 , which is 
considerably smaller than Schiitz's value for nitrogen alone. 
A more recent measurement of a' was made by van der Held 



174 



COLLISION PROCESSES 



and Ornstein[28] for a sodium flame. The resulting value of 
a', 0-53, is in good agreement with that calculated by Schiitz. 

3/. THE SHIFT OF THE ABSORPTION LINE. The most com 
plete experiments on the shift of a Lorentz-broadened absorp 
tion line were made by Fiichtbauer, Joos and Dinkelacker[22] 
on the mercury resonance line. The shift was found to be 
always toward the red, and, from Fig. 38, it is seen that the 
shift is proportional to the foreign gas pressure. It is apparent 
also that, in a rough way, those foreign gases which produce 
large broadening also produce large shifts. 



i-Or 




Fig. 39. Graphical method of indicating asymmetry. 

3g. THE ASYMMETRY IN BROADENING. The most extensive 
study of the asymmetry in the frequency distribution of a 
Lorentz-broadened absorption line was made by Minkowski [61] 
on the sodium D lines. If Fig. 39 represents an asymmetrically 
broadened absorption line, with ordinates equal to the ratio of 
the transmitted to the incident light, then the curved line 
marked C is drawn by dividing the ordinate axis into a number 
of parts and indicating at each level the centre of the line. In 
this way the asymmetry of a sodium resonance line broadened 
by a number of gases is indicated in Fig. 40. It is seen that, with 
H 2 and He, the asymmetry is toward the violet, and with all 
the other gases the asymmetry is toward the red. It is also 
apparent that, in a rough way, those gases which produce the 
most asymmetry are also those which broaden the most. These 



INVOLVING EXCITED ATOMS 175 

results were explained by Minkowski in a qualitative way by 
assuming that there is an interchange of kinetic energy and 
excitation energy during collision, whereby an atom, capable 
of absorbing the frequency v , can absorb a frequency smaller 
than VQ plus a small amount of the kinetic energy of the colli 
sion. Or vice versa: an atom, capable of absorbing the fre 
quency v Q , can absorb a frequency larger than i> and at the 
same time give up the remainder to the kinetic energy of the 
collision. These ideas are in agreement with similar ideas 
advanced by Oldenberg[74j to explain the appearance of bands 
that were emitted by a mixture of mercury vapour and some 

I -O r 




0-1 0-1 0-2 

Fig. 40. Minkowski's measurements of the asymmetry of the 
sodium resonance line. 

of the inert gases. They are also contained implicitly in the 
general theory of Lorentz broadening developed by Weisskopf 
and extended by Lenz, which will be discussed in the next 
section. 

4. QUANTUM THEORY OF LORENTZ BROADENING 
4 a. PKELIMINABY THEORIES. The first attempt at a quan 
tum theory of Lorentz broadening was made by Jablonski pi], 
He considered a collision between an absorbing atom and a 
foreign gas molecule as a temporary formation of a quasi- 
molecule. In Fig. 41 are shown the Franck-Condon curves of 
the two states of this molecule, the first state corresponding 
to the molecule : normal absorbing atom A plus foreign gas 



176 



COLLISION PROCESSES 



molecule F, and the second state corresponding to the mole 
cule : excited absorbing atom A r plus foreign gas molecule F. 
The difference between the two Franck- Condon curves deter 
mines the frequency absorbed (or emitted) as a function of the 
separation r. Jablonski's ideas were only qualitative and were 
not capable of yielding an expression for the frequency dis 
tribution of the absorption line, or for the half -breadth. 

The next important step in the development of an accurate 
theory of Lorentz broadening was made by Margenau [53, 54] in 



V(T) 




K'M 



Nuclear separation r 



J?ig. 41. Franck-Condon curves referring to collision broadening. 

America and at about the same time by Kulp [41] in Germany. 
These authors extended the ideas of Jablonski, and, applying 
the statistical theory of density fluctuations, were able to 
calculate the shift of an absorption line in terms of the pressure 
of the foreign gas and of atomic constants. The shift was shown 
to be proportional to the pressure, in agreement with experi 
ment. London's theory of van der Waals' forces was used by 
both authors, which is tantamount to considering only the 
right-hand portions of the Franck-Condon curves (at large 
values of r) where the mutual potential energy of the quasi - 
molecule is due to polarization, or V (r) - V (r) = O~ 6 . 



INVOLVING EXCITED ATOMS 177 

46. WEISSKOPF'S THEORY. The first really successful theory 
of Lorentz broadening was developed by Weisskopf [105], who 
showed the quantum-mechanical principles involved, and gave 
the mathematical tools (which, by the way, are identical with 
those used in classical electron theory) for calculating the 
frequency distribution of the broadened line. According to 
Weisskopf, Lorentz broadening is regarded as a conversion of 
translational energy into light energy and vice versa, accord 
ing to the ideas of Minkowski[6i] and Oldenberg[74j. Wave 
mechanically, it is analogous to the electron- vibration bands 
of a diatomic molecule in which the energy of motion of the 
nuclei can be either added to or subtracted from the electron 
terms. In the case of the diatomic molecule, the spectrum 
is discrete, because of the regular character of the nuclear 
motions. In the case of Lorentz broadening, however, the two 
sides of the broadened line represent continuous spectra due to 
the irregularity of the motions involved. The process of Lorentz 
broadening is to be considered as the quantum analogue of a 
change in the frequency of vibration of an oscillator atom 
caused by the approach of a perturbing foreign gas atom, so 
that the phases of the normal vibration before and after the 
collision no longer agree. This idea was first put forward by 
Lenz [46], If we imagine the absorbing atom stationary, and 
the perturbing atom flying past along a line which is at a dis 
tance r from the absorbing atom, then the phase change will 
depend upon r. The distance of closest approach, />, was 
defined by .Weisskopf as that value of r for which the phase 
change is 1. Replacing the whole Franck- Condon curves by 
their right-hand portions, and using London's expression for 
the potential energy due to polarization, 

V'(r)-V(r)=-Cr+ ...... (108), 

p was found to be approximately 



where c is the relative velocity of the colliding partners. 

London has given a rigorous expression for (7, but it is more 
convenient to calculate the maximum and minimum possible 



178 



COLLISION PROCESSES 



values of C for purposes of comparison with experiment. From 
London's formula 



(HO), 



^mln. ~< 



and a' = - 

7 

where a^ is the polarizability of excited atom A, 

oc 2 is the polarizability of normal foreign molecule 
/ is the /-value of the line in question, 



= mean excitation energy of F, 
' = energy difference between excited state of atom A 

and the next highest combining state, 
" = energy difference between excited state of atom A 
and ionization. 

The upper and lower limits of C can be calculated from data 
in Table XX. 

TABLE XX 



Atom or 
molecule 


Polarizability 
a x 10 24 


Smallest 
excitation 
energy in volts 


Ionization 
energy in 
volts 


He 


0-20 


19-8 


24-6 


A 


1-63 


11-5 


15-6 


Ne 


0-39 


16-5 


21-5 


N 2 


1-74 


6-5 


17 


2 


1-57 


8 


13 


C0 2 


2-7 





14-3 


CO 


1-9 


6-4 


10 


Na(3 2 P) 


96 


2-1 


5-1 


Hg(63F 1 ) 


20 


4-7 


10-4 



A comparison of values of p calculated by means of Weiss- 
kopf J s formulas, and experimental values of a L , are given in 
Tables XXI and XXII, which have been taken from Weiss- 
kopf } s report in the Physikalische ZeitscJirifttiosi. 

Two facts are immediately evident from the tables. First, 
there is a fair agreement between the theoretical values of p 
and the experimental measurements of a L . Second, there is no 



INVOLVING EXCITED ATOMS 



179 



clear-cut relation between the ability of a foreign gas molecule 
to broaden a line and to take energy from the excited atom, 
because <J L and a Q (a Q refers to quenching of resonance radia 
tion) are quite different. To the agreement between p and & L 
very little importance can be attached. <J L was obtained from 
either direct or indirect measurements of the Lorentz half- 

TABLE XXT 
BROADENING or MERCURY RESONANCE LINE 



Foreign 


Fiichtbauer, 
Joos and 
Dinke- 


i 
Zemansky 


Kunze 


Theo 
retical 


Theo 
retical 


Quenching 


molecule 


lacker 


L 


L 


max. 
pxlO* 


min. 
pxlO* 


fi x 


Hj 


5-27 


4-95 


, 








2-94 


He 





3-88 


4-63 


5-0 


3-2 





A 


9-44 


7-85 


7-88 


8-3 


5-4 





Ne 








5-98 


6-7 


4-4 





N 2 


8-05 


7-15 





7-9 


5-1 


0-524 


2 


8-07 














4-46 


C0 2 


11-2 








9-1 


6-0 


1-88 


CO 





6-68 










2-42 



TABLE XXH 

BROADENING OF SODIUM RESONANCE LINE 



Foreign 
gas 
molecule 


Schiitz 
a^xlO 8 


Minkowski 
a^xlO 8 


Theoretical 
max. p x 10 s 


Theoretical 
min.px 10 s 


Quenching 
a^xlO 8 


H, 


5-8 











2-52 


He 


5-6 





6-3 


4-8 





A 


9-0 


7-9 


10-0 


7-6 





Ne 


6-15 





7-9 


6-0 





N 2 


8-3 


7.7 








3-09 



breadth through the agency of a specific relation connecting 
<J L and the half-breadth. In Weisskopf J s theory, however, no 
expression was obtained for the half-breadth, and therefore it 
is not clear what quantity should be compared with p* 

4c. LEKZ'S THEORY. This point was finally cleared up by 
Lenz [47] in a very important paper which carries the theory of 
Lorentz broadening to a point much farther than it was brought 
by Weisskopf. On the basis of a more general expression for 



180 COLLISION PROCESSES 

the mutual potential energy of the quasi-molecule formed by 
the colliding partners, namely 

F'(r)-F(r)=-ar* (113), 

Lenz was able to obtain an analytic expression for the fre 
quency distribution of a line which contained all three known 
phenomena broadening, asymmetry and shift; and also ex 
pressions for the half-breadth and shift in terms of atomic con 
stants and a distance /> defined as the distance of closest 
approach. The distance of closest approach, p , is defined as 
the distance from an absorbing atom to the line representing 
the relative velocity of the absorbing and perturbing atoms, 
at which a phase change of 2?r occurs. Calling the relative 
velocity c , this distance is found to be 



from which p Q can be calculated once the constants a and p are 
known. It should be remarked that Lena's definition of p Q 
differs from Weisskopf 3 s definition of p to the extent that 

/> = 1-5 (ar^.p ......(115). 

Instead of assuming p = 6 and attempting to determine the 
value of a in order to compute /> , Lenz determined ^ from ex 
perimental measurements of shift and half-breadth, and p 
from measurements of half-breadth, in the following way. The 
shift of the line, in sec." 1 , was shown to be 



and the half-breadth, also in sec." 1 , to be 



sm- 



wherenis the number of perturbing (foreigngas) atoms per c.c., 



INVOLVING EXCITED ATOMS 



181 



c is the relative velocity of the absorbing and perturbing 
atoms, and the quantity K\L has the values 0-57, 0-49, 0-44 when 
p = 6, 8, 10 respectively. The above formulae hold only when 
the absorbing atom is very much heavier than the perturbing 
atom, which is approximately satisfied in the case of the 
broadening of the mercury line. Dividing Av s by A^ , the very 
interesting result is obtained that 



Av 



7T 



=-Jtaja 

i 2*- 1 



(118), 



which provides a method of determining p from experimental 
values of Av s and Av z . In Table XXIII the values of Ai^/Ai^ 
obtained by Fiichtbauer, Joos and Dinkelacker for the broad 
ening of the mercury resonance line by several foreign gases 
are given along with the values of p calculated therefrom. 
Recent values obtained by Margenau and Watson [54 a] for the 
sodium D lines are also included. 

TABLE 











p in A. 




Absorbing 
atom 


Foreign 
gas 


Av* 
to> L 


P 


from. 
Eq. (117) 
and ex 


/> in A. 
from Eq. (115) 
Theoretical 










periment 




Hg 


A 


0-39 


5-8 


14-4 


Between 11-7 












and 18 





H, 


0-16 


11 


8-3 





JJ 


N 2 


045 


5-3 


12 





9> 


C0 2 


0-244 


8 


18 





>t 


HaO 


0-22 


8-6 


13 





Na 


N 2 


0-44 


5-3 








SJ 


A 


0-34 


6-4 





Between 16-5 












and 21-6 





H 2 


0-23 


8-3 









With the aid of the known values of p and of the experi 
mental measurements of Ai^ , /> can now be obtained from 
Eq. (117). These are listed in the fifth column of Table XXIII, 
and are seen to be larger than the values of V L obtained with 
the aid of the old Lorentz theory. It is interesting to note that 
argon, for which p = 5-8, is the only gas to which the London 
theory (p = 6) can be applied. It is therefore worth while to 



182 COLLISION PROCESSES 

compute the /? for argon from Weisskopf 's value of p and to 
compare the resulting theoretical value with the value ob 
tained from Avj . Since Weisskopf 's value of p lies between 5-4 

i 

and 8- 3 A., and Lenz's /> is l-50(27r)^- 1 times as large, the 
theoretical value of p comes out between 11*7 and 18 A. in 
agreement with the value 14-4. 

The frequency distribution of the Lorentz-broadened line 
was found by Lenz to be 



where e = 0-31-0-01 1>, a> = 

and T = P O /CQ . This formula represents a curve whose maximum 

is shifted by the amount Aco - Ao> H 2 .r . The second factor, 

8 

however, is small in comparison with the first, and may be 
neglected when the foreign gas pressure is not too high. The 
experiments of Fiichtbauer, Joos and Dinkelacker justify this, 
since the shift was found to be proportional to the foreign gas 
pressure. The quantity Aco^ represents the half-breadth of the 
line. The formula must not be expected to hold at very great 
distances from the centre of the line. 

As a last result, Lenz calculated the asymmetry of the line, 
by using, as a measure, the difference between the intensities 
at equal distances on both sides of the line, divided by the 
sum. He found 

j* ~ j~_ = tanh {g K + Aco - co) T O } (120) 

to be independent of the pressure of the foreign gas and to hold 
only near the centre of the line and for small foreign gas pres 
sures (less than one atmosphere). Unfortunately, there are no 
experiments at hand with which to compare the above expres 
sion with any degree of accuracy. 

It is remarkable that Lenz was able to obtain so many useful 
results on the basis of the simple law of interaction, 
V'(r)-V(r)=~ar-P. 



INVOLVING EXCITED ATOMS 183 

This may mean that only the right-hand portions of the 
Franck-Condon curves are significant in treating Lorentz 
broadening. It would be an interesting problem, however, to 
represent analytically the complete Franck-Condon curves 
suggested by Kuhn and Oldenberg[40] from an analysis of the 
mercury-rare gas bands, and to follow through Lenz's theory 
with these expressions substituted for 7' (r) -V(r). It is to be 
expected, of course, that the mathematical difficulties would 
be very great. 

5. HOLTSMABK BROADENING 

The broadening of an absorption line that takes place when 
the pressure of the absorbing gas is increased (with no foreign 
gas present), which we have called Holtsmark broadening, was 
first treated by Holtsmark [30] on the basis of classical theory. 
He calculated the mean frequency shift due to interaction of 
similar oscillators and found it to vary as VNf. Measurements 
of the Holtsmark broadening of the mercury and sodium 
resonance lines made by Truinpy [98] were apparently in agree 
ment with Holtsmark's theory. There were, however, objec 
tions to the theory, and both Frenkel[2i] and Mensing[57] 
attempted to handle the problem on the basis of quantum 
mechanics. Recently Schutz-Mensing [89] has pointed out that 
Holtsmark's original classical treatment was unjustified and, 
when carried out properly, gives rise to a line breadth that 
varies directly as Nf. In no case was it possible to calculate the 
actual line form. 

Recently the problem has been attacked from an entirely 
different point of view by Weisskopf [105]. In the of inion of this 
author, Holtsmark broadening is to be regarded in the same 
light as Lorentz broadening, namely as a result of damping due 
to collisions among the absorbing atoms. On the basis of 
classical dispersion theory, the absorption coefficient of a gas 
when both natural damping and collision damping are present 
is found to be 



4 /(6-A) 2 +l . 



184 COLLISION PROCESSES 

e*Nf 

- 



where b = - , A = - 



2 27ri/ m 



y=2 T " t " z/w=:= ^" i " 4t<T ^ lv -/"I"- ( 123 ) 



and A 

7 <* 

In the above formula, N stands for the number of absorbing 
atoms per c.c., Z H for the number of Holtsmark broadening 
collisions per sec. per c.c. per absorbing atom, and cr H 2 for the 
effective cross-section associated with Holtsmark broadening. 
Assuming that the interaction between two absorbing atoms 
is equivalent to the interaction between two dipoles,Weisskopf 
was led to an approximate expression for o^ 2 , namely 

, *#L 



Introducing the above value of a H 2 into Eq. (123) and using 
Eqs. (122), b is found to be 



2r 4v m 

There are two important limiting cases. (1) When N is very 
small, b is very small, A is equal to 4-Trr (v v ), and Eq. (121) 
reduces to the classical dispersion formula 

b 



which, at the edges of the line, even in the presence of the 
Doppler effect, has been shown to reduce to 



(2) When N is so large that collision damping far outweighs 

natural damping, 6 = 4, A is equal to -= - + - , and the 

Z/ o 



INVOLVING EXCITED ATOMS 

absorption coefficient is given by the expression 

4 



185 



7 
KOC 



sin fare tan - 
2 



A 2 +1 2~ A(A _ 4H1 -V 

which is represented graphically as a heavy curve in Fig. 42. 
Eq. (127) would still be expected to hold when the Doppler 
effect is present, provided the Holtsmark broadening was much 
larger than the Doppler broadening. The dotted curve in 
Fig. 42 is the simple Lorentz curve, and it is seen that the 




^ 1 

-5-4-3-2-1012345678 

Fig. 42. Form of absorption line with large Holtsmark broadening. 

heavy curve and the dotted curve agree at the edges of the line. 
We have then the result that, in the two extremes, vanishingly 
small absorbing gas pressure, and very high pressure, the 
frequency distribution at the edges of the line is identical, 
depending only on the damping. At intermediate values of N 
(when b lies between and 4) the frequency distribution of the 
edges of the line will be given by 

jfcccjzr^ ^ (128), 



where 



1 

y = ol 



1 

: 2r" 



M 



(129). 



186 



COLLISION PROCESSES 



Now this is precisely the formula that has been used by 
Minkowski[60], Schiitz[87] and WeingeroJBE[i03] to calculate the 
damping from experiments performed on the edges of the 
sodium D lines (see Chap, in, 5). If, therefore, Weisskopf's 
theory is correct, these experimentally determined values of 



0-8 



0-7 



0-6 




I 



0123456 
Fig. 43. Weingeroff 's measurements of the damping of the NaD lines as a function 
of vapour pressure. (A smooth curve was drawn through the original 
experimental points.) 



0-7 



0-6 



0-5 




p//fxI0 3 



O'l 



0-2 



0-3 



0-4 



0-5 



Fig. 44. Minkowski's measurements of the damping of the 
function of vapour pressure. 



0-6 
lines as a 



the damping should vary linearly with NVT or, in terms of 
the vapour pressure, with p/VT. 

In Fig. 43, the damping v (which is exactly twice y) is 
plotted against p/VT for the experiments of Weingeroff, and 
in Kg. 44 for those of Minkowski. Both sets of experi- 



INVOLVING EXCITED ATOMS 187 

ments yield straight lines, but with different slopes. Since 



TrRT 
~W~ 

'~M~\f*r 9 
and from Weingeroff's results: 

r = 1-7 x 10~ 8 sec., a s = 14 x 10~ 8 cm., 
whereas from Minkowski's results: 

r = 1-7 x 10- 8 sec., a H = 31 x 10~ 8 cm. 

These two values of <J H are to be compared with Weisskopf 's 
theoretical value 44 x 10~ 8 cm., obtained with the aid of 
Eq. (125). 

Margenau [54] has given an interesting theory of Holtsmark 
broadening in terms of the screening effect upon a particular 
absorbing atom by other absorbing atoms that continually 
pass in and out of its line of sight . A wave-mechanical calculation 
yields the result that the half-breadth of an absorption line 
produced by such screening should be 0-445 divided by the 
mean time between collisions a formula very much the same 
as Lorentz's formula. As far as the final formulas are con 
cerned, Margenau and Weisskopf agree in their treatment of 
Holtsmark broadening. Their main difference of opinion lies 
in the fact that Weisskopf regards Holtsmark broadening as an 
example of Lorentz broadening, whereas Margenau considers 
that a part of Holtsmark broadening may be due to the 
screening effect of neighbouring atoms. 

6. EARLY MEASUREMENTS OF THE QUENCHING 
OF RESONANCE RADIATION 

6 a. QTJENCHING OF RESONANCE RADIATION BY FOREIGN 
GASES. It was first noticed by Wood DOS] that the introduction 
of a small amount of air into a mercury resonance lamp reduced 
the intensity of the emitted resonance radiation. Further 
experiments on mercury, sodium and cadmium resonance 



188 COLLISION PROCESSES 

radiation, to be described later, indicated that this is a very 
general phenomenon that takes place whenever the foreign 
gas atoms or molecules are capable of receiving some or all of 
the excitation energy of the excited atoms in the resonance 
lamp. In the current terminology, the resonance radiation 
whose intensity is reduced by the introduction of a foreign gas 
is said to be "quenched", and a collision between an excited 
atom and a foreign gas molecule in which some or all of the 
excitation energy of the excited atom is given over to the 
foreign gas molecule, thereby preventing the excited atom from 




_ Foreign 

Photographic V -/ Gas Inlet 

Plate 



Fig. 45. Stuart's apparatus for studying the quenching of 
Hg resonance radiation. 

radiating, is said to be a "quenching collision". The "quench 
ing", Q, is defined as 

^ _ Intensity of resonance radiation with foreign gas 

"~ Intensity of resonance radiation without foreign gas 3 
and the results of a quenching experiment are expressed by a 
" quenching curve ", in which Q is plotted as a function of the 
foreign gas pressure. 

66. EXPERIMENTS OF STUART WITH MEBCTJBY. The most 
extensive early investigation of the quenching of mercury 
resonance radiation was made by Stuart [93], who used the 
apparatus shown in Fig. 45. Tke main resonance lamp .B n into 
which the foreign gases were introduced was excited by the 
very narrow line emitted by the resonance lamp R I} and the 
quenching of the resonance radiation from J? n was measured 



INVOLVING EXCITED ATOMS 



189 



with a number of foreign gases. The experimental results are 
shown in Fig. 46 in the form of quenching curves. The following 
features of Stuart's experiments are to be emphasized: (1) The 
mercury vapour pressure corresponded to room temperature, 
at which there was considerable diffusion of imprisoned reso 
nance radiation. (2) The main resonance lamp & was excited 
by a very narrow line. (3) In the case of the inert gases, He, A 
and N 2 , appreciable quenching occurred only at high foreign 




Fig. 46. 



12345 
Foreign gas pressure in mm. 

Stuart's quenching curves for Hg resonance radiation. 



gas pressures, from 10 to 200 mm. (4) Even at high pressures, 
the quenching of the inert gases was very much smaller than 
that of H 2 , 2J CO, C0 2 and H 2 0. 

6c. EXPERIMENTS WITH SODIUM AND CADMIUM. With 
apparatus similar to that of Stuart, Mannkopff [52] measured 
the quenching of sodium resonance radiation by H 2 , N 2 and a 
mixture, Ne-He. He found that both N 2 and H 2 were very 
effective in quenching, and that Ne-He was very ineffective, 
even at high pressures. The sodium vapour pressure in these 
experiments was high enough to give rise to considerable re- 



190 COLLISION PROCESSES 

absorption of the resonance radiation on its way out of the 
lamp. 

The quenching of cadmium resonance radiation 3261 was 
studied qualitatively by Bates [5] and by Bender [8], who showed 
that H 2 was very effective in quenching cadmium resonance 
radiation. Further experiments by Bender indicated that N 2 
and CO also quench, but not as effectively as H 2 . 

6d. DIFFICULTY OF INTERPRETING EARLY EXPERIMENTS. 
Experiments on the quenching of resonance radiation are 
undertaken mainly for two reasons: (1) to ascertain whether a 
foreign gas does or does not quench, and if so, to decide what 
mechanism is responsible for the quenching; and (2) to obtain 
an accurate numerical estimate of the effectiveness of those 
gases which are known to quench. Attempts to obtain this in 
formation from the experiments of Stuart were made by Stuart 
himself, by Foote[i9] } Gaviola[24] and Zemansky[ii2], with 
indifferent success. It is quite clear that, with all foreign 
gases at all pressures, reabsorption of the resonance radiation 
(diffusion of imprisoned resonance radiation) played an im 
portant role, the effect of which, in Stuart's experiments, it is 
impossible to calculate accurately, because of the complicated 
geometrical conditions under which the experiments were per 
formed. Furthermore, with the inert gases at high pressure, 
Lorentz broadening altered the width of the absorption line 
relative to the width of the exciting line to such an extent that 
it is doubtful whether the so-called quenching curves obtained 
with the inert gases can be regarded as being due to quenching 
at all. MannkopfTs experiments on sodium resonance radia 
tion also are difficult to interpret, not only because of re- 
absorption of resonance radiation but also because of a reaction 
which appears to take place between normal sodium atoms and 
some foreign gases, notably nitrogen and hydrogen, with the 
result that the sodium vapour pressure, and consequently the 
rate of formation of excited atoms, is reduced, causing a reduc 
tion in the intensity of the emitted resonance radiation that 
is not to be confused with the phenomenon of quenching. 

It is rather important to emphasize that a quenching curve, 



INVOLVING EXCITED ATOMS 191 

that is, an experimental curve of Q against foreign gas pres 
sure, by itself, without further details as to line breadths, 
vapour pressure, geometry of apparatus, etc., can give no in 
formation of an absolute nature whatever, and indeed in some 
cases is not convincing evidence that quenching takes place 
at all. To read from a quenching curve the half -value pressure 
(the foreign gas pressure at which Q = 0-5), and to say that, at 
this pressure, the time between collisions is equal to the life 
time of the excited atoms, may lead to errors of several hundred 
per cent. The most that can be inferred from a series of quench 
ing curves, all taken under the same conditions but with 
different foreign gases, is the relative quenching ability (if it is 
quenching) of the various gases ; and, as an approximate method 
of describing the relative effectiveness of various gases, the 
half- value pressure may be used. To obtain accurate informa 
tion of an absolute character about quenching collisions be 
tween excited atoms and foreign gas molecules, methods must 
be developed to enable one to take into account the effect of 
radiation diffusion and of Lorentz broadening, or, better still, 
the experiments should be performed under conditions in 
which these effects are absent. To see how this is done it is 
necessary to consider these two effects at a little greater length. 

7. THEORY OF THE QUENCHING CURVE FROM 
AN IDEAL RESONANCE LAMP 

7 a. THE STERN-VOLMEB FORMULA. Let us suppose that a 
beam of radiation is incident upon an ideal resonance lamp 
such as that depicted in Fig. 24, and let us assume that the 
following conditions are fulfilled: 

(1) The absorbing gas in the resonance lamp is at such a low- 
pressure that only primary resonance radiation is emitted 
which is not further absorbed on its way out. 

(2) There is a foreign gas present at such a low pressure that 
Lorentz broadening of the absorption line is negligibly small. 

If n represents the number of excited atoms per c.c. in the 
emitting layer of the resonance lamp, r the lifetime of the 
excited atoms, and Z Q the number of times per sec. that an 
excited atom gives up its excitation energy upon collision to 



192 COLLISION PROCESSES 

one c.c. of molecules of foreign gas (number of quenching 
collisions per sec. per c.c. per excited atom), then, in the steady 
state, 

Rate at which excited atoms] _ (Rate at which excited atoms 
are being destroyed J j are being formed 



or 

r 

E 



and n 



where E, under the conditions imposed above, is independent 
of the foreign gas pressure, and remains constant so long as the 
absorbing gas pressure and the intensity of the exciting light 
remain constant. 

The radiation emitted by the resonance lamp is a constant 
fraction (depending on geometry), say e, of the total energy 
emitted by the n excited atoms, thus 

M 

Emitted radiation with foreign gas = e - hv 



Now, the emitted radiation without foreign gas ehvE, whence 



This formula was first obtained by Stern and Volmer[92], 
Since Z Q varies linearly with the foreign gas pressure, a quench 
ing curve obtained in an experiment performed under these 
conditions should follow a simple curve of the tvpe 

Q- l 

1 + const, p* 

or, plotting IjQ against p, a straight line should result. It 
would seem, therefore, that the criterion for applying the 
Stern- Volmer formula to an experimental quenching curve 
would be to see whether the experimental values of l/Q vary 
linearly with p. It appears, however, that this is not a very 
sensitive criterion. For example, Stuart's quenching curve 



INVOLVING EXCITED ATOMS 193 

obtained with H 2 obeys this formula, whereas the other curves 
do not, and yet the formula is equally inapplicable to all the 
quenching curves. Similarly, bothMannkopff'sandvonHamos* 
experimental values [26] for the quenching of sodium resonance 
radiation by N 2 obey the formula, although Mannkopff 5 s ex 
periments were performed under conditions which definitely 
preclude its use. The fact of the matter is, that almost any 
small portion of a descending curve can be fitted with some 
degree of accuracy to a formula of the Stern- Volmer type. The 
only way to tell whether the use of the formula is justified is to 
test whether the conditions that are assumed in the derivation 
are satisfied or not. For example, in working with sodium 
resonance radiation, it is easy to see whether primary reso 
nance radiation alone is excited, or whether radiation diffusion 
is present, by merely noticing whether resonance radiation is 
coming only from the direct path of the exciting light or from 
the resonance lamp as a whole. In the case of ultra-violet 
resonance radiation, the easiest procedure is to obtain several 
quenching curves with the same foreign gas but at different 
absorbing gas pressures. If the same quenching curve is 
obtained at various low absorbing gas pressures, then the 
region in which the Stern-Volmer formula is applicable has 
been attained. If not, the absorbing gas pressure must be 
reduced until the quenching curve becomes constant. 

The only quenching experiment, involving the excitation of 
normal atoms in a resonance lamp by the resonance line, which 
seems to warrant the use of the Stern-Volmer formula, is that 
of von Hamos on the quenching of sodium resonance radiation 
by N 2 . The value of the effective quenching cross-section <r Q 2 
obtained from von Hamos' experiments is listed in a table at 
the end of 8. 

76. EFFECT OF LORENTZ BROADENING ON QUENCHING. 
Even when the absorbing gas pressure is low, the Stern-Volmer 
formula may be inapplicable. This is the case when the foreign 
gas pressure is high enough to produce Lorentz broadening of the 
absorption line. To understand how this affects the quenching 
curve, let us consider two extreme cases: (1) the exciting line 



194 COLLISION PROCESSES 

is a broad, self-reversed line, such as that emitted by a hot arc; 
and (2) the exciting line is a narrow, unreversed line such as that 
emitted by a resonance lamp. These two cases are depicted in 
Mg. 47. The figures show the relation between the exciting line 



Three Stages 
in the Broadening 
of the Absorption Line 




xciting 
Line 



Cased) 




Exciting 
Line 



Three Stages 
in the Broadening 
of the Absorption Line 



Case (2) 
Fig. 47. Lorentz broadening in a resonance lamp. 

(which remains constant) and the absorption line of the gas in 
the resonance lamp as it is broadened by increasing the foreign 
gas pressure. The area on the graph, which the exciting line 
and the absorption line have in common, is an indication of the 
energy absorbed in the resonance lamp, and therefore of the 



INVOLVING EXCITED ATOMS 195 

rate at which excited atoms are forming. It is evident from the 
figure illustrating case (1) that, when the exciting line is wide, 
this area increases as the absorption line gets broader. In this 
case, therefore, if the foreign gas does not quench at all, the 
quenching curve should rise, and if quenching does take place, 
it would be partly or completely offset by the increased absorp 
tion. In case (2), it is evident that the net effect of Lorentz 
broadening of the absorption line is to cause the emitted 
radiation to decrease whether real quenching is present or not. 

The experiments of Bates [6] and von Hamos[26] are in sup 
port of these conclusions. Bates obtained the quenching curve 
of mercury resonance radiation for the foreign gas methane. 
For small values of the methane pressure (0 to 10 mm.), the 
curve descended slightly, due to a small amount of true 
quenching. When the methane pressure was increased (10 to 
200 mm.), the quenching curve showed a marked rise. Since 
the exciting light was obtained from an arc, the conditions 
under which Bates worked were equivalent to case (1). 

Von Hamos studied the emission of sodium resonance radia 
tion under conditions in which the exciting line could be made 
broad or narrow by running the arc hot or cold, and in which 
the absorption line could be either broadened by a foreign gas, 
or shifted with respect to the exciting line by a magnetic field. 
His results confirm in every detail the conclusions stated above, 
and also indicate that the inert gases do not quench sodium 
resonance radiation at all. It seems to be quite certain from 
these considerations that the quenching of mercury resonance 
radiation by the inert gases observed by Stuart, and the 
quenching of sodium resonance radiation by the mixture 
Ne-He observed by Mannkopff , are not true quenching at all 
but are due entirely to Lorentz broadening. 

In view of the difficulty of interpreting Stuart's quenching 
curves, experiments were performed by Zemansky under con 
ditions in which Lorentz broadening was absent but radiation 
diffusion played the main role. Before these experiments can 
be understood, it is necessary to give a brief account of Milne's 
theory of radiation diffusion. 



196 COLLISION PROCESSES 

8. RADIATION DIFFUSION AND QUENCHING 

8a. MILNE'S THEORY. Consider a mass of gas, enclosed 
between the planes x = and x = Z, exposed to isotropic mono 
chromatic radiation at the face x = } which is capable of 
raising atoms from the normal state 1 to the excited resonance 
state 2. Suppose at any moment that there are n normal atoms 
per c.c. capable of absorbing this radiation and n 2 excited 
atoms per c.c. capable of emitting this radiation. Then it has 
been shown by Milne [59], on the basis of Einstein's radiation 
theory, that n 2 at any point is given by 



where r is the lifetime of the excited atoms, and k is the absorp 
tion coefficient of the gas in cm.- 1 (k contains n x ) for the radia 
tion in question. This equation holds for all values of n 2 and % 
provided n 2 <%, which is undoubtedly the case for light in 
tensities employed in the laboratory. Dividing the radiation 
into two parts, in the manner of Schuster [86], Milne showed 
that the net forward flux of radiation at any point is given by 

1 3 



and the net backward flux by 



where 



and g and g 2 are the statistical weights of the normal and the 
excited states respectively. 

The dn 2 jdt that appears in these expressions represents the 
resultant rate of formation of excited atoms under the influence 
of the three processes: absorption of radiation, spontaneous 
emission and stimulated emission. If there should be any other 
rate of formation of excited atoms, say R, then dn 2 /dt must be 
replaced by dn 2 /dt-R. It must be emphasized that the above 
theory is good only for the one-dimensional flow of radiation, 



INVOLVING EXCITED ATOMS 



197 



and that the motions of individual atoms and any radiation 
frequency changes that accompany such motions have not 
been taken into account. 

86. USE off MILNE'S THEORY TO STUDY QUENCHING. In 
order to apply Milne's theory to the actual conditions of a 
quenching 'experiment, consider the arrangement depicted in 
Pig. 48. The absorption cell containing the absorbing gas and 
a foreign gas is an experimental approximation to an infinite 



Collimated, Unabsorbed 
Radiation Ke" hl 



Scattered 
Radiation 



Colli-mated I ^+(je~Z) 

Radiation Isotropic 
K Radiation 

Fig. 48. Conditions postulated by Milne. 

slab. Incident on the face x is the isotropic radiation postu 
lated by Milne and, in addition, a collimated beam of intensity 
K. The effect of the collimated beam is to provide a further 
rate of formation of excited atoms equal to 

_^ xx , 



By virtue of Einstein's relation, 

n r* 1 1 
r> __/2 C L _ L 

1~^2 -t "OTi,^* ^.' ' 



we can write 

Rate of formation of excited atoms) _ n^K _ kx 
due to collimated beam J J 






198 COLLISION PROCESSES 

The effect of the presence of the foreign gas is to provide a 
further rate of destruction of excited atoms equal to 

Rate of destruction of excited atoms ] 

. . . ,,. . [ = Z n* ...... (136), 

due to quenching collisions J w 

where Z Q depends on the foreign gas pressure according to 
Eq. (91). It must be emphasized that all collision processes 
between an excited atom and a foreign gas molecule, at the con 
clusion of which the excited atom is no longer in exactly the 
same state, are included in the symbol Z Q . Z Q n% may therefore 
include a number of different quenching collisions, of which 
one may involve a lowering of the excited atom from the 
resonance (radiating) state to a neighbouring metastable level. 
If such a process takes place, the assumption is made that the 
metastable atom is not raised again to the resonance state. 
This limits the applicability of the theory to experiments which 
are performed at very low foreign gas pressures, where the 
number of collisions capable of raising atoms to the resonance 
state is negligible. 

Replacing now the dn z /dt of Eqs. (131), (132) and (133) by 



and putting the new dn 2 jdt equal to zero, in order to represent 
the stationary state, Eq. (131) becomes 



and Eqs. (132) and (133) become 



If now we do away entirely with the isotropic radiation, and 
keep only the collimated beam, we have the boundary con 
ditions that 

when # = 0, / + = 0; 

when x-l> /_ = 0. 



INVOLVING EXCITED ATOMS 



199 



The details of the solution of Eqs. (137), (138) and (139), sub 
ject to the boundary conditions above, are given in a paper by 
Zemansky [115], where it is shown that the scattered radiation 
emerging from unit area of the face x = I is given by 



= l) = KG (Id, rZ Q ) 



where G(kl,rZ Q ) 



...... (140), 



rZ n 



l+rZ Q 



sinh 2kl -~ 



...... (141). 



rZ Q -0 




0-15- 



0-10 - 



0-05 -, 



0-5 



1-0 1-5 2-0 2-5 3-0 3-5 
Fig. 49. Values of the function G. 



4-0 



4-5 



It is clear that the function G depends only on the two quan 
tities kl (called, in astrophysics, the " opacity "), and rZ^ , the 
number of quenching collisions per lifetime. In a table in the 
Appendix, values of G are given for many values of kl and rZ Q , 
and the function G is plotted in Fig. 49. It can be seen from the 
figure and can also be shown from Eq. (141) that, as " 

r 1 kl 
{?-> 



200 COLLISION- PROCESSES 

whence the quenching Q approaches 

9- ' 



1+rV 

which is the Stern-Vohner formula of Eq. (130). 

Since the above calculation concerns an infinitesimally 
narrow range of frequencies which are not altered upon re 
peated absorptions and re-emissions, it is necessary to develop 
methods for handling the actual situation in which the exciting 
light is a fairly broad spectral line, and in which the absorbing 
gas has an absorption line with a Doppler distribution. It if be 
assumed that each narrow frequency band dv, present in the 
exciting light, diffuses without change of frequency according 
to Eq. (140) with the appropriate k v l, then a knowledge of the 
frequency distribution of both the exciting and the absorption 
lines will enable one to integrate graphically to obtain the 
resultant emerging radiation. This procedure was adopted by 
Zemansky with some success, but has the disadvantage that it 
is tedious, and that the error introduced by assuming that each 
frequency band diffuses as a unit without change of frequency 
is difficult to estimate. It is far simpler and probably more 
accurate to assume that the effect of the broad exciting line 
and the various frequency changes that take place as the 
radiation diffuses is the same as that which would be produced by 
an infinitesimal frequency band for which the absorbing gas has 
an "equivalent absorption coefficient". In other words, we can 
describe the whole diffusion process by attributing to the 
diffusing radiation an equivalent opacity, say Tel, which, when 
substituted for kl, in Eq. (140) will enable us to calculate the 
intensity of the emerging radiation. The success of this method, 
of course, depends entirely upon the degree of accuracy with 
which the equivalent opacity can be calculated. Samson [84] 
has given a method of calculating an equivalent opacity which 
is reliable at low absorbing gas pressures at which most ex 
periments are performed. 

8c. EQUIVALENT OPACITY AT Low PRESSURE. Samson 
assumed that the scattered or diffused radiation had a fre 
quency distribution determined only by the Doppler effect and 



INVOLVING EXCITED ATOMS 201 

independent of the breadth of the exciting line. He defined an 
equivalent absorption coefficient as that value of kl, say kl, 
which a gas would have to possess for an infinitesimal frequency 
band in order that this infinitesimal band would be trans 
mitted to the same extent that the actual Doppler radiation 
is transmitted. It has already been shown in Chap, m, 4d, 
that the transmission of a Doppler line is given by [seeEq. (61)] 



where, for a simple line [see Eq. (35)], 

2 /S2 

fvf\ A / 

77 

The transmission, however, of an infinitesimal frequency band 
for which the gas has an opacity Tel is e-, whence Tel can be 
calculated from the formula 




/QQ 



da> 



J 



(142), 



once k Q lis known. There will be found in the Appendix a table 
of values of Samson's kl for a number of values of k L 

Sd. DERIVATION OF A THEORETICAL QUENCHING CTTRVE. 
Once the equivalent opacity has been calculated, the scattered 
radiation emerging from the face x = I can be obtained for a 
number of values of rZ Q from the curves of Fig. 49. Dividing 
by the result when rZ Q = 0, the quenching Q is obtained as a 
function of rZ Q . A number of such theoretical quenching 
curves are shown in Fig. 50 along with the Stern- Volmer curve, 
which is valid only when Tel is vanishingly small. From the 
correct theoretical quenching curve the value of rZ Q may be 
read off corresponding to any experimentally observed value 
of Q, and therefore, an experimental quenching curve of Q 
against foreign gas pressure can be converted into a curve of 



202 COLLISION PROCESSES 

-rZ Q against foreign gas pressure which, by virtue of the gas- 
kinetic expression for Z Q , should be a straight line whose slope 
contains a Q 2 , the quenching cross-section. 

Be. EXPERIMENTAL DETERMINATIONS OF QUENCHING 
CROSS-SECTIONS. Zemansky[ii5] and Bates [6, 7] used the 
apparatus depicted in Fig. 51. Resonance radiation from a 
mercury resonance lamp E was passed through a thin quartz 
absorption cell containing mercury vapour and a foreign gas 

Q 
i-o- 

0-9 
0-8 
0-7 
0-6 



0-4 
0-3 
0-2 
0-1 




0-1 0-2 0-3 0-4 0-5 

Fig. 50. Theoretical quenching curves for various equivalent opacities. 

at some known pressure. The difference between the readings 
of the photoelectric cell, P, in positions (1) and (2) gave the 
intensity of the scattered radiation, since, in position (1) the 
photoelectric cell received only the transmitted collimated 
beam, whereas in position (2) both the transmitted collimated 
beam and the scattered radiation were received. The incident 
radiation was measured often (through the cellophane window 
C, which cut it down to an easily measurable value), in order 
to take account of any variation in intensity of the radiation 
from R. The ratio of the intensity of the scattered radiation 
with a foreign gas to that without a foreign gas gave the 
quenching Q, which was measured for many foreign gases. 



INVOLVING EXCITED ATOMS 



203 



In Zemansky's experiments, the mercury vapour pressure 
in the absorption cell corresponded to a temperature of 20-0 C. 
throughout. Assuming the mercury resonance line to consist of 
five equal hyperfine-structure components, and taking r to be 
1-08 x 10~ 7 sec., k^l is found to be, from Eq. (35), 



At 20 C., N = 4-19 x 10 13 , and Z was 0-792 cm., whence k l was 
found to be 4-35. Substituting this value of k l in Samson's 




Fig. 51. Quenching apparatus satisfying the provisions of Milne's theory. 

formula, Eq. (142), Td was calculated to be 2-24. From the 
curves in Fig. 49, the theoretical quenching curve appropriate 
to these experiments was plotted. From the theoretical 
quenching curve, and experimental measurements of Q at 
various foreign gas pressures with several foreign gases, curves 
of rZ Q against p were obtained, and, from the slopes of these 
lines and the gas-kinetic expression for Z Q , the value of cr^ 2 
appropriate to each foreign gas was finally obtained. All such 
values are given in Table XXIV along with values obtained 
by Bates. All the foreign gases were studied within a pressure 
range in which Lorentz broadening was entirely negligible. In 



204 



COLLISION PROCESSES 



this pressure range no appreciable quenching was observed for 
helium or for argon, proving that Stuart's quenching curves 
for these gases are due entirely to Lorentz broadening. 



TABLE XXIV 



Foreign gas 
molecule 


V 
cm. 2 x 1C 16 


Foreign gas 
molecule 


*<? 

cm. 2 x 10 16 


CH 4 


0-0852 


2 


19-9 


H 2 


1-43 


H 2 


8-60 


NH 3 


4-20 


C0 2 


3-54 


NO 


35-3 


C 2 H 6 


5-94 


CO 


5-82 


C,H 8 


2-32 


N 2 


0-274 


C 4 H 10 


5-88 






C,H 6 


59-9 






Other 


Very- 






hydro 


large 






carbons I 



9. COLLISIONS OF EXCITED ATOMS PRODUCED 
BY OPTICAL DISSOCIATION 

It is clear from the preceding sections that the interpretation 
of quenching experiments, performed under conditions in 
which the excited atoms are produced by the absorption of 
resonance radiation, is rendered complicated by the presence 
of such phenomena as radiation imprisonment and Lorentz 
broadening, which preclude the possibility of using the simple 
Stern- Volmer formula. It has been seen how these complica 
tions can be avoided or how, when radiation imprisonment is 
present, it may be taken into account by Milne's theory. Since, 
however, this last method is very tedious, it is therefore for 
tunate that another method is at hand which is not only sim 
pler from an experimental and a theoretical point of view, but 
is also more powerful as a tool for studying quenching. 

9 a. THE OPTICAL DISSOCIATION OF Nal. This method de 
pends upon a very important process first observed by 
Terenin[95], namely, the dissociation of the Nal molecule into 
an excited sodium atom and a normal iodine atom by light of 
wave-length 2430 or less. The process may be represented by 
the equation: 

to 



INVOLVING EXCITED ATOMS 205 

Since the dissociation potential of Nal into an excited sodium 
atom and a normal iodine atom is 5-078 volts, corresponding 
to A = 2430 A., it is clear that, when the dissociation is accom 
plished by means of light of wave-length shorter than 2430, 
the excess energy is transformed into relative kinetic energy 
of the resulting atoms, as was shown by HognessandFranck[29]. 
The excited atoms formed by the dissociation emit the D lines, 
whose intensity in the presence of a foreign gas is diminished, 
enabling one to measure the quenching under particularly 
advantageous conditions, namely, (1) at any moment the con 
centration of normal sodium atoms is very small, hence very 
little of the D light is absorbed by sodium atoms on its way out 
of the vessel, and the Stern-Volmer formula can be used with 
confidence; (2) the velocity of the excited sodium atom can be 
varied at will by performing the dissociation of Nal with 
various wave-lengths, and therefore the dependence of the 
effective quenching cross-section on the velocity can be 
studied; (3) foreign gases may be used which react chemically 
with normal sodium atoms. 

96. EXPERIMENTAL RESULTS. Three different molecules 
have been usedforthe production of excited atoms. Winans [107], 
Terenin and Prileshajewa[96], and Kisilbasch, Kondratjew and 
Leipunsky [36] used Nal, and Winans, in another experiment, 
used NaBr to produce excited sodium atoms, and Prilesha- 
jewa[79, so] used Til to produce excited thallium atoms. The 
apparatus in all cases was substantially the same, so that a 
description of Terenin and Prileshajewa's procedure with Nal 
will suffice. Solid Nal was warmed to about 550 C. in a quartz 
vessel until the vapour pressure was about 0-015 mm. Exciting 
light from a spark was focused on a warmer part of the vessel 
and the D radiation, emitted perpendicular to the exciting 
light, was measured as a function of the foreign gas pressure. 
A visual photometric method was used in all cases, a second 
vessel containing Nal without a foreign gas being used as a 
comparison standard by Winans, and another source of yellow 
light being employed for this purpose by Terenin and Prile- 
shajewa. Winans used three different exciting wave-lengths, 



206 



COLLISION PROCESSES 



whereas Terenin and Prileshajewa used eight different wave 
lengths. Corrections were made by Terenin and Prileshajewa 
for the absorption of both the exciting light and the emitted D 
light by the foreign gas. 

In Fig. 52 are shown some typical quenching curves in 
which the exciting source was a cadmium spark and the dis 
sociated molecule was Nal. The fact that these curves obey 
the Stern-Volmer formula is indicated in Fig. 53, where l/Q is 
plotted against foreign gas pressure and a straight line is 



Exciting Source Cd Spark 
Dissociated Molecule Nal 




25 



30 



10 15 20 

Foreign gas pressure in mm. 

Fig. 52. Quenching of Na resonance radiation by foreign gases. 

obtained. The effect of the wave-length of the exciting source 
upon the quenching is shown in Fig. 54, where the quenching 
of I 2 is shown for three different exciting sources. 

9c. EVALUATION OF EFFECTIVE CROSS-SECTIONS. It has 
already been mentioned that, if the dissociation of the Nal 
molecule is accomplished by means of light of wave-length less 
than 2430, the excess energy is transformed into relative kinetic 
energy of the resulting atoms. In calculating the collision rate 
of excited atoms it is incorrect, therefore, to attribute to them 
the usual kinetic energy of thermal motion. It was shown by 
Terenin and Prileshajewa that, in comparison to the speed of 
the excited sodium atom after dissociation, the molecules of 
Nal could be regarded, with negligible error, to be stationary, 




C0 2 




5 10 15 20 25 

Foreign gas pressure in "mini. 
Fig. 53. Applicability of Stern- Volmer formula. 



30 




Cd Spark 
Ni Spark 



5 10 15 20 

Iodine pressure in mm. 

Fig-. 54. Dependence of quenching on velocity of excited N& atom. 



208 



COLLISION PROCESSES 



in which case the number of quenching collisions per excited 
sodium atom per sec. per c.c. is given by 

Z Q = ira Q *nM (143), 

where ?i 2 is the number of foreign gas molecules per c.c. and v I 
is the velocity with which the excited sodium atom escapes 
from the Nal molecule upon dissociation. Since the velocity 
of escape is uniformly distributed as regards direction in space, 
as was shown by Mitchell [62], it follows from elementary 
mechanics that 

2 _m 2 2w 

1 -yy. 



where m^ and m 2 are the masses of the sodium atom and iodine 
atom respectively, and w is the excess energy of the dissociating 
quantum. Using the Stern- Volmer formula: 



with r= 1-6 x 10~ 8 sec., and denoting the foreign gas pressure 
in mm. by p, we get finally 



1-83 x 1C" 9 
pv I 



(H 



.(145). 



In Tables XXV and XXVI are given values of v l for various 
exciting sources for both the Nal and NaBr molecules, cal 
culated with the aid of Eq. (144). 

TABLE XXV 

FOR THE Nal MOLECULE ( WAVE-LENGTH LIMIT 2430) 



Exciting 
source 


Mean 
wave-length 


Velocity v l in 
cm./sec. x 10~ 5 


Fe 


2400 


0-7 


Tl 


2380 


0-7 


Sb 


2311 


1-3 


Ni 


2300 


14 


Cd 


2232 


1-7 


Zn 


2082 


2-4 


Mg 


2026 


2-6 


Al 


1990 


2-8 



INVOLVING EXCITED ATOMS 

TABLE XXVI 
FOE THE NaBr MOLECULE (WAVE-LENGTH LIMIT 2144) 



209 



Exciting 
source 


Mean 
wave-length 


Velocity v^ in 
cm./sec. x 10~ 5 


Cd 
Zn 
Al 


2232 
2082 
1990 


0-4 
1-2 
1-8 



In Table XXVII, the quenching cross-sections, calculated 
with the aid of Eq. (145), are listed along with the values ob 
tained by Mannkopff and vonHamos. Comparing Mannkopff's 



TABLE XXVTE 



Optically 
dis 
sociated 
molecule 


Foreign 
gas 


Excitation 


Velocity of 
excited Na 
atom in 
cm./sec. x 10~ 6 


^ 
cm. 2 x 10 16 


Author 


_ 


H 2 


Resonance 


~0-7 


17 


Mannkopff 










(corrected 












about 8) 




Nal 


99 


Cd 


1-7 


64 


Winans 






Zn 


2-4 


5-7 





!L 


N! 


Resonance 


~0-7 


61 


Mannkopff 









~0-7 


29 


von Hamos 


Nal 




Zn 


24 


6-08 


Kisilbasch, Kon- 












dratjew and Lei- 






Al 


2-8 


10-6 


puns Ky 







Al 


2-8 


9-6 


Winans 


" 


CO 


Zn 


24 


4-04 


Kisilbasch, Kon- 


" 










dratjewandLei- 












punsky 




co ft 


Cd 


1-7 


16-9 


Winans 


" 


v/vg 

I 


Fe 


0-7 


38-2 


Terenin and Prile- 


1 










shajewa 


1 




9t 


Ni 


14 


60-5 


it 




It 


Zn 


24 


414 







I 2 


Fe 


0-7 


239 


99 




99 


Tl 


0-7 


191 






9 


Sb 


1-3 


127 









Ni 


14 


153 









Cd 


1-7 


89*2 








Zn 


24 


38-2 




j 


\ 


Mg 


2-6 


47-8 








Al 


2-8 


54-1 




NaBr 


Br 2 


Cd 


04 


366 


Winans 




> 


Zn 


1-2 


124 


99 


99 




Al 


1-8 


102 


99 



210 COLLISION PROCESSES 

value of o- Q 2 for nitrogen with that of von Hamos (which was 
obtained under more advantageous experimental conditions), 
it is seen to be approximately twice as large. Assuming then 
that Mannkopff's value for H 2 is also about twice as large as the 
correct value, we can estimate a corrected value for H 2 . This 
is given in brackets. The dependence of a Q 2 on the velocity of 



30t- 



20-- 



10- - 




0123 

Velocity of excited Na atom in "x 10~ 8 
Fig. 55. Dependence of cr fl * on velocity when foreign gases are H 8 and N 2 . 

the excited sodium atom is shown graphically in Figs. 55 
and 56. 

In the experiments of Prileshajewa with excited thallium 
atoms, the Til molecule was dissociated by light of wave 
length less than 2100 into a thallium atom in the 7 2 S 1/2 state 
and a normal iodine atom, according to the equation 

hv [A < 2100] + Til = Tl (7 2 S 1/2 ) + 1. 
A thallium atom in the 7 2 S 1 / 2 state may return spontaneously 



INVOLVING EXCITED ATOMS 



211 



either to the normal 6 2 P 1/2 state, emitting the line 3776, or to 
the metastable state 6 2 P 3/2 , emitting the green line 5350. The 
reduction in intensity of either of these lines, as the pressure 
of the foreign gas is increased, may be used to measure the 
quenching of the 7 2 S 1/2 state. Prileshajewa measured the 



300 



200 



100 




Velocity of excited Na atom in - x 10 5 
Fig. 56. Dependence of a/ on velocity when foreign gases are I 2 and Br 2 . 

quenching of the green line for three exciting wave-lengths and 
with three foreign gases: I 2 , 1 and Til. 

The derivation of the quenching formula appropriate to this 
case is accomplished by appeal to Fig. 57, showing the various 
processes that take place. Calling the rate of formation of 
7 2 S 1/2 atoms E, and denoting the Einstein A coefficients of the 



212 COLLISION PROCESSES 

lines 3776 and 5350 by A and A 2 respectively, the number of 
excited atoms per c.c., n, is given by 

E ^A- L n+A 2t n + Z Q n. 

The observed intensity of the green line is proportional to 
An and 



' 


E e 


c 




s 





_, B 


f 


^ 


N3 


1 




^ ^ 
2 co 



1ft 


1 


i 


1 


1 1 


d 


1 


1 






o 






fe 


2 "S 


3 








pu .| 
W 


1 








> 


r 


^ 




t 


Volts 



-6'P, 



6'Pi 



Kg. 57. Energy level diagram of Tl atom showing emission of 3776 
and 5360 and impacts of the second kind. 

Without foreign gas 



whence the "quenching", Q, is 
Q=^T 



or 



Q- 



(146). 



It is shown at the end of Chap, m ( 76) that 



and therefore Z Q and finally cr Q 2 can be obtained from experi 
mental measurements of Q. 



INVOLVING EXCITED ATOMS 



213 



The final results are shown in Table XXVIII. With I 2 and I 
as foreign gases, the dependence of <7 2 on velocity is the same 
as that found by Terenin and Prileshajewa with excited 
sodium atoms; i.e. with I 2 , cr Q 2 decreases with increasing 
velocity, and with I there is substantially no change. The 
results, however, with TU indicate just the reverse, namely an 
increase of a Q 2 with increasing velocity. 

TABLE XXVHI 



Optically 
dissociated 
molecule 


Foreign gas 


Velocity of 
excited Tl 
atom in 
cm./sec. x 10~ 5 


af x 10 15 


TU 


I 2 


0-30 


98 






0-36 


93 






0-40 


69 




I 


0*35 


45 






0-36 


37 






0-40 


27 






0-46 


40 




Til 


0-33 


29 






0-38 


63 






0-44 


86 



10. OTHER COLLISION PROCESSES 

Collisions of the second kind involving sensitized fluorescence 
and chemical reactions have already been described in Chap, n, 
along with their interpretation in the light of quantum- 
mechanical principles. We are concerned in this chapter with 
only those experiments which yield a quantitative estimate 
of effective cross-sections associated with collisions of the 
second kind. Besides pressure-broadening collisions and 
quenching collisions there are three other types of collisions 
from experiments on which quantitative data may be obtained. 

10 a. COLLISIONS INVOLVING THE SODIUM TRANSITION 
3 2 P 3/2 ->3 2 P 1/2 . it was first observed by Wood[i09, no] that, 
upon excitation of sodium vapour at low pressure by one of the 
D lines, only that line appeared as resonance radiation; where 
as, upon introducing a foreign gas, or by raising the sodium 
vapour pressure, both D lines appeared. It is clear that the 



214 COLLISION PROCESSES 

appearance of, say, the D x line, when sodium vapour mixed 
with argon is excited by D 2 , must be due to a collision which 
lowers a sodium atom from the 3 2 P 3/2 state to the 3 2 P 1/2 state, 
that is, a collision of the type 

Na (3 2 P 3/2 ) + A =Na (3 2 P 1/2 ) + A. 

Similarly, by exciting with the D x line, in the presence of argon, 
the collision 

Na (3 2 P 1/2 ) + A = Na (3 2 P 3/2 ) + A 
takes place. 

Lochte-Holtgreven[49] repeated Wood's experiment under 
better conditions, and measured the ratio of the intensities of 
the two D lines emitted by sodium vapour upon excitation 
first with D 2 and then with D l5 using four different foreign 
gases: argon, a mixture of neon and helium, nitrogen and 
hydrogen. Lochte-Holtgreven expected that, as the foreign 
gas pressure was increased, the ratio IVD 2 should approach 
1/2 upon excitation with D 2 , and the ratio Dg/D-L should 
approach 2 upon excitation with D^ . Thes? expectations were 
confirmed within the limits of experimental error in the case 
of the inert gases. In the case of nitrogen and of hydrogen, the 
results were influenced by quenching. The resonance lamp was 
so constructed that a layer of unexcited sodium atoms lay 
between the emitting layer and the exit window, which, by 
absorbing the two D lines unequally, was partly responsible 
for the failure of the experimental ratios to reach completely 
their theoretical values. Control experiments showed the 
effect of this absorbing layer as well as the effect of diffused 
resonance radiation. In Fig. 58, the ratio of the intensity of 
the D! line to that of the D 2 line is plotted against the argon 
pressure, when the exciting light was D 2 , and when the 
absorption within the resonance lamp was reduced to a 
minimum. It is seen that the ratio approaches the theoretical 
value 1/2 at high argon pressures. From the initial portion of 
the curve it is possible to estimate the effective cross-section 
associated with the process 3 2 P 3/2 -^ 3*?^ caused by collisions 
with argon. The value of o- 2 for this process is very roughly 
40 x 1C- 16 , whereas for the process 3 2 P 1/2 - 3 2 P 3/2 it is roughly 



INVOLVING EXCITED ATOMS 215 

18 x 10~ 16 . In the case of a neon-helium mixture, the two 
values of a 2 are also approximately in the ratio of 2 to 1. 

106. COLLISIONS CONNECTED WITH PHOTO-IONIZATION. It 
was first shown by Mohler, Poote and Chenault[64] that an 
ionization current was established in caesium vapour when it 
was illuminated by various lines in the principal series of the 
caesium spectrum. Similar results were obtained by Lawrence 



0-7- 



0*6- 




24 



28 



8 12 16 20 

Argon pressure in mm. 

Fig. 58. Effect of argon in causing the emission of Dj when sodium 
vapour is illuminated with D 2 . 

and Edlefsen [45] with rubidium vapour illuminated by rubi 
dium lines. It was at first assumed that an excited atom, 
formed by line absorption, received sufficient energy during a 
collision with a normal atom to ionize it. Thus: 

Cs (m 2 P) + Cs= Cs+ + Cs + e, 

where the Cs (m 2 P) atom is produced by the absorption of the 
caesium line 6*Sy$-m 2 P. Although this collision process is 
reasonable in the case of an atom excited to a state within a 



216 



COLLISION PBOCESSES 



few hundredths of a volt of ionization (such as 15 2 P or higher), 
it is improbable when m =* 8 or 9, since the number of collisions 
involving the requisite amount of energy is too small to account 
for the observed photo-ionization. The explanation therefore 
was advanced by Franck and Jordan that a collision between 
an excited atom and a normal atom resulted in the formation 
of a molecular ion and an electron. This explanation was borne 
out by further investigations of photo-ionization in caesium 
vapour by Mohler and Boeckner[66]. According to this point 
of view, the photo-ionization process consists of two parts, the 
collision process 

Cs=(CsCs)', 



where the dash indicates a high electronic level of the molecule, 
and then the spontaneous process 



The first of these processes would be expected to depend on the 
pressure and the second to be independent of the pressure. On 
the basis of photo-ionization experiments in caesium vapour, 
Mohler and Boeckner were able to calculate roughly the pro 
duct of the lifetime of a caesium atom, r, and the effective 
cross-section, o- 2 , associated with the collision in which an 
excited molecule is formed. The probability of ionization of an 
excited molecule, E c , was found to be independent of pressure. 

TABLE XXIX 



m 


6 2 S 1/2 -w 2 P 


EC 


TO 2 X 10 19 


8 


3888 


0-003 


0-22 


9 


3612 


0-154 


1-0 


10 


3477 


0-26 


M 


11 


3398 


0-40 


1-1 


12 


3347 


0-50 


1-0 


13, 14 


3300 


0-77 


1-2 


16, 17 


3250 


0-89 


3-3 


20 


3225 


0-93 


16 


29 


3200 


1-00 


48 



The values of rcr 2 and E c are given for nine different wave 
lengths in Table XXIX. Since the various r's are not known, 
the absolute values of the effective cross-sections cannot be 



INVOLVING EXCITED ATOMS 217 

calculated. A rough estimate of r, however, seems to indicate 
that a is large compared with usual atomic dimensions. 

In the presence of a foreign gas the photo-ionization was 
found to be diminished. This was explained by Mohler and 
Boeckner[67] on the basis of collisions of the type 



where F is a foreign gas molecule and n 2 P is a lower excited 
state. From measurements of the diminution of photo- 
ionization by foreign gases, it was possible to estimate the 
effective cross-section associated with the above collision, and 
it was found in the case of argon, helium, nitrogen and hydro 
gen to be very nearly the gas-kinetic value. 

lOc. COLLISIONS INVOLVING THE ENHANCEMENT OF SPARK 
LINES. The statement was made in Chap, I, in connection 
with sources for exciting resonance radiation, that an inert gas, 
in which an electric discharge is maintained, is very effective 
in exciting the atoms of an admixed vapour. This phenomenon 
was described at greater length in Chap, n under the heading 
" Sensitized Fluorescence". The collision process in question 
is an example of a collision of the second kind between an 
excited inert gas atom and a normal atom, in which the normal 
atom is raised to a level from which it can radiate. Upon com 
paring the spectral lines emitted by the admixed vapour with 
the normal arc spectrum of the vapour, a qualitative estimate 
of the effectiveness of the sensitizing collisions is obtained. 
Recently, a series of experiments have been performed by 
Duffendack and Thomson [16] which can be interpreted quanti 
tatively and which yield relative values of effective cross- 
sections . In these experiments, the relative intensities of certain 
spark lines of silver, gold, aluminium and copper, emitted by 
reason of impacts with helium and neon ions, was measured 
and compared with the relative intensities of the same lines 
emitted by a condensed spark. The ratio of the intensities of a 
group of lines originating from the same upper level under 
these two conditions was called the "enhancement", and was 
used as a measure of the effectiveness of the sensitizing colli 
sion. A typical collision of this type is as follows : 



218 



COLLISION PROCESSES 



and Table XXX explains how the enhancement for this 
collision was calculated. 

TABLE XXX 



Copper 
line 


Initial 
level 


Normal 
intensity 


Intensity 
in neon 


Enhance 
ment 


2485-95 
2590-68 


(d^Di 


4-3 
2-1 


57 
32 


13-2 
15-2 


2703-34 




3-8 


57 


15-0 


2721-84 




1-9 


27 


14-7 










(Aver.) 14-6 



In Tables XXXI and XXXII are given a number of results 
which will be discussed from the standpoint of quantum theory 
in the next section. 

TABLE XXXI 

COPPER ION LEVELS EXCITED BY NEON IONS 



Copper ion level 
Cu+(ds) 


Relative enhance 
ment by neon ions 


Energy discrepancy 
in volts 


'Da 
D, 
'D, 
^ 


1-0 

2-7 
14-6 
9-7 


0-40 
0-36 
0-16 
0-12 



TABLE XXXII 

ALtfMINIUM ION LEVELS EXCITED BY NEON IONS 



Aluminium 
ion level 


Relative enhance 
ment by neon ions 


Energy discrepancy 
in volts 


5 1 ? 

3 P 

4 iF 
4 3 F 


12-2 
>30 
1-0 
2-6 


0-022 
0-003 

0-27 
0-28 



11. THEORETICAL INTERPRETATION OF 
QUENCHING COLLISIONS 

11 a. GENERAL PRINCIPLES. Collision processes involving 
an interchange of excitation energy between the two colliding 
particles have been of considerable interest to theoretical 
physicists, since the publication in 1929 of an important paper 



INVOLVING EXCITED ATOMS 219 

on the subject by Kallmann and London [32]. Later papers by 
Morse and Stueckelberg[69], Rice [82, 83], Zener [117], London [50], 
Landau [43, 44], Morse pro], and Stueckelberg[94], have all con 
tained applications of various methods of the quantum 
mechanics to collisions of this type, with varying degrees of 
success, depending upon the validity of the assumptions that 
were made. A brief survey of the various collision processes 
that have been dealt with in the preceding sections and in 
Chap, n will show such a wide range in regard to type, nature 
of interaction between colliding partners, amount of energy 
transferred, etc., that it is not surprising that the whole range 
has not been embraced completely by one theory. Certain 
general principles, however, stand out as being fundamental 
in all these treatments, and will be found to be adequate to 
interpret some of the existing experimental results. From a 
quantum-mechanical standpoint, a collision of the second kind 
is a special case of the general problem of the molecule. A colli 
sion is regarded as the temporary formation of a quasi-mole- 
cule, and the Franck-Condon curves of this molecule, repre 
senting conditions before and after collision, play the main role 
in the theoretical calculation. In general, the effective cross- 
section associated with a particular collision process depends 
upon (1) the relative kinetic energy before impact, (2) the law 
of interaction between the two systems, and (3) the difference 
between the relative kinetic energies before and after impact. 
The dependence of effective cross-section upon relative 
kinetic energy before impact is shown in Figs. 55 and 56, and 
in Table XXVIII, in connection with excited sodium and 
excited thallium atoms. It is seen that the effective cross- 
section at first decreases, and then seems to increase as the 
velocity of the excited atom increases. These curves are the 
analogue of the Ramsauer curves for electrons. According to 
Morse [70], the decreasing part of these curves is in agreement 
with theory, but the theory does not predict a rise in effective 
cross-section at high velocities. Instead, it is consistent with 
the theory that, at low velocities, <r 2 should attain a maximum, 
and at still lower velocities, decrease. This effect has not yet 
been observed. Both the theory and the experimental results 



220 COLLISION PEOCESSES 

are in too undeveloped a state to warrant any further dis 
cussion. 

It has already been mentioned in Chap, n that the conditions 
favouring a collision of the second kind are (1) the difference 
in the relative kinetic energies before and after impact (which 
must equal the difference between the energy that one system 
has to give up and the energy that the other system can take, 
and which is therefore termed by Duffendack the " energy 
discrepancy") should be as small as possible, and (2) the total 
spin angular momentum of both systems should be conserved 
(known as Wigner's rule). The experiments of Cario, Beutler, 
and many others, discussed in Chap, n, illustrate how colli 
sions giving rise to sensitized fluorescence satisfy these prin 
ciples. The method of sensitized fluorescence is particularly 
well adapted to the study of these points, because it allows 
only the energy discrepancy to be varied, while the other 
factors remain fairly constant. The energy discrepancy can 
be accurately calculated in such experiments, because the 
colliding systems are atoms whose energy levels are completely 
known. In collisions involving sensitized fluorescence, how 
ever, it is difficult to estimate effective cross-sections. The 
results given in Chap, n, therefore, had to be discussed in a 
qualitative manner. 

116. ENHANCEMENT OF COPPER AND ALUMINIUM IONIC 
LEVELS. The experiments of Duffendack and Thomson on the 
enhancement of copper and aluminium spark lines by neon 
ions, described in 10c, allow a more quantitative inter 
pretation than the experiments on sensitized fluorescence in 
Chap. u. The " enhancement", as defined by Duffendack and 
Thomson, can be regarded as roughly proportional to the 
effective cross-section associated with the collision process 



In the third column of Tables XXXI and XXXII are given 
the values of the energy discrepancy corresponding to each 
ionic level that was excited. The relation between enhance 
ment and energy discrepancy is shown graphically in Fig. 59. 

It is clear from the figure that the triplet levels of both copper 



INVOLVING EXCITED ATOMS 221 

and aluminium are excited more strongly than the correspond 
ing singlet levels. Taking all the triplet levels together, it is 
seen that the enhancement increases as the energy discrepancy 
decreases. The same is true for all the singlet levels. These two 
results are in accord with all previous work on sensitized 
fluorescence. The preference of the triplet levels over singlet 
levels with smaller energy discrepancy is, however, not in 



25 



20 

+3 


a 

8 
I 15h 



Copper Levels 
Aluminium Levels 



07),. 

">[- 'D 2 

5- 



O 3 D 



"0 0-1 0-2 0-3 0-4 

Energy discrepancy in volts 

Fig. 59. Relation between enhancement and energy discrepancy. 

accord with Wigner's rule concerning conservation of spin 
angular momentum. It is difficult to say whether this con 
stitutes a serious objection to Wigner's rule or not. 

lie. ENERGY INTERCHANGE WITH MOLECULES. It has 
been mentioned that, in experiments on sensitized fluorescence, 
although the energy discrepancy can be determined un 
ambiguously, the absolute value of the effective cross-section 
cannot. Just the opposite is true of experiments on the quench- 



222 



COLLISION PROCESSES 



ing of resonance radiation. Although the effective cross- 
sections associated with the quenching of mercury, sodium 
and thallium resonance radiation can be regarded as known 
with a fair degree of accuracy, it is not always possible to 
decide precisely what transition the excited atom or the 
foreign gas molecule performs. One reason for this lies in our 
ignorance of the energy levels of some molecules. The vibra- 
tional levels of the higher electronic states of the Nal, Til and 

TABLI; XXXIII 



Atom 



Hg 

Na 

Tl 

Cd 

I 

Br 



Transition 



Energy 
in volts 



0-218 

2-306 
0-0669 
0-758 
0455 



Transition 



3 2 P->3 2 S 1 



Energy 
in volts 



4-862 
2-094 
3-267 
3-783 
6-741 
7-82 



TABLE XXXIV 



Molecule 


Energy of dissociation 
into normal atoms 
in volts 


Molecule 


Energy of dissociation 
into normal atoms 
in volts 


H2 

2 
H 2 

I* 
Br 2 


4-44 
5-09 
5-05 
(H 2 = OH+H) 
1-54 
1-96 


NaH 
CdH 
HgH 
Nal 
TU 
NaBr 


2-25 
0-67 
0-369 
2-98 
2-61 
3-66 



NaBr molecules, for example, are unknown. There are some 
cases where two or three different processes seem to be equally 
suited to explain quenching. In these cases, there is always 
the possibility that all the processes occur, and that the 
measured effective cross-section is only an average value. In 
order to calculate the energy discrepancy in quenching colli 
sions by molecules, it is necessary to know the energy that the 
excited atom can give up, and, in some cases, the energy 
necessary to dissociate the molecule. These quantities are 
given for convenient reference in Tables XXXIII and XXXIV. 
It is also necessary to know the energies of those vibrational 



INVOLVING EXCITED ATOMS 223 

levels of a molecule which lie nearest to some given value. 
These will be found throughout the next four tables. Knowing 
the heat of dissociation and the energies of various vibrational 
levels of the hydrogen molecule, Kaplan [33] was able to explain 
the experiments of Bonhoeffer[9] and Mohler[65] on the ex 
citation of spectral lines by recombining hydrogen atoms. 
These experiments indicate that, when two hydrogen atoms 
combine to form H 2 in the presence of various metals, certain 
spectral lines of these metals are excited. In most cases it 
was possible to connect the intensity of a spectral line with the 
difference between the heat of recombination and the energy 
of a vibrational level. This difference was the energy effective 
in exciting the line. This energy minus the excitation energy of 
the line then constituted the energy discrepancy. In agreement 
with the ideas of quantum mechanics, the smaller the energy 
discrepancy was, the larger was found the intensity of the line. 

lid. COLLISIONS WITH EXCITED MERCURY ATOMS. The inter 
pretation of experiments on the quenching of mercury reso 
nance radiation may be best discussed in connection with 
Table XXXV, in which the various possible quenching pro 
cesses are listed. The behaviour of CH 4 , CO and N 2 seems to 
indicate that the mercury atom is lowered to the 6 3 P state in 
causing the transition of the molecule from the zero vibra 
tional state to the first vibrational state of the normal elec 
tronic level. None of the molecules has an electronic level near 
4*86 volts, and, although a high vibrational level may lie near 
this value, a transition to such a high level does not seem 
probable. In the case of quenching by hydrogen, on the 
other hand, it appears that the mercury atom gives up all of 
its energy. A complete discussion of this point was given in 
Chap. n. 

In the case of H 2 0, three possibilities are shown in the table. 
The first certainly exists, because H 2 molecules are known 
to be very effective in producing metastable mercury atoms. 
The other two processes are energetically possible. The be 
haviour of NO is very interesting, in that its effective cross- 
section is the second largest listed in the table. This value was 



224 



COLLISION PROCESSES 



obtained by Bates, who considers that both processes listed in 
the table are possible. This view was confirmed by the work of 
Noyes[73], 

As regards the quenching of C0 2 and NH 3 , there is not 
sufficient evidence to enable one to distinguish between the 
processes listed in the table. The explanation of the quenching 
of mercury resonance radiation by 2 is still in doubt. Of the 

TABLE XXXV 

[Hg' denotes 6^; Hg w denotes 6 3 P ; ( ) v denotes a vibrational level 
of the normal electronic state; chemical symbols alone denote the normal 
state.] 



Foreign 

gas 
mole 
cule 



Possible quenching 
process 



Energy 
avail 
able 
volts 



Energy 

required 

volts 



Energy 
discre 
pancy 
volts 



cm. 2 
xlO 16 



CH 4 
CO 

N 2 
H 2 



Hg'+H 2 = 



Hg'+H 2 0=H g + OH + H 
Hg'+H 2 0=HgH + OH 



NO 
C0 2 



Hgf + NO^Hg + fNO), 

f +OO!=B|+(OO I ); " 



2 =Hg + + 



C 6 H 6 



2 = (Hg'0 2 ) 
g ' + C 6 H 6 =Hg + C 



218 

218 

218 
4-86 

218 
4-86 
4-86 
+ 0-37 

218 
4-86 

218 
4-86 

218 
4-86 
4-86 
4-86 
4-86 

4-86 



161 
265 
288 

4-44 
197 

5-05 

5-05 

231 
4-90 

238 
5-50 

202 
4-90(?) 
5-09 
4-86 
4-90 



+ 057 
-047 
-070 
+ 42 
+ 021 
-19 
+ 18 

-013 
-04 
-020 
-64 
+ 016 
-04 
-23 

-04 



0852 
5-82 

274 
8-60 
1-43 
1-43 
1-43 

35-3 
35-3 
3-54 
3-54 
4-20 
4-20 
19-9 
19-9 
19-9 
19-9 
60 



four processes listed in the table the second was suggested by 
Mitchell [63], the third by Bates [7] and the fourth by Noyes [72]. 
Some of these processes were discussed in Chap, n in connec 
tion with the formation of ozone. The quenching ability of 
C 6 H 6 was explained by Bates as being due to the removal of a 
hydrogen atom. 

In the case of those molecules which are either known to 
produce metastable mercury atoms, or which have a first 



INVOLVING EXCITED ATOMS 225 

vibrational state near enough to 0-218 volt to make this a 
possibility, the variation of effective cross-section with energy 
discrepancy is instructive. In Fig. 60, the effective cross- 
section is plotted against the energy of the first vibrational 
state. No curve can be drawn through the points because the 



35 



30 



o25 
x 

en 

i 

.a 20 

I 

o 

* 

1 15 



10 



NH 3 
O 



CH 4 



H 2 
O 



NO 

G 



C0 2 
O 



CO 

o 



0-15 



0-20 



0-218 



0-25 



0-30 



Fig. 60. Relation between effective cross-section and energy discrepancy. 

law of interaction between the excited mercury atom and the 
foreign molecule is different in each case. The effective cross- 
section, therefore, is not a function of the energy discrepancy 
only. Nevertheless the points in Kg. 60 show quite definitely 
that large effective cross-sections are associated with small 
energy discrepancies. 

lie. COLLISIONS WITH EXCITED CADMIUM ATOMS. In re 
gard to the quenching of excited cadmium atoms by N 2 and 



226 



COLLISION PROCESSES 



CO, one can be fairly certain of the collision processes that take 
place. These are shown in Table XXXVI. 

It is not reasonable to regard the cadnaium transition 
5*T?i->5*PQ, which must, of course, take place frequently, as 
a quenching process, in view of the fact that the converse tran 
sition 5 3 P -> 5 3 P 1 also takes place very often. In order that 
cadmium resonance radiation be quenched, it is quite likely 
that the 5 3 P 1 atoms must be brought all the way to the normal 
level. Two possibilities are present to explain the quenching 
ability of H 2 . The first, involving the formation of the CdH 
molecule, is almost certain to take place, not only because the 

TABLE XXXVI 

[Cdf denotes 5 3 Pi, Cd denotes 5 1 S , ( ) v denotes a vibrational level of 
the normal electronic state.] 



Foreign 
gas 
molecule 


Possible quenching 
process 


Energy 
available 
volts 


Energy 
required 
volts 


Energy 
discrepancy 
volts 


N 2 
CO 
H, 

S, 


Od'+N a =Cd + (N t ), 
Cd / + CO=Cd+(CO) t , 
Cd' + H 2 = CdH4-H 

Cd' + H 2 =Cd + (H 2 ) i; 


3-783 
3-783 
3-783 
+ -67 
3-783 


4-44 

About 
3-84 


+ 013 
-06 



energy discrepancy is so small, but also because the CdH band 
spectrum was observed by Bender in mixtures of cadmium 
vapour and H 2 . The second process has been included merely 
because it is energetically possible, with a small energy 
discrepancy. 

1 1/. COLLISIONS WITH EXCITED SODIUM ATOMS. The possible 
quenching processes involved in collisions between excited 
sodium atoms and foreign gas molecules are shown in Table 
XXXVII. The behaviour of N 2 , CO and C0 2 is fairly certain. 
N 2 and CO have vibrational levels in the neighbourhood of 
2-094 volts, and it is reasonable to assume the same for CO 2 . 
According to the energy discrepancies, CO ought to have a 
larger effective cross-section than N 2 , but this is not the case. 
The disagreement, however, is not serious. With H 2 , the two 



INVOLVING EXCITED ATOMS 227 

processes listed in the table are about equally reasonable from 
the standpoint both of possibility and of energy discrepancy. 
Of the three processes listed for I 2 , the first is the least reason 
able. The vibrational levels of the first excited electronic level 
of I 2 lie between 1-92 and 2-77 volts, so that the energy dis- 

TABLB XXXVII 

[Na' denotes 3 2 P; ( ) and ( )/ denote a vibrational level of the normal 
and of an excited electronic state respectively; a chemical symbol alone denotes 
the normal state. I m refers to the metastable 2 P 1/2 state.] 



Foreign 
gas 
mole 
cule 


Possible quenching 
process 


Energy 
avail 
able 
volts 


Energy 
required 
volts 


Energy 
dis 
crepancy 
volts 


*t 
cm. 2 x 10 16 


N 2 


Na'+N^Na+fNJ, 


2-094 


1-94 or 


+ 15 or 


-6 








2-20 


-11 




CO 


Na' + CO=Na + (CO)<, 


2-094 


2-03 or 


+ 06 or 


-4 








2-26 


--17 




C0 2 


Na' + CO t =Na+(CO ), 


2-094 







-15 


H 2 


Na' + H t =Na+(H t ) 1 , 


2-094 


1-93 or 


+ 16 or 


-6 








2-34 


-25 







Na' + E^NaH+H 


2-094 


4-44 


-10 


-6 






+ 2-25 








i* 


Na' + I 2 =Na+I m +I 


2-094 


1-54 


-21 


-40 








+0-76 






> 


Na' + I^Na + ft)/ 


2-094 


Between 





-40 








1-92 and 2-77 









Na'+I 2 =(NaI) t , / +I 


2-094 


1-54 





-40 






+2-98 


+ ? 






Br s 


Na' + Br 2 =Na + Br + Br 


2-094 


1-96 


+ 13 


-100 





Na' + Br 2 =Na + (Br 2 )/ 


2-094 


Between 





-100 








1-93 and 2-39 









Na' + Br 2 =(NaBr)/ 


2-094 


1-96 





-100 






+ 3-66 


+ ? 






I 


Na' + I=(NaI) r ' 


2-094 


? 





-40 






+2-98 









crepancy in the second process would presumably be quite 
small. The third process is preferred by Terenin and Prile- 
shajewa, but without a knowledge of the vibrational levels of 
the excited electronic states of Nal the energy discrepancy 
cannot be calculated. Similarly, in the case of Br 2 , the second 
and third processes are more reasonable than the first, for 
reasons similar to those given for I 2 . In the case of I, nothing 
of a definite character can be said, except that a theoretical 



228 COLLISION PROCESSES 

calculation of the effective cross-section to be expected for 
such a process, made by Terenin and Prileshajewa[97], yields 
a value about a million times smaller than the measured value, 

110. COLLISIONS WITH EXCITED THALLIUM ATOMS. The 
possible collisions between excited thallium atoms and I 2 and 
I are given in Table XXXVIII. 

Of the four processes listed in connection with I 2 , the first is 
preferred, because of its extraordinarily small energy dis 
crepancy. The second process is also very reasonable and would 

TABLE XXXVIII 

[TT denotes 7 2 S 1/2 ; Tl m denotes 6 2 P 3/2 ; I m denotes the metastable 2 P 1/2 state; 
( )' refers to a vibrational level of an excited electronic state.] 



Foreign 
gas 
molecule 


Possible quenching 
process 


Energy 
avail 
able 
volts 


Energy 
required 
volts 


Energy 
discrepancy 

volts 


cm.* x 10 16 


j 


Tl / +I 2 =Tl m +I TO +I 


2-306 


1-54 


+ 008 


-70 








+ 758 








Tr+i =TI+I +i 


3-267 


1-54 


+ 21 


-70 


" 


tn m 




+ 76 + -76 









Ti'+i 2 =Ti TO +(i 2 y 


2-306 


Between 
1-92 and 2-77 





-70 


fj 


Tr+i 2 =(Tii)/+i 


3-267 


1-54 





-70 






+ 2-61 


+ ? 






1 


Tr+i=(Tii)/ 


3-267 


9 





-30 






+ 2-61 









presumably have a very small energy discrepancy. The third 
and fourth processes involve the emission of a band spectrum 
as fluorescence. The fact that Prileshajewa did not observe any 
fluorescent bands is an objection to these processes. This point, 
however, is not completely settled. In connection with the 
behaviour of I, the same objection that was made before for 
this kind of process holds here. Theoretically, it should have 
an effective cross-section of about 10~ 22 cm., whereas the 
measured value is about a million times larger. 

12. RAPIDITY OF ESCAPE OF DIFFUSED RESONANCE 
RADIATION FROM A GAS 

12a. EXPERIMENTS WITH MERCCTRY VAPOUR AT Low 
PRESSURES. In Chap, m the experiments of Webb and 



INVOLVING EXCITED ATOMS 229 

Messenger [ioi] and those of Garrett[23] were described in con 
nection with their significance as measurements of the lifetime 
of the 6 3 P X state of the mercury atom. It was emphasized that 
the decay constant of the exponential curve, representing the 
decay of the resonance radiation emitted by mercury vapour, 
could be interpreted as the Einstein A coefficient (1/r), only if 
the vapour pressure was so low that the diffusion of the reso 
nance radiation, through repeated absorptions and emissions, 
could be neglected. When this is not the case, the lifetime of 



10-O 




Fig. 61. Eelation between decay constant of escaping mercury resonance 
radiation and vapour pressure. 

(Vapour pressure range from to about 0-001 mm.) 

the radiation escaping from the mercury vapour is consider 
ably longer than the lifetime of an atom. This is shown in 
Fig. 61, where the exponential constant of decay of the radia 
tion, j8, in sec." 1 , is plotted against the expression -ZVZ/Av^, 
where N is the number of absorbing atoms, Z the thickness of 
the layer of mercury vapour and Ai/^ the Doppler breadth 
of the diffusing radiation. Since I is constant and Av^ varies 
only slightly in the temperature range covered by Webb and 
Messenger's results, the quantity Nlj^v^ is very nearly pro 
portional to the vapour pressure. The decrease in ft as the 
vapour pressure increases from zero to about 0-001 mm. in- 



230 COLLISION PROCESSES 

dicates the increase in the lifetime of the escaping radiation. 
To explain these results it is necessary to make use of Milne's 
theory, which was introduced in 8 of this chapter. 

126. MILNE'S THEORY. Imagine an infinite slab of gas 
bounded by the planes x = and x = I. Suppose the gas has been 
excited for a while and, when t = 0, there is a distribution of 
excited atoms, n a , depending on x, thus n 2 =f(x). Due to re 
peated absorptions and emissions from moving atoms, the 
radiation diffusing through the gas will have a Doppler distri 
bution. Calling the equivalent absorption coefficient of the 
gas for this radiation k, and the lifetime of the excited atoms r, 
the concentration of excited atoms at any point and at any 
time after the excitation has been removed is given by 

S 2 



and the net forward and backward fluxes of radiation are 
represented respectively by 

...... <> 



In these expressions dn 2 /dt represents the total rate of 
change of excited atoms due to the three Einstein processes, 
since there is no other process of formation after the cut-off of 
the excitation, and no other process of decay in the absence of 
impacts of the second kind. The problem is to calculate TT/+ at 
x = I on the basis of the boundary conditions 

(1) 



(2) when>0, / + = 0atx = 0; 

(3) when>0, J_ = Oatz = Z. 

It was shown by Milne [59] that the radiation escaping from the 
face x = I could be represented by a series of the form 

(150), 



INVOLVING EXCITED ATOMS 231 

where the A' a depend upon the original distribution of excited 
atoms when Z= 0, and the jS's are given by 

o_ 1/r 



1+ r 



(151).. 



(152). 



where A,- is the ith root of the equation 

ll 

~y 

It can be shown that j8 a , j8 8 , etc., are aU larger than & , and that 
fizt, j8 8 *, etc., are so large when t is of the order of 10~ 4 sec. or 
more, that all terms except the first can be neglected. Milne's 

TABLE XXXIX 



Temp. 
K. 


Av D x 10~ 9 
=5-97xl0 7 V? 


N x 10~ 13 


Nl 

A^ 
xlO~ 4 


V = l-33 
x!0-^ 

&V D 


kl 
(Samson) 


jSxlO- 6 
Theor. 


^xlO- 6 
Exp. 


254 


95 


078 


15 


20 


16 


8-0 


10 


263 


97 


22 


41 


55 


38 


6-5 


6-3 


273 


99 


66 


1-2 


1-6 


1-0 


3-8 


5 


280 


1-00 


1-3 


2-3 


3-1 


1-8 


2-3 


2-3 


290 


1-02 


3-1 


5-5 


7-3 


2-9 


1-3 


1-3 


295 


1-03 


4-7 


8-3 


11-1 


3-5 


1-05 


75 



result is therefore as follows: After a time has elapsed, the 
radiation escaping from a gas decays exponentially with the 
time, with an exponential constant, /?, given by 



where A x is the first root of Eq. (152). 

In order to compare Webb and Messenger's results with 
Milne's theory, it is necessary to calculate kl at the various 
vapour pressures in the experimental range. This is done by 
Samson's method and is described in detail in 8c. Table 
XXXIX contains the theoretical values of j8 along with Webb 
and Messenger's experimental results, and the heavy curve in 
Fig. 62 is a graph of the theoretical results. It must be em 
phasized that the experimental tube of Webb and Messenger 



232 



COLLISION PROCESSES 



was only a very rough experimental approximation to an 
infinite slab, and, in the absence of an accurate knowledge of 
the thickness of the mercury vapour layer, a value of I equal 
to 1-8 cm. was chosen for purposes of calculation. The agree 
ment is satisfactory in view of the lack of correspondence 



I 

i-H J'} 

X ^ L 

eB* ?O 

'S 

* 18 

8 

!l6 
8 
a 14 
3 l4 



a 12 

H 


\ 






























4 








































































































1-95cm.cell 
1-30cnucell 












1 




















\ 


























































1 ' 


L 




















^x 


^ 


^X) 






\ 












^ 


sr- 


-^ 


^ 


'^ 








\ 




V 


- 


c 


^ 


***'**' 

^-^ 


^^ 


*** 












Ofttf 


f 


Jfr- 


"lod 


. - 


^-* 

lii 


* 






,M> 










130' 



4 6 8 10 12 14 16 18 20 22 24 26 28 

Number of atoms per c.c. ( x 10~ 15 ) 

Fig. 62. Decay of Hg resonance radiation escaping from mercury vapour. 
(Vapour pressure range from 0-01 to 1 mm.) 

between the experimental conditions and those postulated by 
the theory. The discrepancy between the experimental and 
theoretical values of j8 at the highest temperature, where Jc Q l 
is 1M, may be due partly to the inadequacy of Samson's 
method of calculating the equivalent opacity at this vapour 
pressure. 

12 c. EXPERIMENTS WITH MERCURY VAPOUR AT HIGHER 
PRESSURES. The rapidity of escape of mercury resonance 



INVOLVING EXCITED ATOMS 233 

radiation from a slab of mercury vapour after the cut-off of 
the excitation, was measured by Webb[ioo] and by Hayner[2T] 
by an electrical method. A repetition of this experiment with 
optical excitation was made by Zemansky[iii] for vapour 
pressures ranging from about 0-01 mm. to 1 mm., and with two 
different thicknesses of the mercury layer, l-95cm. and l-30cm. 
The results of Zemansky indicated a rapid increase in the 
lifetime of the radiation in the pressure range 0-01 to about 
0-3 mm., and then a slower decrease in lifetime from 0-3 to 
1 mm. In terms of /?, the exponential constant of decay, this 
means first a decrease and then an increase, as shown in Pig. 62. 
The interpretation of these experiments is not yet certain. 
A discussion of the left-hand part of the curves (decreasing /?), 
separate from that of the right-hand part, will tend to point 
out more clearly the nature of the problem. In regard to this 
left-hand part, there are two theories : ( 1 ) that the fundamental 
process at hand is the diffusion of resonance radiation com 
posed of those frequencies that are absorbed and emitted by 
virtue of the Doppler effect; (2) that collisions between excited 
6^ atoms and normal atoms produce metastable 6 3 P atoms 
which, in diffusing through the mercury vapour, either reach 
the walls and give up their energy, or are knocked up again to 
the 6^ state from which they radiate. 

On the basis of the first theory, Milne's theory gives the 
same result as in Webb and Messenger's experiments, namely 



_ 

with the distinction that k, in this case, is the equivalent 
absorption coefficient at high vapour pressure, where Samson's 
method of calculation would not be expected to hold, and A 1? 
under these conditions, is very nearly equal to 7r/2. 

12 d. EQUIVALENT OPACITY AT HIGH PRESSURE. At high 
pressures, k can be calculated by a method due to Kenty [34, lie] 
which, in contradistinction to Samson's method, breaks down 
at low pressures. According to Kenty, the motions of both 
emitting and absorbing atoms are assumed to have a Max- 



234 COLLISION PROCESSES 

wellian distribution. The radiation diffusing through a gas is 
then found to have a diffusion coefficient, Z>, given by 

<\/~2i 

where r is the lifetime of the excited state, I the thickness of 
the layer of gas, & the absorption coefficient at the centre of 
the line, and 

(156). 



TABLE XL 



Temp. 
K. 


N x 10~ 15 


-*>* 

&V D 


V 


kl 
(Kenty) 


P 
Theor. 


P 
Exp. 


333 


-770 


1-38 


183 


30 


29500 


26600 


343 


1-40 


1-64 


218 


33 


24500 


28100 


343 


1-40 


2-46 


327 


42 


15000 


14200 


353 


2-50 


2-90 


386 


47 


12000 


19300 


353 


2-50 


4-35 


578 


58 


7940 


8810 


363 


4-40 


5-02 


668 


63 


6750 


12100 


363 


4-40 


7-53 


1000 


78 


4380 


7070 



On the basis of Mine's theory, the diffusion coefficient of 
radiation for which the absorption coefficient is k is equal to 

(157). 



Equating the two expressions for the diffusion coefficient, the 
equivalent opacity M, at high pressures, is found to be 



kl-- 



3 ITT 

4V 2 



(158). 



A table of values of kl for many values of k 1 will be found in the 
Appendix. In Table XL, the experimental values of ft (corre 
sponding to the left-hand part of the experimental curves) are 
compared to the theoretical values calculated by Milne's theory 
with the aid of ELenty's equivalent opacity. The agreement is 
seen to be satisfactory enough at least to lend credence to the 
theory of radiation diffusion. 



INVOLVING EXCITED ATOMS 235 

Now, on the basis of the theory of metastable atom diffusion, 
it was shown by Zemansky [113] that the left-hand part of the 
curve could be represented by 



where the constant depends on the velocity of the atoms and 
the geometry of the layer of vapour, and a d 2 can be regarded as 
an effective cross-section for diffusion. This was shown to agree 
well with the shape of the curve, and enabled a value of 
v d to be inferred from the experiments. The resulting value, 
2-3 x 10~ 8 cm., is remarkable in that it is smaller than the usual 
"gas-kinetic value", 3*6 x 10~ 8 cm. This result, by itself, does 
not constitute a serious objection to the metastable atom 
theory, since effective cross-sections for various processes 
depend upon the nature of the processes and can be expected 
to vary from very small to very large values. A much more 
serious objection to the metastable atom theory was pointed 
out by Kenty[34], namely, the doubt as to the existence of 
sufficient metastable atoms to give rise, by being raised to the 
6 3 P X state, to a measurable amount of radiation. The formation 
of a metastable atom would depend upon a collision of the type 



and the production of radiation would involve the two 
processes 



For the transition 3 P 1 -> 3 P , 0-218 volt of excitation energy 
must go into relative kinetic energy of the colliding partners, 
since a normal mercury atom has no energy level lower than 
4-7 volts. In other words, the ability of normal mercury atoms 
to effect this transition ought to be about the same as the 
ability on the part of inert gas atoms to perform the same 
transition. From experiments on the quenching of mercury 
resonance radiation, it is found that the inert gases do not 
quench at all, or if they do, to a very small extent. Moreover, 
from theoretical considerations, the probability of any colli 
sion involving the transfer of 0-218 volt of excitation energy 



236 COLLISION PROCESSES 

into the kinetic energy of the gas is expected to be extremely 
low. Substantially the same objections may be made in con 
nection with the transition 3 P -> 3 P 15 so that it appears ex 
tremely doubtful whether the experiments can be explained 
on the basis of the metastable atom theory. A final decision, 
however, cannot be made without further experimental work. 

In reference to the right-hand portion of the experimental 
curves for /?, there are also two possible theories: (1) impacts 
destroying either 3 P X atoms or 3 P , and (2) Holtsmark broad 
ening of the absorption line giving rise to a smaller value of Tel 
than is given by Kenty's formulas, thereby causing /J to in 
crease. It is impossible to decide which of these points of view 
is to be preferred, since they both seem equally suited to 
account for the somewhat slow rise in jB that is observed. The 
whole matter must be left open until further experiments are 
performed, and further theoretical calculations on the effect 
of Holtsmark broadening upon the equivalent opacity are 
made. 

The difficulties that arise in the interpretation of experi 
ments on the decay of radiation from a gas appear also when 
an attempt is made to explain the large currents found at con 
siderable distances from the end of a noble gas discharge. 
According to Kenty[35], resonance radiation is capable of 
diffusing through the gas at a much faster rate than was 
formerly supposed, because the equivalent opacity of the gas 
for the resonance radiation, as calculated on the basis of his 
theory, was small. The observed currents therefore could be 
interpreted as photoelectric currents. An equivalent inter 
pretation, however, has been given by Found and Lang- 
muir[20] on the basis of metastable atoms. Since this subject 
is beyond the scope of this book, the reader is referred to the 
original papers for a more complete discussion. 

13. DIFFUSION AND COLLISIONS OF 
METASTABLE ATOMS 

13a. EABLY WOEK. The first measurements of the life 
time of metastable atoms were made by Meissner [55] and by 
Dorgelo [H], An inert gas in an absorption tube was electricaUy 



INVOLVING EXCITED ATOMS 237 

excited for a while, and then the excitation was stopped. After 
a short time had elapsed, a beam of light, capable of being 
absorbed by metastable atoms (thereby raising the metastable 
atoms to a higher energy level), was sent through the absorp 
tion tube. The length of time beyond which absorption was no 
longer perceptible was measured, and called roughly the life 
time of the metastable atoms. Various methods of starting and 
stopping the excitation of the absorbing gas, and of starting 
and stopping the emitting lamp, were employed. They all had 
the disadvantage that the time between the cut-off of the 
excitation and the passage of the light could not be determined 
accurately enough to yield a reliable curve of decay of absorp 
tion against time. An improvement was made by Dorgelo and 
Washington [15], in that both the absorption tube and the 
emission lamp were operated on A.C. with a constant phase 
difference of 180. The time between the cut-off of the excita 
tion and the absorption of the light was varied by altering the 
frequency of the A.C. These qualitative experiments indicated 
that metastable inert gas atoms lasted approximately a few 
thousandths of a second after the excitation was removed, and 
that the lifetime depended on the gas pressure and temperature. 
Since these early experiments, there have been many in 
vestigations on metastable atoms, which have not only been 
of interest in themselves, but have yielded information of the 
utmost importance in explaining phenomena occurring in gas 
discharges. Before these later experiments can be explained, 
it is advisable to consider first the general theory of the method. 

13&. THEORY OF MEASTJEEMENT WITH INEBT GASES. After 
considering and trying out various methods of exciting an inert 
gas, and of allowing a beam of light to traverse this gas after 
a known time has elapsed after the excitation, Meissner and 
Graffunder [56] finally came to the conclusion that the following 
method was most suitable. Both the emitting lamp and the 
absorption tube were operated with A.C. of the same frequency. 
The generators supplying the A.C. were so arranged that the 
phase of the alternating excitation of the emitting lamp could 
be made to lag behind that of the absorption tube by any 



238 COLLISION PROCESSES 

amount. In this way, a beam of light from the lamp could be 
made to traverse the absorption tube at any desired time after 
the excitation of the absorption tube had ceased. For a detailed 
description of the circuits, the reader is referred to the paper 
of Meissner and Graffunder, and also to a more recent paper 
by Anderson [2], 

The gas pressure in the emitting lamp is made quite small, 
and the current is kept as low as possible. The emitting layer 
is very small, almost a capillary. Under these conditions, it is 
wholly reasonable to assume that the frequency distribution 
of the emission line, arising from a transition from a high level 
to one of the metastable levels, is determined by the Doppler 
effect alone, uninfluenced by self-reversal. The absorption of 
this line by the metastable atoms in the absorption tube is 
measured by a photographic method, and is determined as 
a function of the time which elapses between the cessation of 
the excitation of the absorbing gas, and the passage of the 
absorbable light. The experimental results are expressed in 
the form of a "curve of decay", with absorption, A^ plotted 
as ordinates, and time plotted as abscissas. 

The next step is to translate the curve "A against t" into 
ft n' against t", where n r is the average number of metastable 
atoms per c.c. responsible for the absorption. Although it is 
impossible to calculate n' in absolute magnitude, the quantity 
k l, which contains n', can be calculated on the basis of the 
assumption that both the emission and the absorption lines 
are simple Doppler lines, or, if they show hyperfine structure, 
that they consist of a number of approximately equal, separate, 
Doppler components. Let Jc Q be the absorption coefficient of 
the gas in the absorption tube at the centre of the line (or at 
the centre of each hyperfine-structure component), and I the 
length of the absorption tube. Then the absorption, A l9 is 
given by 



...... (160). 



f co 

J 



The above expression will be recognized as the quantity A^ 



INVOLVING EXCITED ATOMS 239 

defined in Chap. ni 3 4d, with a= 1. From the table of values 
of A 1 given in the Appendix, a graph may be drawn connecting 
log w A 1 and log 10 (10& Z). This curve is shown in Fig. 63, and 
enables one to read off Iog 10 (10& Z) (which is equal to log Cri, 



8r- 



1-6 



^ 
o 

I 1 

0-8 



0-6 



0-4 



0-2- 



0-8 



1-2 



1-4 



1-8 2-0 



Eig. 63. Dependence of absorption on number of absorbing atoms. 

where G is a constant) for any observed value of A^. The 
experimental curve, " A l against t", can therefore be converted 
into a curve of "Iog 10 Cri against t". It will be shown later 
that, when t is large enough, 

..... .(161) 



or 



240 COLLISION PROCESSES 

B 
whence Iog 10 On' = const. - -^~ t ...... (162), 

A'dO 

which shows that the curve "Iog 10 On' against t" should be a 
straight line, whose slope, multiplied by 2-30, is the exponen 
tial constant of decay of the metastable atoms. 

The exponential constant, /3 y may be obtained directly from 
the original experimental curve of " A against t", provided 
one uses only that portion of the experimental curve in which 
A lies between 0-3 and 0-8. For, upon plotting log 10 (10 Z) 
against A l9 it is immediately evident that 

logio (10fc Z) = 0-3 + 1-4^ 3 [0-3 < A l < 0-8], 
and again setting 10& Z equal to CV, 

lgicX = const. 4- 1-4^ [0-3 <A 1 < 0-8], 
Anticipating, as before, 



01 

we get finally 



1 . 42 .3^ [0-3 < -^ < 0-8] ...(163), 

which shows that the original experimental curve of A- 
against t should be a straight line, in the region where A l lies 
between 0-3 and 0-8, whose slope, multiplied by 1-4x2-3, is 
the exponential constant of decay of the metastable atoms. 

13c. EXPERIMENTAL RESULTS WITH NEON, ARGON, AND 
HELIUM. Meissner and Graffunder[56] measured the absorp 
tion of excited neon for the lines 6402 and 6143 as a function 
of the time after excitation and for various values of the neon 
pressure in the absorption tube. It can be seen from Pig. 64 
that the absorption of these lines is determined by the number 
of 3 P 2 atoms. As a matter of fact, aU three 3 P states lie so close 
together that the total energy difference, 0-09 volt, is com 
parable to the average kinetic energy of the gas, JcT, which, at 
300 K., is 0-026 volt. Therefore, after the excitation has 
ceased, transitions occur so frequently among the three states 
that they may be regarded as one state. The experiments 



INVOLVING EXCITED ATOMS 



241 



therefore may be considered to indicate the way in which atoms 
in all three states decrease in number after the excitation has 
ceased. From the experimental curves of A l against t, j3 was 
obtained in the manner described in 136. The values of ft at 
various neon pressures are given in Table XLI. In Fig. 65 a 



J 


^ 


J 

IP 


(^ 


16-77 


3p 1 


sO 


\f\~f\? 






16*58 


3p 




1^' 



2'5 n 





t 

Volts 

Fig. 64. Formation and detection of metastable 3 P 2 neon atoms. 
TABLE XLI 



Neon pressure 
p, in mm. 


Exponential constant 
j8, in sec." 1 


0-24 
0-50 
1-02 
1-42 
2-15 
3-02 
5-60 


6100 
4400 
3500 
2800 
3200 
3900 
5800 



straight line is obtained when p is plotted against^ 2 , showing 
that ft depends on the pressure according to the relation 






242 COLLISION PROCESSES 

where B and C are constants. Meissner and G-raffunder's 
results yield the following values for B and C: S = 2000 and 
(7-1100. 

With apparatus very similar to that used by Meissner and 
Graffunder, Anderson [2] studied the absorption of the argon 
line 7635 by excited argon as a function of the time after 




4 8 12 16 20 24 28 32 

Kg. 65. Dependence of exponential constant on neon pressure. 

excitation, at various argon pressures. It will be seen from 
Fig. 66 that the absorption of 7635 is an indication of the 
number of argon atoms in the metastable 3 P 2 state. Un 
fortunately, Anderson did not give curves of absorption against 
time, and hence /? cannot be calculated by the methods of 13 b. 
The values of j3, given in Table XLII, are therefore slightly 
inaccurate, but can still be used to obtain worth-while in 
formation. Plotting ftp against # 2 for the temperature 300 K., 
all points except the last lie roughly on a straight line, in- 



INVOLVING- EXCITED ATOMS 243 

dicating that Eq. (164) is approximately satisfied with B = 160 
and C = 120. At the temperature 80 K., the curve of pp against 
p 2 is quite a good straight line with the constants 5= 15 and 



- 11*77 



V 



-11-66 

-1 1*56 
-IM9 



Volts 
Fig. 66. Formation and detection of metastable 3 P 2 argon atoms. 



TABLE XLII 



Temp. = 300 K. 


Temp. = 80 K. 


Argon pressure 
p, in mm. 


Exp. constant 
ft 


Argon pressure 
p t in mm. 


Exp. constant 



0-215 
0-42 
0-61 
0-694 
0-805 
1-0 


815 
408 
347 
283 
315 
660 


0-050 
0-080 
0-125 
0-23 
0-36 
0-605 
1-0 


330 
183 
120 
97-6 
84-5 
142 
183 



C = 170. This line is shown in Fig. 67. The fact that Anderson's 
results agree well with Eq. (164) at the low temperature, and 
not so well at the high temperature, may be due to the fact 
that the three 3 P levels of argon are separated more than those 



244 



COLLISION PROCESSES 




0-1 0-2 0-3 0-4 0-5 0-6 0-7 0-8 0-9 1-0 
Fig. 67. Dependence of exponential constant on argon pressure. 
(Temperature 80 K.) 



p n . - _ 


on.ni 


0,1,2 
2 1 Sn~ 


^ 


on. cc 


2\ 


cO 

o 


. 1Q.77 





I 

Volts 
Fig. 68. Formation and detection of metastable 2 3 S X helium atoms. 



INVOLVING EXCITED ATOMS 



245 



of neon, and, at room temperature, they cannot be regarded 
as one composite level as in neon, but that transitions among 
the levels play a role which necessitates a much more com 
plicated formula. At 80 K. these transitions are probably few 
in number ^ and hence the results express the behaviour of 3 P 2 
argon atoms alone. 

With apparatus also similar to that of Meissner and Graff - 
under, Ebbinghaus [17] measured the absorption of the helium 
line 10830 by excited helium as a function of the time after the 
cut-off of the excitation. From Pig. 68 it is clear that the 
absorption of the 10830 line is an indication of the number of 
metastable 2 3 S 1 helium atoms. The experiments can be ex 
pected to yield information concerning the 2 3 S X state alone, 
since there are no other states that lie as close to it as in the 

TABLE XLIII 



Thickness of 


Helium 


Exp. 


absorption 


pressure 


constant 


tube a, in cm. 


p, in mm. 


f 


1-65 


2-5 


810 


1-65 


3-7 


760 


3-0 


3-7 


60^ 



case of neon and argon. Using the method of 136 to calculate 
/? from the experimental curves of A l against t, the values given 
in Table XLIII were obtained. For reasons which will be 
given in the next section, /? can also in this case be expected 
to obey Eq. (164), and the following values of B and C are 
obtained: when a is 1-65, B= 1350 and G = 107; when a is 3-0, 
B -770 and (7=107. 

13d. THEORETICAL INTERPRETATION OF RESULTS WITH 
INERT GASES. The manner in which /? varies with pressure 
gives an immediate clue as to the processes which metastable 
atoms perform in an excited gas after the excitation has been 
removed. The large values of f$ at low pressures indicate the 
rapidity with which metastable atoms diffuse to the walls, 
where they give up their energy. In this region an increase in 
pressure causes a decrease in diffusion rate. At higher pres 
sures, the slowly rising values of /J indicate a collision process 



246 COLLISION PROCESSES 

which either lowers the metastable atom to the normal state 
or raises it to a higher state of short life from which it radiates. 
The experiments that have just been described are capable 
therefore of yielding information concerning the diffusion and 
collision of metastable atoms. To obtain this information it 
is necessary to solve the following problem, which was first 
handled by Meissner and Graffunder [56] and later by Zeman- 
sky[H3]. Consider a cylindrical tube of length I and radius c 
placed with its centre at the origin of cylindrical co-ordinates. 
Suppose that the tube is filled with a gas that has been electric 
ally excited for a while and that a distribution of metastable 
atoms has been set up in the tube. Let the excitation be cut off, 
and let a cylindrical beam of light of radius b, which the meta 
stable atoms are capable of absorbing, traverse the tube. 

We shall make the following assumptions: (1) After the 
excitation has ceased, there is no further rate of formation of 
metastable atoms. (2) Metastable atoms diffuse to the walls 
where they lose their energy. (3) Metastable atoms perform 
impacts with normal atoms which raise the metastable atoms 
to a higher energy level. (4) The rate at which metastable atoms 
are being raised to a higher state by the absorption of the light 
is negligible compared to the rate at which (2) and (3) go on. 

If n represent the number of metastable atoms per c.c., 
then, at any moment after the excitation has ceased, n will be 
given by 

dn ^fi*n 1 dn d*n\ ,, N 

...... (165), 

' 



-,- 

dt 

where D is the diffusion coefficient for metastable atoms, and 
Z is the number of impacts per sec. per metastable atom that 
are effective in raising the metastable atom to a higher 
radiating state. The boundary conditions are : 

when t 0, n ~f(r, x) ; 

!at r = c, 
at x= 1/2, 
at#= +1/2. 

The details of the solution of this problem will be found in the 
paper by Zemansky. The result is that, after a short time has 



INVOLVING EXCITED ATOMS 247 

elapsed, the average number n' of metastable atoms per c.c. 
in- the path of the light beam is 

*' = *o<H* (166), 

where ^f^ + ^Wz (167). 



It will be seen that Eq. (166) is the result that was anticipated 
in 136. 

In the case of a rectangular absorption cell of infinite height, 
of thickness a, and length I, traversed by a beam of light 
travelling in the direction in which I is measured, the problem 
is very similar, and has been solved by Ebbinghaus[iT]. The 
result is that, after a short time has elapsed, the average 
number n' of metastable atoms per c.c. in the path of the light 
beam is again an exponential function of the time, with an 
exponential constant, /3, given by 



...... (168). 

From kinetic theory, the diffusion coefficient is given by 

/BT 

4 N M 
D=^-^=r ...... (169), 

37rV^ d *N V h 

where R is the universal gas constant, M is the molecular 
weight, N is the number of atoms per c.c. through which the 
metastable atoms are diffusing, and <r d 2 the diffusion cross- 
section for a metastable atom. If p represent the pressure in 
mm., Eq. (169) becomes 

FT 

T 

D = 2-25xW-^ 1 - ...... (170). 

<V* P 

Kinetic theory gives for the number of collisions capable of 
raising an atom to a state whose energy is e volts higher, the 
expression 



where a 2 is the cross-section for the process and y is the fraction 



248 COLLISION PROCESSES 

of all collisions of energy greater than e. Two expressions have 
been used for y in the past, namely 



__ _ 

= e kT ...... (172) 



and y =,i + 



but it is not yet clear which is to be preferred. Since, in all 
cases, e is also not definitely known, it seems best to let the 
question remain open, and not to attempt to calculate <r 2 alone, 
but to allow the experiments to yield values of ycr 2 . Writing 
Eq. (171) in terms of pressure, p, in mm., we have 



We are now in a position to give the empirical constants B 
and C a meaning in terms of a d z and ycr 2 . From Eqs. (167), 
(170) and (174), it is clear that j8 obeys the equation given 
empirically in 13 c, namely, 



and, in the case of a cylindrical absorption tube, 




and for the case of a rectangular absorption tube, 

T 



and in both cases, 



In Table XLIV all the experimental quantities are given 
which, with the aid of the above equations, enable us to 
calculate or d 2 and yo- 2 . 



INVOLVING EXCITED ATOMS 



249 



TABLE XLIV 



Gas 


Mole 
cular 


Temp. 

T Tf 


Radius 
c, 


Thick 
ness a, 


Length 
I, 


E 


C 




weight If 




in cm. 


in cm. 


in cm. 






Ne 


20-2 


300 


1-8 





12 


2000 


1100 


A 


39-9 


300 


2-5 





Large 


160 


120 


A 


39-9 


80 


2-5 





Large 


15 


170 


He 


4 


300 





1-65 


5-2 


1350 


107 


He 


4 


300 





3-0 


5-2 


770 


107 



The final results are given in Table XLV. 



TABLE XLV 



Metastable 
atom 


Conditions 


d~ 
cm. 2 x 10 16 


ycr* 
cm. 2 x 10 16 


Ne( 3 P 2tl>0 ) 
A( 3 P 2 ) 
A( 3 P 2 ) 
He (2%) 
He(2 3 S 1 ) 


T=300K. 
T = 80K. 
a = 1-65 
a = 3-0 


2-44 
10-8 
15-9 
17-3 
11-1 


00136 
000208 
000153 
000059 
000059 



Not very much that is definite can be said about the values 
of a d * and ya 2 in Table XLV. In the first place, the theory 
which enabled these quantities to be calculated has one serious 
deficiency. It was assumed that, after the removal of the 
excitation, no further rate of formation of metastable atoms 
took place. This means that all sorts of collision processes that 
might be present were neglected. It is conceivable, for ex 
ample, that metastable atoms could be formed by recombina 
tion of ions and electrons, or by collisions of atoms in higher 
states with either normal atoms or electrons. If such processes 
were taken into account, the exponential constant would not 
be represented by the simple Eq. (164) and would involve so 
many unknown quantities as to be useless. Furthermore, if 
collisions with electrons play an important role, the electron 
temperature would have to be considered, since the experi 
ments of Kopfermann and Ladenburg[39] and Mohler[68] in 
dicate that this temperature determines the number of atoms 
in the different excited states when the electron concentration 
is high, and, therefore, would affect the results e \renat moderate 



250 COLLISION PROCESSES 

electron concentrations. An attempt was made by Anderson [i] 
to formulate a theory, taking into account collision processes 
other than the one considered in the present theory, but with 
little success. The mathematical complications are great, and 
too many unjustified simplifying assumptions had to be made. 
If the present theory is at all justified, the values of a/ can 
be regarded as satisfactory, except in the case of neon, where 
it is unexpectedly low. The values of ya 2 can also be regarded 
as sensible with the exception of helium, where it is much too 
large, considering the fact that the metastable helium atom 
must be raised to the 2 1 S state, which is 0-78 volt higher. On 
the whole, neither the experimental nor the theoretical parts 
of this field have yet been developed to a point where they are 
capable of yielding very reliable information. 

13 e. METHODS OF STUDYING METASTABLE MERCURY ATOMS 
IN NITROGEN. To produce metastable 6 3 P mercury atoms in 
the presence of nitrogen, it is merely necessary to excite the 
mercury atoms to the 6 3 P X state by illuminating with 2537, 
and then rely upon collisions with the nitrogen molecules to 
bring them to the 6 3 P state. The number of metastable atoms 
can then be measured in various ways, of which three have 
been used. Pool [77] illuminated a quartz cell containing a 
mixture of mercury vapour and nitrogen with the whole arc 
spectrum from a water-cooled mercury arc, and then, with a 
rotating wheel, cut this light off. A moment later, a beam of 
light of wave-length 4047 was allowed to traverse the tube. By 
a photographic method, the absorption of the 4047 line was 
measured as a function of the time that elapsed after the 
excitation ceased. From Fig. 1 it is clear that the 4047 line is 
absorbed only by 6 3 P atoms, and therefore a curve of absorp 
tion against time is an indication of the decay of 6 3 P atoms. 
A rough determination of the exponential constant of decay 
at various nitrogen pressures [113] yielded a curve of /? against p 
which had the same characteristics as that of neon and argon, 
i.e. as the nitrogen pressure was increased, j8 first decreased to 
a minimum, and then increased. More recently, Pool [78] re 
peated these experiments under more advantageous conditions, 



INVOLVING EXCITED ATOMS 251 

and found that the curves of absorption against time showed 
an anomalous behaviour, which he interpreted as being due to 
long-lived metastable nitrogen molecules. This interpretation 
is somewhat in doubt, for the reason that the method of trans 
lating the values representing the absorption of 4047 into the 
number of metastable atoms is inaccurate. To understand this 
point, it must be emphasized that the lamp which emitted the 
4047 line was not like the emission lamps used by Meissner 
and Graffunder, Anderson, and Ebbinghaus. It was not con 
structed and operated so as to emit a pure Doppler line, but 
instead, under conditions in which one is entitled to expect 
both broadening and self-reversal of the 4047 line. The rela 
tion, therefore, between absorption and the number of ab 
sorbing atoms was presumably quite different from the simple 
exponential one assumed by Pool. The anomalous character of 
the absorption-time curves is, in the opinion of the authors, to 
be attributed to this cause, rather than to the presence of 
metastable nitrogen molecules. 

A very ingenious method of measuring the decrease in the 
number of metastable mercury atoms present in a mixture of 
mercury vapour and nitrogen, after the removal of the excita 
tion, was used by Asada, Ladenburg and Tietze[3]. They 
allowed the metastable mercury atoms to absorb the line 4047, 
and at the same time measured the intensity of the green line 
5461. It is clear from Kg. 1 that the intensity of the 5461 line 
depends on the number of 7 3 SjL mercury atoms, which in turn 
depends on the amount of absorption of 4047. Asada [4] used 
this method to study the decay of metastable mercury atoms 
in nitrogen, but, unfortunately, did not give enough data to 
enable a calculation of <r d 2 and yo- 2 to be made. 

Webb and Messenger [102] and, at about the same time, Sam 
son [84] studied the same problem by still a third method. They 
relied on collisions between 6^ mercury atoms and nitrogen 
to produce metastables, and collisions between metastables 
and nitrogen to produce G^P^ atoms again. The radiation from 
these 6^ atoms, after the optical excitation had ceased, was 
used as an indication of the number of 6 3 P atoms. The 
experiment was carried out in a very simple manner. The light 



252 COLLISION PROCESSES 

from a cooled mercury arc was sent through a slit past which 
a toothed wheel rotated at high speed. In the time interval 
when the slit was not covered, this light fell on a quartz cell 
containing mercury vapour and nitrogen. During the time 
interval when the slit was covered, a small hole in another 
wheel rotated between the other face of the cell and the colli- 
mator of a spectrograph. The radiation emitted by the cell 
during this time interval caused a circular trace on a photo 
graphic plate, which represented the decay of the radiation. 
The decay was found to be exponential after about 10~ 4 sec. 
had elapsed, and the exponential constant was measured at 
various nitrogen pressures. The mercury vapour pressure 
remained constant during the experiment at a value corre 
sponding to a temperature of 28 C. 

13/. RESULTS AND INTERPRETATION WITH METASTABLE 
MERCURY ATOMS IN NITROGEN. The theory of this method was 
worked out in great detail by Samson. On account of its com 
plexity, only the salient features can be given here. First of 
all, both 6 3 P and 6 3 P X atoms were considered to diffuse 
through the nitrogen with the same diffusion coefficient, and 
to be destroyed at the walls. Second, the diffusion of the 2537 
radiation that was imprisoned in the mercury vapour was 
taken into account by calculating the rate at which this 
radiation would leave the mercury vapour if no nitrogen were 
present. This involved the calculation of an equivalent absorp 
tion coefficient [see 8c] and the use of Milne's theory [ 126]. 
Finally, collision processes were considered in which nitrogen 
molecules produced the following transitions in 6 3 P and 6 3 P X 
atoms: (1) e^-^ 3 ?!, (2) G^^G 3 ?,,, (3) 6 3 P : -> 6%, and 
(4) 6 3 P -^ 6 1 S . On the basis of these ideas, Samson obtained 
the result that the exponential constant, /?, should depend 
upon the nitrogen pressure according to the relation 



where W, X, T and Z are constants at a given temperature. 
The experimental curves, which were obtained for three 
different temperatures, 301 K., 374 K. and 486 K., were 



INVOLVING EXCITED ATOMS 253 

found to fit Eq. (178) very satisfactorily, enabling the values 
of the constants to be obtained. From these constants the 
following results were obtained: the diffusion cross-section, 
a d 2 , increased very slowly with temperature, being 15-5 x 10~ 16 , 
17-7 xlO~ 16 and 18-4 xlQ- 16 at the temperatures 301K., 
374 K. and 486 K. respectively. The other cross-sections 
remained independent of temperature and were for 

6 3 P ->6 3 P 1? <7 2 = 6-7 x 10- 18 cm. 2 , 
oi 2 =3-l x 10- 17 cm. 2 , 
S! 2 ^2-2x 10- 18 cm. 2 , 

6 3 P -> 6 *S , S 2 ^ 2-0 x 10- 22 cm. 2 . 

The value of c^ 2 , 3-1 x 10~ 17 cm. 2 , can be compared with 
Zemansky's value of the same quantity [see Table XXIV], 
obtained by measuring the quenching of mercury resonance 
radiation by nitrogen, namely, 2-74 x 10~ 17 cm. 2 . The agree 
ment is quite satisfactory. 

13 g. METASTABLE MERCURY ATOMS IN MERCURY VAPOUR. 
Webb [ioo] showed that, when a metastable mercury atom 
strikes a metal plate, an electron is liberated. Experiments of 
Oliphant [75] on metastable helium atoms, and quite recent 
experiments of Sonkin[9i] on metastable mercury atoms, con 
firm this result. In Webb's experiments, the electrons liberated 
from a plate by metastable mercury atoms were drawn to a 
positive grid, and the resulting current was used as a measure 
of the number of metastable atoms striking the plate. The 
metastable atoms were produced in another part of the tube 
by electrons liberated from a hot cathode and accelerated by 
a grid near by. By applying an alternating accelerating poten 
tial, and another alternating potential between the plate and 
its grid, and by varying the frequency of these potentials, 
Webb was able to measure the rate at which metastable mer 
cury atoms arrived at the plate after diffusing through mercury 
vapour. This same experiment was carried out in a more re 
fined manner by CouUiette [12], who was able to calculate from 
his experiments the effective diffusion cross-section of a 
metastable mercury atom. The result was 20 x 1Q- 16 cm. 2 . 



254 COLLISION PROCESSES 

Coulliette's experiments also indicated that collisions between 
metastable and normal mercury atoms occur which destroy 
the metastable atom (probably by raising it to the 6 3 P X state, 
from which it radiates). The value of ycr 2 for this process was 
found to be 0-016 x 10~ 16 cm. 2 . 

13 h. THE SIMULTANEOUS PRODUCTION AND DESTRUCTION 
OF METASTABLE ATOMS. During an arc discharge in an inert 
gas, or during the optical excitation of a mixture of mercury 
vapour and nitrogen, metastable atoms are being formed, are 
diffusing and are performing collisions, all at the same time. 
The situation is a steady state, where, in any unit volume, the 
rate at which metastable atoms are forming, due to excitation 
and diffusion, is equal to the rate at which they are being 
destroyed by collision. Many experiments have been per 
formed on metastable atoms in the steady state, but they are 
not suited for quantitative treatment because of the lack of 
knowledge of the rate at which the metastable atoms are being 
formed. It is clear that, to calculate this rate, it would be 
necessary to know the electron concentration, the electron 
excitation function, and the number of transitions from higher 
states, in the case of an arc discharge; and, in the case of optical 
excitation, the intensity of the exciting light, absorption 
coefficient, etc. The advantage of experiments of the kind 
described in the preceding sections is that most of these pro 
cesses, in the after-glow, do not exist or can be ignored. Chief 
among the experiments on the steady state should be men 
tioned those of Eckstein [18] on neon and mixtures of neon with 
foreign gases. These experiments indicate that metastable neon 
atoms are destroyed by impact with foreign gas molecules, 
hydrogen being the most effective, then nitrogen, and helium 
the least. An attempt at a quantitative treatment of Eckstein's 
experiments is to be found in a paper by Zemansky [113], 

The measurements of Kopfermann and Ladenburg[39] of 
the number of metastable neon atoms in the positive column 
of a neon arc indicate that, at low current densities, metastable 
neon atoms are destroyed by collisions with normal neon atoms, 
and at high current densities, impacts of the second kind take 



INVOLVING EXCITED ATOMS 255 

place with electrons. As a result of collisions of the first and 
of the second kind with electrons, at high current densities, 
neon atoms are distributed among the various excited states 
according to the Boltzmann equation, in which the tempera 
ture is the electron temperature. 

The experiments of Klumb and Pringsheim[38] on the 
absorption by metastable mercury atoms of the 4047 line at 
various foreign gas pressures indicate very graphically the 
various collision processes that a metastable mercury atom 
can perform. Finally the works of Found and Langmuir[20], 
Kenty [35], and many others, show that metastable atoms may 
play a very important role in the maintenance of an arc dis 
charge in an inert gas. 

REFERENCES TO CHAPTER IV 

[1] Anderson, J. M., Can. Journ. Res. 2, 13 (1930). 

[2] ibid. 4, 312 (1931). 

[3] Asada, T., Ladenburg, R. and Tietze, W., Phys. Zeits. 29, 549 (1928). 

[4] Asada, T., ibid. 29, 708 (1928). 

[5] Bates, J. R., Proc. Nat. Acad. Sci. 14, 849 (1928). 

[0] Journ. Amer. Chem. Soc. 52, 3825 (1930). 

[7] M. 54, 569 (1932). 

[8] Bender, P., Phys. Eev. 36, 1535 (1930). 

[9] Bonhoeffer, K. F., Z.f. Phys. Chem. 116, 391 (1925). 
[10] Bonner, T. W., Phys. Rev. 40, 105 (1932). 
[11] Child, C. D., ibid. 38, 699 (1931). 
[12] Coulliette, J. EL, ibid. 32, 636 (1928). 
[13] Dennison, D. M., ibid. 31, 503 (1928). 
[14] Dorgelo, H. B., Physica, 5, 429 (1925). 
[15] Dorgelo, H. B. and Washington, T. P. K., Ak. Wet. Amst. 35, 1009 

(1926). 

[16] Duffendack, 0. S. and Thomson, K., Phys. Rev. 43, 106 (1933). 
[17] Ebbinghaus, E., Ann. d. Phys. 7, 267 (1930). 
[18] Eckstein, L., ibid. 87, 1003 (1928). 
[19] Foote, P. D., Phys. Rev. 30, 288 (1927). 
[20] Found, C. G. and Langmuir, I., ibid. 39, 237 (1932). 
[21] Frenkel, J., Z.f. Phys. 59, 198 (1930). 
[22] Fiichtbauer, C., Joos, G. and Dinkelacker, 0., Ann. d. Phys. 71. 

204 (1923). 

[23] Garrett, P. H., Phys. Rev. 40, 779 (1932). 
[24] Gaviola, E., ibid. 33, 309 (1929); 34, 1049 (1929). 
[25] Gouy, G. L., Ann. Chim. Phys. 18, 5 (1879). 
[26] v. Hainos, L., Z.f. Phys. 74, 379 (1932). 
[27] Hayner, L. J., Phys. Rev. 26, 364 (1925). 



256 COLLISION PROCESSES 

[28] v. d. Held, E. F. M. and Ornstein, S., Z. f. Phys. 77, 459 (1932). 

[29] Hogness, T. R and Franck, J., ibid. 44, 26 (1927). 

[30] Holtsmark, J., ibid. 34, 722 (1925). 

[31] Jablonski, A., ibid. 70, 723 (1931). 

[32] Kallmann, H. and London, F., Z.f. Phys. Chem. B 2, 207 (1929). 

[33] Kaplan, J., Phya. Rev. 31, 997 (1928). 

[34] Kenty, C., ibid. 42, 823 (1932). 

[35] ibid. 43, 181 (1933). 

[36] Kisilbasch, B., Kondratjew, V. and Leipunsky, A., Sow. Phys. 2, 201 

(1932). 

[37] Klein, 0. and Rosseland, S., Z. f. Phys. 4, 46 (1921). 
[38] Klumb, H. and Pringsheim, P., ibid. 52, 610 (1928). 
[39] Kopfermann, H. and Ladenburg, B., Naturwiss. 19, 513 (1931). 
[40] Kuhn, H. and Oldenberg, 0., Phys. Rev. 41, 72 (1932). 
[41] Kulp, M., Z.f. Phys. 79, 495 (1932). 
[42] Kunze, P., Ann. d. Phys. 8, 500 (1931). 
[43] Landau, L., Sow. Phys. 1, 89 (1932). 

[44] ibid. 2, 46 (1932). 

[45] Lawrence, E. 0. and Edlefsen, N. E., Phys. Rev. 34, 233 (1929). 
[46] Lenz, W., Z.f. Phys. 25, 299 (1924). 

[47] ibid. 80, 423 (1933). 

[48] Locher, G. L., Phys. Rev. 31, 466 (1928). 

[49] Lochte-Holtgreven, W., Z.f. Phys. 47, 362 (1928). 

[50] London, F., ibid. 74, 143 (1932). 

[51] Lorentz, H. A., Proc. Amst. Acad. 18, 134 (1915). 

[52] Mannkopff, R, Z.f. Phys. 36, 315 (1926). 

[53] Margenau, H., Phys. Rev. 40, 387 (1932). 

[54] ibid. 43, 129 (1933). 

[54 a] Margenau, H. and Watson, W. W., ibid. 44, 92 (1933). 

[55] Meissner, K. W., Phys. Zeits. 26, 687 (1925). 

[56] Meissner, K. W. and Graffunder, W., Ann. d. Phys. 84, 1009 (1927). 

[57] Menaing, L., Z.f. Phys. 34, 611 (1925). 

[58] Michelson, A., Astrophys. Journ. 2, 251 (1895). 

[59] Milne, E. A., Journ. Lond. Math. Soc. , I (1926). 

[60] Minkowski, R, Z.f. Phys. 36, 839 (1926). 

[61] ibid. 55, 16 (1929). 

[62] Mitchell, A. C. G., ibid. 49, 228 (1928). 

[63] Journ. FrankL Inst. 206, 817 (1928). 

[64] Mohler, F. L., Foote, P. D. and Chenault, E. L., Phys. Rev. 27, 37 

(1926). 

[65] Mohler, F. L., ibid. 29, 419 (1927). 
[66] Mohler, F. L. and Boeckner, C., Bureau of Stand. Journ. Res. 5, 51 

(1930). 

[67] ibid. 5, 399 (1930). 

[68] Mohler, F. L., ibid. 9, 493 (1932). 

[69] Morse, P. M. and Stueckelberg, E. C. G., Ann. d. Phys. 9, 579 (1931). 

[70] Morse, P. M., Rev. Mod. Phys. 4, 577 (1932). 

[71] Neumann, E. A., Z.f. Phys. 62, 368 (1930). 

[72] Noyes, W. A., Jr., Journ. Amer. Chem. Soc. 49, 3100 (1927). 



INVOLVING EXCITED ATOMS 257 

[73] Noyes, W. A., Jr., Journ. Amer. Chem. Soc. 53, 514 (1931). 

[74] Oldenberg, 0., Z.f. Phys. 51, 605 (1928). 

[75] Oliphant, M. L. E., Proc. Roy. Soc. A 124, 228 (1929). 

[76] Orthmann, W., Ann. d. Phys. 78, 601 (1925). 

[77] Pool, M. L., Phys. Rev. 33, 22 (1929). 

[78] ibid. 38, 955 (1931). 

[79] Prileshajewa, N., Sow. Phys. 2, 351 (1932). 

[80] ibid. 2, 367 (1932). 

[81] Beiche, P., Verh. d. D. Phys. Qes. 15, 3 (1913). 

[82] Rice, 0. K., Proc. Nat. Acad. 8ci. 17, 34 (1931). 

[83] Phys. Rev. 38, 1943 (1931). 

[84] Samson, E. W., ibid. 40, 940 (1932). 

[85] Schonrock, 0., Ann. d. Phys. 20, 995 (1906). 

[86] Schuster, A., Astrophys. Journ. 21, 1 (1905). 

[87] Schiitz, W., Z.f. Phys. 45, 30 (1927). 

[88] ibid. 71, 301 (1931). 

[89] Schutz-Mensing, L., ibid. 61, 655 (1930). 

[90] Senftleben, H., Ann. d. Phys. 47, 949 (1915). 

[91] Sonkin, S., Phys. Rev. 43, 788 (1933). 

[92] Stern, 0. and Volmer, M., Phys. Zeits. 20, 183 (1919)* 

[93] Stuart, H., Z. f. Phys. 32, 262 (1925). 

[94] Stueckelberg, E. C. G., Helv. Phys. Acta, 5, 370 (1932). 

[95] Terenin, A., Z.f. Phys. 37, 98 (1926). 

[96] Terenin, A. and Prileshajewa, N., Z.f. Phys. Chem. B 13, 72 (1931). 

[97] Sow. Phys. 2, 337 (1932). 

[98] Trumpy, B., Intensitat und Breite der Spektrattinien, Trondhjem 
(1927). 

[99] Voigt, W., Munch. Ber. p. 603 (1912). 

[100] Webb, H. W., Phys. Rev. 24, 113 (1924). 

[101] Webb, H. W. and Messenger, H. A., ibid. 33, 319 (1929). 

[102] ibid. 40, 466 (1932). 

[103] Weingeroff, M., Z.f. Phys. 67, 679 (1931). 

[104] Weisskopf, V., ibid.75, 287 (1932). 

[105] Phys. Zeits. 34, 1 (1933). 

[106] Wilson, H. A., Phil. Trans. Roy. Soc. 216, 63 (1916). 

[107] Winans, J. G., Z. f. Phys. 60, 631 (1930). 

[108] Wood, R. W., Phys. Zeits. 13, 353 (1912). 

[109] Phil. Mag. 27, 1018 (1914). 

[110] Wood, R,. W. and Mohler, R L., Phys. Rev. 11, 70 (1918). 

[Ill] Zemansky, M. W., ibid. 29, 513 (1927). 

[112] ibid. 31, 812 (1928). 

[H3] #^.34,213(1929). 

[114] ibid. 36, 219 (1930). 

[115] ibid. 36, 919 (1930). 

[116] ibid. 42, 843 (1932). 

[117] Zener, C,, ibid. 38, 277 (1931). 



CHAPTER 7 

THE POLARIZATION OF RESONANCE 
RADIATION 

1. INTRODUCTION 

It has long been known that the band fluorescence of sodium 
and iodine vapours is polarized if observed in a direction at 
right angles to the exciting light beam, but it was not until 
1922 that Rayleigh [40] discovered that the 2537 line of mercury 
was polarized if excited as resonance radiation by a polarized 
light source. This effect was investigated more completely by 
Wood [53] and by Wood and Ellett[54]. They observed that if 
mercury vapour, at low pressure, is excited by polarized light 
from a quartz mercury arc, then (in zero magnetic field) the 
re-emitted resonance line is polarized with its electric vector in 
the same direction as that of the exciting light. In the absence 
of any magnetic field the resonance radiation was almost 
completely linearly polarized, whereas in the presence of small 
magnetic fields in certain directions the polarization was found 
to decrease. The addition of foreign gases was also found to 
diminish the degree of polarization. On the other hand, experi 
ments on the polarization of sodium resonance radiation, con 
sisting of the two D lines, showed that the D 2 line was about 
20 per cent, polarized and the other completely unpolarized 
under all circumstances. To explain these difficulties, it will be 
well to start with the case of mercury and discuss some further 
experiments by Hanle po] in the light of the classical theory and 
also on the Bohr theory. The modern quantum-mechanical 
theory can be shown to be in accord with the Bohr theory. 

2. GENERAL DESCRIPTION OF APPARATUS FOR 

POLARIZATION WORK 

Before discussing the various experiments which have been 
performed to show the polarization of resonance radiation, it 
will be necessary to describe the essential apparatus used. 
The arrangement of apparatus in the several experiments is 



POLARIZATION OF RESONANCE RADIATION 259 

somewhat varied, but consists essentially of a light source, 
polarizer, resonance tube, analyser and spectrograph or photo 
cell. 

In general, measurements on polarization of resonance radia 
tion are made by observing the resonance radiation coming off 
from a resonance tube in a direction perpendicular to the beam 
of exciting radiation, as is shown in Fig. 69. Radiation from a 
source S is passed through a lens L I9 and Nicol prism JV X , to 
polarize it, and is converged on the resonance tube T. In all 
polarization work the angular aperture, oc, of the exciting beam 
should be kept as small as possible. The reason for this is 





N 2 



Fig. 69. Apparatus for studying polarization of resonance radiation. 

apparent, since the electric vectors of any ray of the beam are 
at right angles to that ray. Thus, if observations are to be made 
in a direction perpendicular to the direction of the exciting 
beam when the primary light is polarized withits electric vector 
perpendicular to the plane of Fig. 69, and is falling on the 
resonance tube under an angular aperture oc, the primary light 
cannot be said to be 100 per cent, polarized, since its electric 
vectors have a maximum deviation a/2 from the plane of 
polarization. A method of correcting for this effect has been 
given by Gaviola and Pringsheim p.6] and Heydenburg[25]. 

In case the activating wave-length of the primary beam lies 
in the ultra-violet, a Nicol prism cannot be used, since the 
Canada balsam cement in such prisms absorbs all light of wave 
length below 3200. In this case a Glans prism of quartz, 



260 THE POLARIZATION OF 

cemented together with glycerine, may be used for wave 
lengths down to about 2000. In order to use this type of prism 
the light must pass through it parallel or under an angular 
aperture less than 6. Otherwise the use of the G-lans prism is 
similar to that of a Nicol. A calcite block, which transmits 
well down to 2000, may be also used as polarizer. When this is 
employed, the convergent light from the lens L^ of Fig. 69 
passes through the block and two images of the source, polar 
ized at right angles to each other, are formed on the resonance 
tube. One of these images is usually screened off, thus giving 
a polarized beam. 

For detection and measurement of polarization of the 
resonance radiation, a Nicol or a Glans prism can be used as 
shown in Fig. 69. In order to obtain the degree of polarization 
when using a Nicol prism it is necessary to measure the 
intensity of the light passing through the Nicol for several 
different settings thereof. When the intensity of the light is 
measured photographically, the method is extremely tedious 
so that usually, when a Nicol is used, the light intensity is 
recorded on a photo-cell. Such an arrangement has been used 
by von Keussler[49] to measure the degree of polarization of 
mercury resonance radiation. One may make a plot of photo 
electric current against the setting of the Nicol (in degrees), 
from which the degree of polarization can be obtained by 
measuring the height of the maxima of the curve and com 
paring them with a light source of the same intensity which is 
known to be fully polarized. 

When photographic measurements of intensity are to be 
made, using a spectrograph for example, it is found convenient 
to employ a double-image prism of the Wollaston or Rochon 
type. If light from the resonance tube is made to converge 
through the prism on to the slit of a spectrograph two images 
of the line or lines emitted in the resonance tube are seen on the 
photographic plate, the two images being polarized at right 
angles to each other. By measuring the relative intensity of 
these two images the degree of polarization of the light may be 
calculated. In using this method a certain amount of pre 
caution must be taken, since the loss of light in the spectro- 



RESONANCE RADIATION 261 

graph due to reflection from the faces of the dispersing prism is 
dependent upon the polarization of the light striking it, which 
may easily falsify the results. When using the double-image 
prism the light leaving the prism must be depolarized, or 
calibration experiments must be made. A special double-image 
prism has been described by Hanle in which the two images are 
depolarized after leaving the prism. 

A more exact means of measuring the polarization is by the 
method of Cornu. In this method the light to be investigated 
is made parallel and sent through two Wollaston prisms. If 
partially polarized light is incident on the apparatus, four 
images will, in general, be formed. Suppose the two images 
formed by the first prism are polarized parallel to X and Y, 
respectively, and that the second prism makes an angle a with 
the first. Of the four images formed by the second prism, two 
will be polarized parallel to x and two parallel to y, where the 
angle (X, x) is a. The intensity of the four images will then be 
J Xx = I x cos 2 a; J Xy I x sin 2 a; 
J Yx = I Y sin 2 a; J Yy IY cos2 a 5 

where I x and I Y are the intensities of the original radiation 
polarized parallel to X and 7, respectively. The procedure is 
to find the value of a for which J Xx = J Yx or J Zy = J Yy . At this 
value of a, the polarization is given by 



depending on which images are compared. If a Glans prism is 
used instead of the second Wollaston, two images are formed 
and a similar relation between the intensity of the images 
exists. The advantage of this method is twofold: (1) it is easy 
to find the setting of the prism for which two images are equal, 
and (2) there is no correction to be made to the polarization 
for loss of light due to reflection, since both Glans and Wollas 
ton prisms are cut in such a way that the incident light tra 
verses the prism perpendicular to its face. 

Another means of detecting polarized light, and this is 
especially good for detecting a small degree of polarization, is 
the Savart plate used in conjunction with a Nicol prism. If 



262 THE POLARIZATION OF 

plane polarized white light passes through a Savart plate and 
then through a Mcol prism, coloured fringes are seen for 
certain positions of the Nicol prism. If the light is analysed 
by a spectrograph, the apparatus can be so arranged that each 
spectral line is crossed by light and dark fringes. The distinct 
ness of these fringes gives the degree of polarization. The 
actual amount of polarization is usually obtained by placing 
a number of glass plates between the polarized light source and 
the Savart plate. The plates are rotated about an axis until the 
fringes formed by the Savart plate disappear, indicating that 
the polarization of the original light has been compensated. 
From the angle of rotation of the plates and their index of 
refraction, the degree of polarization can be calculated. If two 
lines are observed which are polarized at right angles to each 
other, the maxima of the fringes of the one line come at about 
the same place as the minima of those of the other line, if the 
wave-lengths of the lines are not very different. 

In order to measure changes in the angle of polarization of 
resonance radiation a system of quartz wedges or a Babinet 
compensator may be used. The angle of rotation is obtained by 
measuring the shift of the position of the fringes formed in the 
system of wedges. 

It is hardly necessary to remark that when lenses are used 
between the resonance tube and the apparatus for detecting 
polarization they should be non-rotatory. In the ultra 
violet region a fused quartz lens or a matched pair of crystalline 
quartz lenses of left- and right-handed rotation should be used. 

3. HANLE'S EXPERIMENTS ON MEECURY VAPOUB 

Hanle[20] made a thorough study of the polarization of the 
mercury resonance line 2537. For this investigation he used a 
Glans prism as polarizer and a Savart plate arrangement as 
analyser. The apparatus was arranged in such a way that the 
exciting light was incident on a resonance tube in the Z direc- 
tion(Fig. 70) and the resonance radiation is observed along OF, 
with Savart plate, Nicol prism and a photographic plate. The 
resonance tube was placed in a system of coils in such a way 
that the earth's magnetic field was always compensated and 



RESONANCE RADIATION 263 

magnetic fields of known strengths in given directions could 
be supplied. The pressure of mercury in the tube was KM mm. 

If the exciting radiation is polarized with its electric vector 
in the X direction and there is no magnetic field on the tube, 
the resonance radiation is found to be highly polarized (about 
90 per cent.) in the X direction. On the other hand, if the 
exciting light is polarized along Y, the resonance radiation is 
unpolarized and its intensity extremely weak. If the direction 
of polarization of the exciting light is changed slowly from T 
to X } the polarization and the intensity of the resonance 
radiation increase. 

If the direction of the electric vector of the exciting light is 
kept constant and parallel to X, and a magnetic field (about 




Observation 
Y 

Kg. 70. 

25 to 100 gauss) placed in the X direction, the polarization of 
the resonance radiation remains unchanged, that is, parallel 
to X. With the field parallel to Z the polarization of the reso 
nance radiation is again high and parallel to X. If, however, the 
field is parallel to F, that is along the direction of observation, 
the resonance radiation is completely unpolarized but is strong. 
Suppose the field in the direction of T is not strong but weak 
and can be varied from zero to a few gauss. With zero field the 
resonance radiation is, of course, 90 per cent, polarized in the 
X direction. On increasing the field the degree of polarization 
is found to decrease and, for small fields, its direction is changed 
slightly from the X direction. As the field increases still 
further the degree of polarization diminishes to zero. 

Finally, if the electric vector of the exciting light is parallel 
to F, and there is a strong field parallel to X, the resonance 



264 THE POLARIZATION OF 

radiation is highly polarized parallel to Z, and on rotating the 
field from X to Z, the direction of polarization rotates from Z 
to X, being always perpendicular to the field and keeping its 
degree of polarization constant. 

Hanle also found that, on using circularly or elliptically 
polarized exciting light, and observing at an angle of 20 to the 
incident beam, the resonance radiation was circularly or 
elliptically polarized in the same manner as the incident beam. 

4. THEORY OF HANLE'S EXPERIMENTS 

4a. CLASSICAL THEORY. It is obvious that the classical 
theory will roughly explain all the results if one considers the 
series electron of the mercury atom to act as a classical oscil 
lator. Thus, the oscillator will vibrate parallel to the direction 
of polarization of the exciting light, and the radiation emitted 
by the oscillator will be polarized in the same direction as the 
exciting light, thus explaining the experiments in zero field 
with the incident beam polarized parallel to X. In the experi 
ments where the incident light is polarized parallel to 7, one is 
looking along the direction of vibration of the oscillator and 
the theory says that the oscillator radiates no energy in this 
direction, in agreement with the facts. The experiments with 
various orientations of magnetic field are also explained on the 
classical theory when one remembers that the electron will 
precess about a magnetic field giving rise to circularly polar 
ized light when viewed along the field (classical Zeeman effect) 
or, when viewed perpendicular to the plane of the field, to 
linearly polarized light (perpendicular to the field), since only 
the simple harmonic components of the circular vibration are 
seen. Thus, when the electric vector of the exciting light is 
parallel to X, and there is a strong field parallel to Z, the 
electron of the classical model will precess about the Z axis and 
the light observed in the direction T will appear polarized 
parallel to X, since only the simple harmonic components of 
the circular vibration are seen. The case in which the plane of 
polarization of the emitted light rotates, when the direction 
of the magnetic field is rotated from X to Z, is also easily 
explained by these considerations. 



RESONANCE RADIATION 265 

In order to explain the fact that, when the resonance radia 
tion is observed in the direction of the magnetic field, it be 
comes depolarized with increasing field, it is sufficient to 
assume the classical model to be a damped oscillator. If the 
oscillator is excited by light polarized in the X direction it will 
start to vibrate parallel to the X axis but will precess about the 




Fig. 71. 

field, its amplitude of oscillation dying down with the time due 
to damping. The path described by the oscillator when viewed 
along the field will take the form of a rosette. If the precession 
velocity is large compared to the damping (that is, large mag 
netic field), the rosette will be symmetrical, as shown in Kg. 7 1 . 
In this case, since the rosette is perfectly symmetrical, it is 
clear that the light from the oscillator (resonance radiation) 
will show no linear polarization. 

On the other hand, if the damping is of the same order of 



266 THE POLARIZATION OF 

magnitude as the precession velocity, the form of the motion 
of the oscillator will be given by Kg. 72. 

In this case the rosette is incomplete, and shows asymmetry 
due to the fact that the oscillations have been damped out 
before a full period of precession takes place. Thus the resulting 
resonance radiation will be partially polarized (less than in a 
zero field), and its plane of polarization rotated with respect 




Fig. 72. 

to that of the incident light, since the plane of polarization 
of the resonance radiation will be given by the direction of the 
maximum electric vector. Making use of the electromagnetic 
equations of a damped oscillator in a magnetic field and the 
coherence properties of the light emitted, Breit[2] was able to 
show that the radiation emitted is partially polarized and its 
plane of polarization (the plane of maximum light intensity) 
rotated through an angle ^ to the X axis. If one measures the 
polarization by means of an apparatus which ke6ps the same 
position with reference to the electric vector of the exciting 



RESONANCE BADIATION 267 

light throughout the experiment (for example a Wollaston 
prism), the degree of polarization of the light is given by 



where P is the polarization observed with a field of intensity H, 
P Q that with zero field, r the mean radiation life of the atom, g 
a factor to take into account the fact that most atoms do not 
precess with classical precession velocities but proportional to 
them, and e, m, c the charge and mass of the electron and 
velocity of light. On the other hand, one may measure the 
polarization, as von Keussler did, by rotating a Nicol prism 
and measuring the maximum and minimum intensities of the 

light, and use the formula, P = * max ~ r mlIL . In this case Breit 

J- max. + * mln. 

has shown that the relation between the degree of polarization 
and the magnetic field is given by 
P' 1 

...... (180) " 




The rotation of the plane of polarization is given by 



eH 
= rg 

WIG 



where oo = - , the classical Larmor precession velocity. Thus 
2rac 

it is easily seen from Eq. (179) that, as the field increases, the 
degree of polarization decreases in agreement with Hanle's 
experiments. Measurements of both effects have been made 
by Wood and Ellett, Hanle, and von Keussler. 

46. QUANTUM THEORY OF POLARIZATION AND THE ZEEMAN 
EFFECT. Although the classical theory is able to explain all 
the polarization phenomena exhibited by the mercury reso 
nance line 2537, it cannot explain the polarization of sodium 
resonance radiation (as will be shown in a following section). 
Furthermore, in order to be consistent, a quantum theory 
explanation must be given. 



268 THE POLARIZATION OF 

Hanle [19] was the first to show that the phenomena can be 
explained on the quantum theory if one considers the Zeeman 
effect components of the line in question. Prom the quantum 
theory of the Zeeman effect it is known that any level of (total 
angular momentum) quantum number j splits into 2j+ 1 sub- 
levels in a magnetic field. The sub-levels are designated by a 
magnetic quantum number m which takes values differing by 
unity from j to +j. In order for an atom to emit light in 
jumping from one state to another, the angular momentum 
quantum number I must change by one unit and m may change 
by 1 or 0. If m does not change (Am = 0), the line emitted is 
analogous to the unshifbed or "TT component" of the classical 
Zeeman effect which is polarized parallel to the field. If m 
changes by one unit (Am = 1) the frequency is not the same 
as that emitted by the atom in a zero field, but differs from it 
as do the "<r components" of the classical Zeeman effect. 
These a components can be shown to be circularly polarized 
about the field. Although in the weak fields used in experiments 
on resonance radiation (0->200 gauss), the Zeeman com 
ponents (of Hg for example) are not separated enough to 
measure except with apparatus of the highest resolving power, 
the polarization characteristics are clearly defined. This 
furnishes a powerful means of studying the Zeeman effect of 
resonance lines whose Zeeman separation is very small. 

To explain the experiments on the polarization of the 2537 
line of mercury it is necessary to draw a Zeeman diagram of the 
two states involved. The lower state 6 1 S is single with ra = 0; 
while the upper state 6 3 P X is triple with m= + 1, 0, 1, as 
shown in Fig. 73. The relative intensities of the several 
components corresponding to the jump from 6^-*- 6*80 are 
given at the bottom of the diagram. 

Suppose the incident light is polarized parallel to X. and 
contains the frequencies of all the Zeeman components (that 
is, the exciting line is broadened due to Doppler effect and also 
due to the magnetic field usually applied to a mercury arc to 
give an unreversed line). If a strong magnetic field is applied 
parallel to the X axis and the resonance radiation observed 
parallel to Y, the electric vector of the incident light is parallel 



RESONANCE RADIATION 



269 



to the field, so that only the TT component is absorbed. Since no 
transitions can occur between the magnetic levels of the 6^ 
state, the radiation emitted will be a TT component and will have 
its electric vector parallel to the field. If the field is parallel to 
the Z axis the o- components will be absorbed in this case and 
will be consequently re-emitted, and these will be circularly 
polarized about thefield. The observation directionis, however, 
along the T axis perpendicular to the field, so that the radia 
tion appears plane polarized parallel to X, as in the corre 
sponding classical case. All other cases discussed under the 



m 
+1 



0- 

-1- 



TT 



J-0 



7121 
A 2 2 2 

Fig. 73. Zeeman diagram for the line 1 S *P^ . 

classical theory when the field is perpendicular to the observa 
tion direction give analogous results. 

Two cases remain to be discussed, (1) when there is no 
magnetic field and the Zeeman separation vanishes, and 
(2) when there is a variable field parallel to the direction of 
observation. In the first case, when there is no magnetic field, 
all of the different m levels of the upper state fall together and 
the level is said to be " degenerate ". In other words, one can 
not tell whether the TT or a components will be excited, since 
their energy is the same. In order to get round this difficulty 
Heisenberg[24] suggested the "Principle of Spectroscopic 
Stability", which postulates that, if a certain degree of polar 
ization is obtained when there is a strong field in the direction 
of the electric vector of the exciting light, then the same result 



270 THE POLAEIZATIOISr OF 

is obtained on decreasing the field slowly to zero. The reason 
for choosing the field in the direction of the electric vector is 
suggested by the classical theory, since the frequency and 
polarization of a classical oscillator are unchanged when a 
field is applied parallel to its direction of oscillation. Hanle's 
and Wood and Ellett's experiments in zero field are thus 
explained. 

Recently Dirac[7] has given a quantum theoretical treat 
ment of an atom in a radiation field which has been very fruit 
ful in giving correct expressions for dispersion and scattering 
of light. Weisskopf [51] has derived expressions for P and 
tan 2<ji, on the basis of this theory, for an atom showing normal 
Zeeman effect, that is, having one single lower magnetic level 
and three upper ones, as in the case of the 2537 line of mercury. 
Weisskopf 5 s expressions for this case agree with Eqs. (179) and 
(181). Recently Breit[4] has shown, by a generalization of 
Weisskopf 's results, that the formulas for the magnetic de 
polarization of any resonance line are the same as the classical 
ones if the g factor is taken to be that of the upper level. 

5. EXPERIMENTAL VEEIFICATION OF THE FORMULAS 
FOR MAGNETIC DEPOLARIZATION AND THE ANGLE OF 
MAXIMUM POLARIZATION IN THE CASE OF MERCURY 

Using the Nicol prism and photo-cell described above, von 
Keussler measured the polarization and tan 2<j> for mercury 
resonance radiation as a function of the magnetic field applied 
in the direction of observation. The pressure of the mercury 
vapour corresponded to -21 C., and the incident radiation 
was polarized. His results, which will be discussed in detail 
in 8, verify in general Eqs. (179) and (181) and lead to a value 
of the mean life of the 6 3 P X state of 1-13 x 10~ 7 sec. 

Instead of using a magnetic field in the direction of observa 
tion, Breit and Ellett[5] and Fermi and RasettilM studied the 
effect of an alternating field, produced by a vacuum tube and 
solenoid, on the polarization of mercury resonance radiation. 
The idea behind the experiment is the following. Suppose the 
mercury atom to be a damped classical oscillator which will 
precess about a magnetic field with a Larmor frequency co. If 



RESONANCE RADIATION 271 

the reciprocal of the mean life of the oscillator (for Hg, 1 7 sec .- 1 ) 
is of the same order of magnitude as the Larmor precession 
velocity, depolarization will occur in a steady field. If, how 
ever, an alternating field of the same strength in gauss is used, 
and its frequency is much greater than the Larmor frequency, 
there will be no great effect on the polarization, since the 
Larmor precession will be first in one direction and then in the 
opposite direction, depending on the direction of the alter 
nating field, and will be very small in either direction, since the 
field changes very rapidly. If the alternating frequency is less 
than the Larmor frequency, the oscillator will have time to 
precess in the field before the direction of the field changes, and 
a consequent depolarization will appear. 

In Fermi and Rasetti's experiments the magnetic field 
strength could be varied from 1* 13 to 2- 13 gauss. (1 gauss gives 
a Larmor precession velocity of about 1-4 x 1C 6 sec."* 1 for a 
classical oscillator.) The frequency of the field could be changed 
from 1*2 to 5x 10 6 sec." 1 . At 1-13 gauss and a frequency of 
5 x 10 6 sec." 1 they found practically no depolarization, whereas, 
at 1-87 gauss and the same frequency, depolarization was 
noted. At 2-13 gauss the depolarization was as large as in a 
stationary field. If the field strengths had been 3/2 as large as 
those given, the results could have been explained satis 
factorily on the basis of the classical oscillator. The factor 3/2 is 
just the factor g which gives the relation of the classical Zeeman 
splitting to that observed; in other words, the precession 
velocity of the orbital electron of the d 3 ?! state of mercury is 
3/2 the classical Larmor precession velocity. The experiment 
gives an independent check on the factor g as well as on r, the 
mean life in the 6 3 P a state. The equation for the polarization, 
as a function of the magnetic field strength and the frequency 
of the oscillator v, has been given by Breit[3] and is 



\P 



where P is the polarization, p = ZTTV, p = ^ g and J n is the 
Bessel function of order n. 



272 



THE POLARIZATION OF 



6. POLARIZATION OF SODIUM RESONANCE RADIATION: 
BREAKDOWN OF CLASSICAL THEORY 

6 a. EXPERIMENTAL RESULTS ON THE POLARIZATION OF 
SODIUM RESONANCE RADIATION. The fact that the D line 
fluorescence of sodium is polarized both in the absence of a 
magnetic field and with certain orientations of the field, was 
first shown by Wood and Ellett[54], and the experiments were 
repeated by Ellett[9] in the hope of getting more quantitative 
results. In these experiments both the T> lines excited the 
fluorescence, and in observing the emergent light from the 
resonance tube no attempt was made to separate the two lines. 



3^{: 






+i 

+7 
;-i 



77 CT 0" 7T 



crrr cr ( 



m:i 



12222 341143 

/I 2 4 4 2 642246 

D, > 2 

Fig. 74. Zeeman diagram for D lines. 

The values they obtained for the polarization, then, are to be 
taken for the two lines together. Pringsheim and Gaviola[38] 
used a spectrograph with Savart plate and Mcol prism in 
observing the polarization of the sodium fluorescence, and 
found that the DJ line was always unpolarized and was un 
affected by a magnetic field; whereas the D 2 line showed 
polarization and was affected by a magnetic field. In their ex 
periments the D 2 line never showed more than 25 per cent, 
polarization. In any theory derived from a classical isotropic 
oscillator one would expect 100 per cent, polarization for both 
lines, which is definitely not in agreement with the facts. 

66. THE ZEEMAN LEVELS FOR SODIUM; VAN VLECK'S 
FORMULAS FOR POLARIZATION. The Zeeman levels for the 
sodium D lines are given in Fig. 74, and under each line is given 



RESONANCE RADIATION 273 

the relative intensity / of the line appearing in the pattern, 
together with the transition probabilities A. 

From the considerations of 46, it will be seen at once that 
the D! line must be unpolarized, since both upper magnetic 
levels are connected with both lower levels.. The absorption 
of 77 components, for example, populates both upper levels 
equally, and the return from these upper levels to the lower 
ones entails an emission of IT and a components of equal in 
tensity, so that the resulting radiation is unpolarized. Due to 
the connection between both upper levels and both lower levels 
it is clear that the presence of a magnetic field in any direction 
will leave the polarization unchanged. When the D 2 line, how 
ever, is excited with light whose electric vector is parallel to 
the field (along OX of Fig. 70), the two TT components are 
excited, populating the two middle upper levels. The atom 
returns to its normal state with the emission of two a com 
ponents of intensity 1 each and two TT components of intensity 
4 each. The polarization observed (along OT) is then 

8 2 
P = - - = 60 per cent. 

8 + 2 

Van Vleck[48] has given formulas for calculating the polar 
ization of any resonance line when the Zeeman transition 
probabilities are known. Consider plane polarized light exciting 
resonance radiation in a magnetic field H. Let 9 be the angle 
between E and H. Let A^ be the transition probability of the 
linearly polarized Zeeman component originating in the upper 
magnetic state p,, and Aj 1 be the sum of the corresponding 
probabilities for the two circularly polarized components. The 
number of electrons reaching the excited state p is proportional 
to / (A^ cos 2 8 + 1/2AJ* sin 2 0), where I is the intensity of the 
incident light. This is true, since absorption and emission 
probabilities are proportional to each other in non-degenerate 
systems and since linearly polarized light is only half as 
effective in exciting circularly polarized as plane polarized 
components. In returning from the state ft, a fraction of the 

A P 
electrons - A Z! return by linearly polarized transitions, 

* 



274 THE POLARIZATION OF 

A P 

and a fraction A ? A by circularly polarized ones. If the 
1 



resonance radiation is observed at right angles to the field, H, 
only half the circularly polarized light can be seen. The in 
tensity of the components polarized along and perpendicular 
to the field is then 



...... (182), 

where the sum is to be taken over all Zeeman transition prob 
abilities of the line in question. The polarization is, then, 



...,.(183). 

The transition probabilities A^ and A/- can be obtained from 
the Zeeman pattern intensities with the convention that 
A^- = intensity of a IT component and A/- = twice the intensity 
of a cr. The intensity of the TT and a components can in turn be 
calculated from the sum rule of Ornstein and Burgers. 

Since the total chance of leaving any upper magnetic level 
p, is the same for each level, we may write 

AS+AJ*=A ...... (184). 

It is therefore seen at once that the denominators of the ex 
pressions for | and ^ in Eq. (182) drop out of the calculation of 
P in Eq. (183). The expression for the polarization, as given by 
Van Vleck, maybe still further simplified when one remembers 
that there are 2j-h 1 upper magnetic levels, so that 

...... (185). 



Furthermore, since, for an atom excited by isotropic radiation, 
the intensity of all the TT components must be equal to that of 
all the or components, we have 

...... (186). 



RESONANCE BADIATION 275 

Substitution in (183) gives the relation 



...... (187). 

This formula has two very interesting consequences. In the 
first place, if the angle between the electric vector of the 
exciting light and the applied magnetic field is such that 
3cos 2 0= 1 (0 = 54 45') the line will be unpolarized. This will 
be true for all resonance lines, as was first pointed out by Van 
Vleck. The so-called angle of no polarization has been measured 
by Hanle for mercury, and by Wood and Ellett for sodium, and 
found to be in agreement with theory. The second result to be 
obtained from Eq. (187) is a relation between the polarization 
to be expected when the electric vector of the exciting light is 
parallel to the field (6 = 0) and when it is perpendicular to the 
field (0 = 7r/2). Calling the two polarizations P\\ and Pj_, 
respectively, one finds the general relation 



which is again true for all resonance lines. 

When resonance radiation consists of two related resonance 
lines, as in the case of the D lines of sodium, the total polariza 
tion of the two lines taken together may be calculated by 
choosing the transition probabilities in such a way that the 
chance of leaving any upper magnetic level \L of any upper state 
j is the same for any such level, and by taking care to bring in 
the correct relative intensities / of the two lines in the exciting 
source. 

In the case of the D lines of sodium a short calculation shows 
that the polarization is given by 

9cos 2 0-3 



where q is the ratio of the intensity of D x to D 2 in the source. 
Several interesting cases arise for computation. Let the in- 



276 THE POLARIZATION OF 

cident beam travel along OZ (Fig. 70) and the resonance 
radiation be observed along OY. 

(1) It follows from Eq. (187) that the D 1 line alone is un- 
polarized. This also follows from Eq. (189) by putting # = 00. 

(2) For the D 2 line alone, q = Q. Let the electric vector of the 
exciting light and the magnetic field be along X. Then = 
and we have P = 60 per cent. 

(3) For D 2 alone, let H be parallel to the exciting beam, then 
6 = 7T/2 and P = 43 per cent. This result holds also if the light is 
unpolarized. 

(4) For both lines together, when q= 1/2; under conditions 
of (2) above, P = 50 per cent. ; and for (3) above, P = 33 per cent. 

When there is no magnetic field the polarization can be 
calculated by putting = 0, on account of spectroscopic 
stability. Other interesting cases can be calculated at the 
pleasure of the reader. 

6c. FURTHER COMPARISON OF EXPERIMENT WITH THEORY. 
In two experiments the polarization of the two D lines was 
measured separately. Pringsheim and Gaviola[38] separated 
the two D lines in the fluorescence by means of a spectrograph, 
while Datta [6] separated the two lines in the exciting beam by 
means of rotatory dispersion of a quartz crystal and measured 
the fluorescence visually. Both observers agree that the D x line 
is always unpolarized in accordance with theory. 

For the D 2 line alone, Datta made observations of the polar 
ization as a function of the pressure of sodium vapour in the 
resonance tube. The results of his experiment, made in the 
absence of a magnetic field, are given in Table XLVI below. 

TABLE XLVI 

EFFECT OF VAPOUR PRESSURE ON POLARIZATION 



Temperatures 


Polarization 


Pressure of Na 


C. 


(per cent.) 


(mm. Hg) 


150 


24 


4-8 x 10- 6 


140 


26 


2-2 x 10~ 6 


135 


27-5 


1-6 x 10~ 6 


125 


31 


8 x 10~ 7 


115 


33 


3x10-7 



RESONANCE RADIATION 277 

It will be seen from the table that the polarization depends 
markedly on the vapour pressure of sodium. The explanation 
of this fact will be fully discussed in a following section, but it 
is sufficient to point out here that this phenomenon is due to 
disturbing effects of neighbouring atoms. At the lowest pres 
sures at which Datta could work, the polarization was never 
more than 33 per cent., whereas the theory predicts 60 per cent. 
He believed that the polarization-pressure curve was approach 
ing 60 per cent, asymptotically, and that if experiments could 
be made at lower pressures the theoretical value of 60 per cent, 
would be obtained. This argument is not convincing when one 
looks at the polarization-pressure curve in question. Ellett [10], 
on the other hand, measured the polarization of the two D 
lines together and found a polarization of 16-3 per cent. This 
degree of polarization remained the same for vapour pressures 
of sodium from 3 x 10- 7 mm.(115C.)to l-9x 10- 8 mm.(80C.), 
i.e. much lower pressures than used by Datta. Assuming that 
theexciting source gave the D lines with the ratio q= 1/2, Ellett 
calculated the polarization for D 2 alone to be 20*1 per cent, 
instead of the 33 per cent, found by Datta. More recent experi 
ments of Heydenburg, Larrick and Ellett [26] give 16-48 0-33 
per cent, for the two D lines together, and about 20-5 per cent, 
for the D 2 line alone. Ellett's work shows thai decreasing the 
vapour pressure certainly did not lead to the theoretically 
expected value of the polarization (for both lines g=l/2, 
P = 50 per cent.). 

In this connection, we shall discuss an experiment by 
Hanle[22] 5 who excited polarized sodium resonance radiation 
by means of the circularly polarized light of both D lines. The 
exciting light contained only the left-handed circularly polar 
ized components of the two D lines. The resonance tube was 
placed in a magnetic field parallel to the exciting light beam 
and observations were made in a direction nearly parallel to 
the exciting beam. With this arrangement one would expect 
only the - 1/2 and - 3/2 levels of D 2 and the - 1/2 level of D! 
to be excited. In fluorescence one should obtain two left- 
handed circularly polarized components and a linearly polar 
ized component (parallel to the field) from D 2 , and one left- 



278 THE POLARIZATION OF 

handed circularly polarized and one linearly polarized com 
ponent from D! . Since the linear components are polarized 
parallel to the magnetic field and hence to the direction of 
observation, one should see no light from these, and the reso 
nance radiation should be 100 per cent, polarized (left circular). 
After making suitable corrections for the fact that observations 
were made at a small angle to the fluorescent beam, Hanle was 
able to show that the polarization, in zero field and at the 
lowest vapour pressures at which the experiment could be 
carried out (100 C.), was only 60 per cent, instead of 100 per 
cent, as expected. With large magnetic fields the polarization 
was not more than 85 per cent. 

With a magnetic field parallel to the electric vector of the 
exciting light Ellett[9] observed 45 per cent, polarization 
(#=60 gauss) for the two D lines, whereas Datta observed 
56 per cent, polarization for the D 2 line alone (H = 250 gauss). 
For large magnetic fields, then, it would appear that the 
theoretical values of the polarization as given by the Zeeman 
effect theory have been approached (see 8/). 

We must remark at this point that the polarization found 
by experiment is usually less than that predicted by the simple 
Zeeman effect theory. This discrepancy may be due to diffi 
culties in carrying out the experiments or to an over-simplified 
theory. The experimental difficulties, such as the pressure 
effect, will fee discussed in following paragraphs, as will also 
theoretical difficulties, such as the effect of hyperfine structure. 
The discussion in the preceding sections is meant to show the 
development of thetheoryin its broad outlines and to correlate 
polarization measurements with the simple Zeeman effect 
theory. 

7. POLARIZATION OF RESONANCE LINES OF OTHER 

ELEMENTS: MEAN LIVES OF SEVERAL 

EXCITED STATES 

7a. RESONANCE LINES. The only other elements, with lines 
having simple Zeeman patterns like mercury, that have been 
investigated are cadmium and zinc. MacNair[30] and Soleil- 
let[44] investigated the resonance line 3261 (5 1 S -5 3 P 1 ) of 



RESONANCE RADIATION 



279 



cadmium. The former, using rather high vapour pressures 
(temperature of cadmium reservoir 210 0.) and a sealed-off 
resonance vessel, found only 30 per cent, polarization. Later, 
Soleillet found higher values for the polarization. At 210 0. 
he verified MacNair's value of 30 per cent., but on decreasing 
the pressure of cadmium vapour to a vapour pressure corre 
sponding to 170 C., he found the polarization to be 73 per 
cent, and to remain constant as the temperature was lowered 
to 115C., in a zero magnetic field. Later experiments, in 
which the resonance tube was always attached to the pumps, 
gave 85 per cent, polarization in a zero field or in a field in the 
direction of the exciting beam (no polarizer was used in these 
experiments). These last experiments of Soleillet are probably 
better than the earlier ones, since the resonance tube was freer 
from any gaseous impurities than in the former. Ellett and 
Larrick [12], by very careful experiments, found 85-87 per cent, 
polarization when the vapour pressure of cadmium in the 
resonance tube corresponded to 146 C. They found that at 
168 C. the depolarizing effect first set in. The experiments 
were performed in a strong magnetic field in a direction parallel 
to the exciting light beam, which was unpolarized. On the 
basis of the simple theory the cadmium 3261 line should show 
100 per cent, polarization in a zero field or one parallel to the 
exciting light beam, since the line is entirely analogous to the 
mercury 2537 line. 

TABLE XLVH 
CADMIUM 3261, MAG:NETIC DEPOLARIZATION 



Magnetic field 
(gauss) 


Polarization 
(per cent.) 


0-00 
0-014 
0-028 
0-056 


85 
55 

27 
7 



Soleillet, using unpolarized exciting light, found that very 
small fields in the direction of observation of the resonance 
radiation had a large depolarizing effect. From the data given 
in Table XLVII, and using </ = 3/2, Soleillet found the mean 
life of the 5^ state to be 2 x 10~ 6 sec. 



280 



THE POLARIZATION OF 



Soleillet also investigated the singlet resonance line of cad 
mium at 2288 and found a polarization of 60 per cent, in the 
absence of a field. According to the theory, this should also 
show 100 per cent, polarization. Ellett and Larrick found 
76-3 per cent, polarization for this line at low pressures and in 
a magnetic field parallel to the exciting light beam. Soleillet 
found, however, that much larger fields in the direction of 
polarization were necessary to depolarize the radiation than in 
the case of the 3261 line, as is shown by Table XLVIII. 

TABLE XLVIII 
CADMIUM 2288, MAGNETIC DEPOLARIZATION 



Magnetic field 
(gauss) 


Polarization 
(per cent.) 



0-03-^1 
25 
50 
100 


60 
49 
43 
38 
31 



From these data he computed a short mean life, of the order 
of 10~ 9 sec., for the S^P^ state of cadmium. Soleillet [45] also 
measured the polarization of the two resonance lines in zinc, 
3076 and 2139. For the 3076 line, he found a maximum polar 
ization of 67 per cent, in the absence of a field or in a field 
parallel to the exciting beam. Extremely small fields in the 
direction of observation were found to depolarize the resonance 
radiation completely, so that he calculated a mean life of 
r=10~ 5 sec. for the 4 3 P t state. The singlet line 2139 showed 
about 50 per cent, polarization in a magnetic field parallel to 
the exciting beam. 

7&. LINE FLUORESCENCE. According to the theory of the 
classical isotropic oscillator, one would expect that, if reso 
nance radiation were polarized, the direction of polarization 
would be parallel to the exciting light beam. In direct con 
tradiction to this, and in qualitative agreement with the 
simple Zeeman theory, are the experiments of Giilke[i8] on 
thallium line fluorescence. According to our discussion of this 
phenomenon given in Chap, i, we note that excitation is due 
to the absorption of the lines 3776 and 2768, and that the 



RESONANCE RADIATION 



281 



emitted line fluorescence contains the four lines 3776 (6 2 P 1/2 - 
7. 2 S 1/2 ), 5350 (6 2 P 3/2 -7 2 S 1/2 ), 3530 (6 2 P 3/2 -6 2 D 3/2 ) and 2768 
(6 2 P 1/2 -6 2 D 3/2 ) . The Zeeman levels of the states in question are 
given in Fig. 75 with only one-half the number of transitions 
drawn. It will be seen at once that, since 6 2 P 1/2 and 7 2 S 1/2 have 
only two magnetic levels each, both magnetic levels of 7 2 S 1/2 
will be equally populated, independent of the polarization of 
the incident beam. Consequently, the lines 3776 and 5350 
emanating from the 7 2 S 1/2 state will show zero polarization in 

2768 3530 m 



^ 



776 5350 










6 2 Di 


















2 


















m 

' 


7 


n 


r 7 


(. 


( 


3 


r-< 


7- 








... i 


<r c 


"1 


r < 


2 

T ( 










































302010 






3 


3 24 24 4 32 
1 










20 40 60 40 20 

Fig. 75. Zeeman diagram for thallium. 



all cases, analogous to the D x line of sodium. The 6 2 D 3/2 state, 
on the other hand, has four magnetic levels, so that differential 
population of the upper levels may occur. Making use of the 
transition probabilities of the various Zeeman components as 
given in Fig. 75, it is easy to show that, in a zero magnetic field, 
2768 should be 60 per cent, polarized parallel to the electric 
vector of the exciting beam (since the intensity of the if com 
ponents is greater than of the a's), and 3530 should be 75 per 
cent, polarized perpendicular to the direction of polarization 
of the incident 2768 beam. 

Using a polarized light source, and observing the resonance 



282 



THE POLARIZATION OF 



radiation with a double-image prism and spectrograph, Giilke 
found that 5350 and 3776 were unpolarized and that 2768 was 
polarized to the extent of 55 per cent, parallel to the polariza 
tion of the exciting beam, and that 3530 was 60 per cent, 
polarized perpendicular to it, in qualitative agreement with 
the theory. Giilke also found that high vapour pressures of 
thallium caused the percentage polarization of both lines to 
decrease. The figures given above refer to the percentage 
polarization at the lowest vapour pressure at which the experi 
ment could be made, and probably represent the maximum 
polarization observable in a zero field. 

Formulas for calculating the polarization of any fluorescent 
line may be derived from considerations similar to those given 
in 66. Consider a fluorescent line be (Fig. 76) which may be 



fc- 



m' 



m 



Pig. 76. 

excited by absorption of the line ab. Let a given magnetic sub- 
level of b be designated by ^, and similar magnetic sub-levels 
of a and c by m and m'. Let the chance of reaching a given 
magnetic level of b by the absorption of TT or cr components of 
ab be A^v- and A^ respectively. Similarly, let the chance 
of leaving the level //, by a TT or a component of the line be be 
AJ** and AJ**. The and f\ components of the intensity of the 
line be will be given by 



r-^oft 






(190). 



RESONANCE RADIATION 283 

Relations similar to Eqs. (184), (185), (186) hold for ab and be, 
so that a calculation shows that 

(3cos 2 0-l) 



(191), 

and for the important case of 6 = 0, 

3 S A 



(192). 

In this formula A ab is the total chance of leaving a level p, of b 
by the path ab, and A** that by the path be. If the polarization 
of only one fluorescent line is to be calculated, one can make 
A ab = A bc and weight the transition probabilities of the various 
Zeeman components in such a way as to give this result. When 
two or more fluoresent lines are not resolved, a case which 
rarely arises when hyperfine structure is not considered, the 
transition probabilities of the Zeeman components must be 
weighted in such a way as to ensure that the relative intensities 
of the fluorescent lines will conform to the sum rule for in 
tensities. 

8. EFFECT OF HYPERFINE STRUCTURE ON THE 
POLARIZATION OF RESONANCE RADIATION 

8 a. DETAILED EXPERIMENTAL INVESTIGATION OF THE 
POLARIZATION OF MERCURY RESONANCE RADIATION. Before 
going on to a description of further experiments on the polar 
ization of line fluorescence and to a detailed discussion of the 
effect of collisions and imprisoned resonance radiation on 
polarization, it will be well to make a more careful examination 
of the agreement between the observed degree of polarization 
of the lines so far discussed and that to be expected from the 
simple theory. Certain discrepancies between experiment and 
the simple theory are apparent at once. The experimentally 
observed degree of polarization of the 2537 resonance line of 



284 THE POLARIZATION OF 

mercury and that of the 3261 resonance line of cadmium are 
about 80 per cent, and 86 per cent, respectively, whereas the 
theory predicts 100 per cent. For the D 2 line of sodium, on the 
other hand, the theoretically predicted degree of polarization 
is 60 per cent, and that observed not more than 20-5 per cent. 
It seems certain that these differences are real and are not due 
to the effect of imprisoned radiation, depolarization by colli 
sion, or finite aperture of the exciting and fluorescent beams. 
Thus, the degree of polarization has been measured as a 
function of vapour pressure to such low vapour pressures that, 
in this region, the polarization was found no longer to depend 
on vapour pressure. It is of interest, therefore, to find a reason 
for the difference for the existing discrepancy. 

Von Keussler [49] suggested that the discrepancy, in the case 
of mercury, might be due to the hyperfine structure of its 
resonance line, MacNair[3i] measured the Zeeman effect of 
these h.f.s. components. In a zero field he found the wave 
lengths of the components to be -25-4, -10-3, 0-00, 11-6, 
21-5 mA. In magnetic fields up to 5800 gauss, the latter four 
became triplets with 3/2 the normal separation, the parallel 
(TT) components of each "line" maintaining the same relative 
positions as the field is increased. The h.f.s. line at - 25-6 is not 
so simple, however. The perpendicular (a) components of this 
line behave as the perpendicular components of a 3/2 normal 
triplet whiclfstarts at 25-6, but the parallel (TT) component 
increases in wave-length with increasing field. He suggested 
that the anomalous behaviour of the 25- 4mA. component 
might account for the fact that mercury resonance radiation 
is only 80 per cent, polarized instead of 100 per cent., as would 
be expected for a 3/2 normal triplet. 

Ellett and MacNair [13], therefore, investigated the h.f.s. and 
polarization of mercury resonance radiation. Their apparatus 
was as follows: a resonance bulb, containing mercury vapour, 
was placed in a large coil capable of producing fields from to 
3450 gauss. The bulb was radiated from either side by polarized 
light from two water-cooled and magnetically deflected mer 
cury arcs. The resonance radiation was observed in a direction 
perpendicular to the two exciting beams by means of a 



RESONANCE RADIATION 285 

Wollaston prism and Lummer-Gehrcke plate. The fringe 
system, formed in the Lummer-Gehrcke plate, from both 
images from the Wollaston prism was photographed simul 
taneously on a photographic plate. 

In one experiment the mercury vapour pressure corre 
sponded to 18 C. ; the electric vector of the exciting light 
was vertical, and the bulb was in zero field. Hyperfine- 
structure pictures of the resonance radiation, previously shown 
to be 80 per cent, polarized with E vertical, showed that the 
vertical component consisted of the four lines 10-4, 0-00, 11-5 
and 21'5mA. and the horizontal component of only one line 
25*4 (perhaps also 21-5). With the mercury vapour pressure 
corresponding to C. the polarization was less, and the added 
intensity in the horizontally polarized beam was distributed 
over all five h.f.s. components. This shows that the depolariza 
tion is due to imprisoned resonance radiation or collision. With 
a strong magnetic field parallel to the exciting light vector, and 
at the lower mercury vapour pressure, the results remained 
the same as in the first experiment for fields up to 3450 gauss. 
Later experiments by Ellett[ii] showed that, when mercury 
resonance radiation is excited by polarized light containing 
only the two outer h.f.s. components, the polarization is 
markedly less than 80 per cent. 

86. THEORY OF THE EFFECT OF HYPERFINE STRUCTURE ON 
THE POLARIZATION OF RESONANCE RADIATION. The formulas 
for the polarization of a resonance line which consists of several 
h.f.s. components may be derived with the help of our discus 
sion of the nature of h.f.s. given in Chap. I and the application 
of the formulas given in 66 of this chapter. Let us first ex 
amine the very simple case of a resonance line of an element 
consisting of only one isotope of nuclear spin i. Each electronic 
level j will therefore split into a number of hyperfine levels/, 
and only those h.f.s. components will appear for which the 
selection rule is obeyed. 

Now, it can be shown that, in the presence of a small 
magnetic field, every hyperfine level / will split into 2/+ 1 
magnetic sub-levels, such that the quantum number m of each 



286 



THE POLARIZATION OF 



sub -level has values differing by unity and ranging from 
f^m^ -/. With these considerations in mind, it is a simple 
matter to construct the Zeeman diagram of any given h.f.s. 
component. It is apparent that the diagram for a h.f.s. com 
ponent, having an upper level / 2 and a lower level / x , will be 
entirely analogous to that of a gross line not showing h.f.s., and 
whose upper state has a quantum number j 2 numerically equal 
to/ 2 an( i a lower state with a quantum number J x numerically 
equal tof^ . The relative intensities and transition probabilities 
of any Zeeman component can be calculated in a manner 
analogous to that for a line not showing h.f.s. by substituting 
/for j in the intensity formulas. 



5'5 













', 2 












*3 












2 


1 


r ( 

U j , . 


'1 


r 7 


T <. 


r 







7T (T TT CT 



642246' 24 

Fig. 77. H.f.s. Zeeman diagram. ( 



H 
- 
--I 



"1 




24' 666 
-^ ; =0, = J.) 



If a line consist of several h.f.s. components which are not 
resolved by the apparatus employed, it is necessary to re 
arrange the transition probabilities of each line so that the 
relative intensity of each h.f.s. component will be in accord 
with the sum rule. This may be done in a variety of ways, but 
is best accomplished by making the total transition probability 
from any upper magnetic sub-level of any h.f.s. level the same 
for all such levels. This process is illustrated in Fig. 77, patterns 
a and b, for a hypothetical line of the form ^Q-^ with i ^ I /2. 
The numbers at the bottom of the diagram are the transition 
probabilities for the Zeeman components in question. It will 
be noticed that the chance of leaving any upper magnetic 
sub-level is in this case 6. 

We may now calculate the polarization to be expected for 
the simple case of an element consisting of one isotope having 



RESONANCE RADIATION 287 

a spin i. Let the lower state have a quantum number j with 
fine quantum numbers / G , each divided into magnetic sub- 
levels designated by m, and the upper state a quantum number 
j b with fine quantum numbers f b , each divided into magnetic 
sub-levels designated by JJL. The number of atoms associated 
with any hyperfine state f a of j will be 

(2 
(2; 

where .ZV is the total number of atoms. The number of atoms in 
any one magnetic level m of the lower state is 

Nm= (2j +l)(2i+l) (193) ' 

Now the chance of an atom arriving in an upper state p of / 6 
will be proportional to the number of atoms in the lower level 
N m , to the intensity of radiation of statable frequency to 
excite the h.f.s. component / v (/&,/J, and to the transition 
probabilities A^, AJw. The chance of reaching a magnetic 
sub-level p, of / 6 is therefore 



The relative chance of leaving the level p by a TT component is 

A hP , 

-T-. g , . . with a similar expression for the o- components. 
AJw+AJtr 9 * * 

The contribution to the intensity of the radiation which is 
polarized along or perpendicular to the field and comes from 
the level f b is 

_ CNI v (f b J a ) 

*h /Oi. j.l\/9A0.1\"7^ 7r .. , ^ 

[^[/^ cos 2 6 + ^^^ sin 2 ^] 



,*w cos 2 6 -f \AJf> v- sin 2 ff\ 
(195). 



288 THE POLARIZATION OF 

The polarization will then be given by 



It is more convenient, however, to make use of a quantity 
which may be called the contribution to the polarization from 
the level f b and is defined by 



fb 

It follows from Eqs. (196) and (197) that 

P = *P(fi>) ...... (196a). 

Using the relations 



S A v fa- 
t* 

it follows that 



Jto2/3_ cos 2m 

/* /* " ' * 3 ^ / v / 

(199), 

and the total polarization P readily foUows from Eq. (I960). 
In order to calculate the polarization for a line of an element 
having several isotopes a with relative abundances N^ and 
nuclear spins i a> one remembers that the number of isotopes 
of kind a which are in a given magnetic sub-level m of a lower 
state is 



RESONANCE RADIATION 289 

The polarization formulas then become 

= 79^Tn J v (A a Ja a ) |3S (4 ff ^) 2 - ^^ (^ &a )4 

\ ^a~*" / I M- J 

x (3 cos 2 6-1) 



(4&a)2 (3 __ CQS 2 0) (200) 



and P = SSP(/ 6 a ) (201). 

a/ ft a 

It follows at once from Eqs. (200) and (201) that the angle of 
zero polarization is the same for all resonance lines and is in 
dependent of h.f.s. The relation, Eq. (188), between Pj_ and P,, 
is also seen to be general for all resonance lines. 

In making a calculation all quantities in Eq. (200) are 
usually known with the exception of the / (/& a ,/ a a ), which 
depend on the type of exciting source used. The polarization 
of a given resonance line is therefore dependent on the character 
istics of the exciting source. Usually the relative intensity of the 
h.f.s. components in a given source is not measured in a given 
experiment. In making the calculation, one of two assumptions 
is made concerning the relative intensity of the h.f.s. com 
ponents in the source: (A) All h.f.s. components have the same 
intensity, I^ b *,f a *)' = I v (fi,*,fa*Y' = '--> etc. or (B) the rela 
tive intensities of the h.f.s. components depend on the relative 
abundance of the isotopes of the element in question and the 
statistical weights of the various h.f.s. states in a calculable 
way. Vacuum arcs, such as those employed in experiments on 
resonance radiation, usually show characteristics of the type 
A. Such excitation is usually called "broad line" excitation. 
When certain discharge tubes, such as the hollow cathode dis 
charge of Schiller, are used as exciting sources, the intensity 
characteristics of the exciting source are of the type B, 
usually designated by " narrow line ' ' . Since most of the present 
experiments on polarization of resonance radiation are per 
formed with vacuum arcs, broad line excitation is usually 
assumed in making the calculation. 



290 THE POLARIZATION OF 

Since a great number of experiments are performed under 
conditions in which the excitation is of type A, the resonance 
tube is in zero magnetic field, the incident light is polarized 
with electric vector vertical, and the observation direction is 
perpendicular to the exciting beam and the direction of the 
electric vector, it will be worth while to write down the 
formula for this case. Here = 0, I y (/ 6 / fl )' = I v (/, ,/)", 
etc.: 

N ( 9f a_i_ 1 

+ 



...... (202). 

8c. THEORY OF THE EFFECT OF HYPERFINE STRITCTURE ON 
THE POLARIZATION OF LINE FLUORESCENCE. The problem of 
the polarization of line fluorescence may be treated in a 
similar manner to that of resonance radiation. Consider three 
atomic energy levels a, b, c in Fig. 76. Let each level be divided 
into hyperfine levels designated by f a , f b , f c . We wish to 
calculate the polarization of the line be excited by the absorp 
tion of ah. By the usual calculation it follows that 



A<*A (3 cos" 6-1) 



6 ) 

- S ; S S A,fif^A,V^ (3 cos 2 6-1) 



(203 ), 



if broad line excitation is used. Here A^ a) t t is the chance of 
reaching the magnetic sub-level p, of / 6 a by the absorption of 
a TT component in the line ab; AJf* is the total chance of 
leaving p. off b by making all possible TT transitions to all states 
f c of c. Similarly A*> is the transition probability for any level 
//, of f b with regard to the line ab, and A*> is the total chance of 
leaving any level //, of f b with regard to the line be. Since ab is 
a resonance line, AJiWn and A 06 may be calculated according 
to the rules for resonance lines. Since be is a fluorescent line, 



RESONANCE RADIATION 291 

care must be taken in calculating AJ^^ so that the correct 
relative intensities of the h.f.s. components of be will be 
preserved. In general, several h.f.s. components may be 
excited by the absorption of one h.f.s. component of ab. 
Since, however, the gross line ab is usually separated from 
the gross line be, it is sufficient to let A^ be numerically 
equal to A bc . 

8d. COMPARISON OF EXPERIMENT WITH PRESENT THEORY 
OF POLARIZATION. Cadmium. Schiller and Keyston[43] have 
shown that the h.f.s. of the cadmium lines may be accounted 
for by assuming that the even atomic weight isotopes have no 
nuclear spin, while those of odd atomic weight have a spin 
i = 1/2. The Zeeman diagrams for the two resonance lines 3261 
and 2288 will be similar and are given in Fig. 77. In this 
diagram the non-spin isotopes are denoted by A and those with 
spin i = 1/2 are denoted by a and b respectively. The adjusted 
transition probabilities for the TT and or components are given 
at the foot of each diagram. The calculation of the polarization 
for various types of exciting sources and of magnetic field has 
been carried through by Mitchell [33] and more correctly by 
EUett and Larrick[i2]. 

Measurements of the polarization of the two lines 22$ 8 and 
3261 were made by Ellett and Larrick. The polarization was 
observed at right angles to the exciting beam, which was un- 
polarized. The resonance vessel was situated in a magnetic 
field of 40 gauss parallel to the exciting beam, and the vapour 
pressure of cadmium in the resonance tube was kept as low as 
possible (90-105 C. for 2288; 146 C. for 3261). The observed 
polarization in the case of 2288 was 76-3 per cent, and in the 
case of 3261 was 86-87 per cent. 

The calculation may be carried out with the following as 
sumptions. The absorption coefficient for the line 2288 is high 
enough, so that the source used may be considered as giving 
broad lines. In the case of the 3261 line, however, the exciting 
lamp was operated in such a way (small amounts of cadmium 
in a hydrogen discharge) that the authors believe that it ex 
hibited narrow line characteristics. If we assume that the 



292 THE POLARIZATION OF 

h.f.s. component due to the even isotopes (A) coincides with 
the stronger line (a) of the odd isotopes, then the relative inten 
sity of the exciting lines will be I A = I a = 2 + 3y ; I b = 1, where 
y is the ratio of the even to the odd isotopes. One can immedi 
ately calculate the polarization to be expected if y is known. 
Schiller and Keyston obtained the value y = 3-34 from their 
measurements on the h.f.s. of certain cadmium lines. Using 
this value of y, 5 = 77/2, and I A = I a = I b , Eqs. (200) and (201) 
give P = 80-5 per cent, for 2288, which is not in good agreement 
with the observed value of 76-3 per cent. Taking the observed 
polarization as correct, a value y = 2-53 is calculated, which, 
when used to calculate the polarization of the 3261 line under 
the above assumptions concerning the source, gives P = 86-l 
per cent., in good agreement with the observed values. The 
reason for the discrepancy between the value of y obtained 
from measurements of the intensities of h.f.s. components of 
visible cadmium lines and that obtained from the polarization 
of ultra-violet lines is not apparent. 

Mercury. As has been shown in Chap, i, 8, the h.f.s. of the 
2537 resonance line of mercury is complicated by the over 
lapping of components due to various isotopes, so that the 
calculation of the polarization becomes rather involved. The 
calculation has, however, been carried out by Larrick and 
Heydenburg [29], von Keussler [50} and Mitchell [34]. The Zeeman 
diagram for all the h.f.s. levels involved is given in Fig. 78. The 
letters X,A,B, a, etc. above each diagram correspond to the 
various h.f.s. components given in Fig. 12 of Chap. I. The 
numbers at the bottom of each Zeeman transition are the 
transition probabilities for the line. In the case of the isotopes 
199 and 201, only half of the transitions are drawn. 

In the case of broad line excitation, the intensity of each 
h.f.s. component is placed equal to unity, and the relative 
numbers of atoms of given isotopic kinds are given by N x 
(even atomic weight) = 0-6988, tf 199 = 0-1645, ^201 = 0-1 367. 
For narrow line excitation, the relative intensities of the 
various components are given in Fig. 12 of Chap. I. The cal 
culation is then carried out with the help of Eqs. (200) and 
(201). The results of the calculation are given in Table XLIX. 



RESONANCE RADIATION 



293 



The results are in substantial agreement with experiment. 
Von Keussler, using the usual mercury arc, found 79* 5 per cent, 
polarization, while Olson [37] varied the current in his source 
and found 79 per cent, with a current of 3-5 amperes, 84 per 



+i- 



ana 




ana 

J1L. 



II 

rra 



20 40 60 40 20 



ana 



Tra ana 



24 4 



24 6 18 



302010 36 24 32 60 36 36 



199 201 

Fig. 78. Zeeman diagram for 2537 (showing h.f.s.). 

TABLE XLIX 

POLARIZATION OF 2537 



Excitation 


Polarization (per cent.) 


0=0 


0=7T/2 


Broad line 
Narrow line 


84-7 
88-7 


73-5 

81-2 



cent, at 1 ampere, and 86 per cent, at 0-4 ampere. Both experi 
ments were performed in a zero magnetic field (6 = 0).' 

The experiments of Ellett and MacNair[i3], on the polariza 
tion of the separate h.f.s. components of 2537, showed that the 
three inner components (11-5, 0, - !O4mA.) were practicaUy 
completely polarized, whereas the two outer components 
showed incomplete polarization. Table L gives the results of 
the calculation for the polarization of each h.f.s. component in 



294 



THE POLARIZATION OF 



zero magnetic field. The agreement between theory and experi 
ment may be considered as satisfactory. 

TABLE L 
POLARIZATION or SEP ABATE H.F.S. COMPONENTS OF 2537 



Component 


Polarization 
(per cent.) 


21-5 
11-5 
0-0 
-104 
-254 


55-9 
100 
100 
84-8 
514 



Sodium. Sodium has but one isotope. The D lines of sodium 
are known to show h.f.s. components, but owing to experi 
mental difficulties an unambiguous value of the nuclear spin 
i has not until recently been found from direct measurement 
of its structure. Heydenburg, Larrick, and Ellett[26] used the 
method of polarization in an attempt to determine the spin. 
By the use of the Cornu method they found the polarization of 
the two D lines together to be 16-48 0-33 per cent., and of the 
D 2 line alone to be 20-5 per cent. They calculated the polariza 
tion to be expected for various values of the nuclear moment, 
and their results are given in Table LI below. The value i = 3/2 

TABLE LI 
SODIUM B LINES 



i 


** 


^2+1)1 





60 


50 


1/2 


40-54 


33-33 


1 


20-50 


16-6 


3/2 


18-61 


15-07 


2 


17-33 


14-02 


5/2 


1647 


13-32 


3 


15-91 


12-84 


7/2 


15-54 


12-56 


4 


15-28 


12-35 


9/2 


15-09 


12-19 


5 


14-28 


11-54 


Observed 1648-33 



RESONANCE RADIATION 



295 



has been obtained from three independent methods by Eabi 
and Cohen [39], Granath and Van Atta[i7], and Urey and 
Joffe[47]. It appears certain, from the work of these in 
vestigators, that the value i = 3/2 is the correct one. It may 
be seen from Table LI that the experiment appears to be in 
agreement with a value i=l. Owing to the fact that the 
separations of the upper h.f.s. levels are small, certain cor 
rections have to be made to the calculation. The necessary 
corrections have been pointed out by Breit[4], and a calcula 
tion, performed by Heydenburg and Ellett, appears to show 
that the experimentally observed value of the polarization 
is in accord with a value of i = 3/2. 

Thallium. Ellett [io] has carried through similar calculations 
for the slightly more complicated cases of thallium resonance 
radiation and line fluorescence. He used the h.f.s. data of 
Schiller and Bruck[42] who found a moment = 1/2, and made 
the calculation for a magnetic field parallel to the electric 
vector of the exciting light (and hence also for a zero field). 
He further assumed that the two isotopes (203 and 205) be 
haved as one entity with a moment i = 1/2. In calculating the 
relative intensities of the h.f.s . components for a c ' narrow ' ' line 
source, he used those obtained from the h.f.s. sum rule. The 
results of the calculation are compared with experiment in the 
following table. 

TABLE LH 



Line 


Polarization (per cent.) 


2768 
3530 
3776 
5350 


Nuclear moment 


Observed 


i=0 


;=i/2 


4-60 
-75 




A 
-i-33-2 
-41-8 




E 
+ 35-1 

-48-8 




+ 55 (470 C.) 
-60 (470 C.) 





+ means parallel to electric vector of exciting light. 
- means perpendicular to electric vector of exciting light. 
Ay broad line excitation; 5, narrow line. 

The experiments used for comparison in the case of 2768 and 
3530 are those of Giilke[i8], taken at the lowest pressure at 



296 THE POLARIZATION OF 

which he worked. The experiments on 3776 and 5350 are due 
to Ellett [8]. It will be seen from the table that the polarization 
of 3776 and 5350 is always zero, independent of the assumed 
nuclear moment, and the results agree with experiment. The 
quantitative agreement between theory and experiment for 
the two polarized lines is, however, not good. 

8e. EFFECT OF HYPERFINE STRUCTURE ON MAGNETIC 
DEPOLARIZATION AND THE ANGLE OF MAXIMUM POLARI 
ZATION. It is of interest now to discuss the effect of h.f.s. on 
the magnetic depolarization of resonance radiation, especially 
since the problem has an important bearing on the value of the 
mean life of a given state as measured by the depolarization of 
a fluorescent line coming from that state. We have seen that 
the classical theory gave a formula connecting the mean life 
with the polarization of a line when it was measured in a weak 
field parallel to the direction of observation. Recently Breit [4] 
has applied the quantum theory of radiation to the problem 
and has derived formulas for the magnetic depolarization and 
angle of maximum polarization of a resonance line in weak 
magnetic fields. 

If plane polarized light is incident on a resonance tube, and 
the resonance radiation is observed in a direction at right angles 
to both the exciting beam and its electric vector, and if a weak 
magnetic field H is applied parallel to the direction of observa 
tion, the polarization as a function of the field is given by 



\mc /6 

In the formula, P (H) is the polarization of a resonance or 
fluorescent line in a field H, P (/ & ) is the polarization in zero 
field of the components coming from an upper hyperfine state 
of an isotope a, g fb a is the hyperfine ^-factor for that state, 
and r is its mean life. The values of P (/ 6 a ) may be obtained 
for any line from Eq. (202), or Eq. (203) in the case of 
fluorescent lines, and the ^-values in question may be calcu 
lated from the usual formula*. The angle of rotation of the 

* See L. Pauling and S. Goudsmit, The Structure of Line Spectra, McGraw 
Hill Book Company, p. 219. 



RESONANCE RADIATION 297 

plane of polarization, i.e. the angle of maximum polarization 
(f>, is given by 



, 

where 

6/7 

tan 2< (/,*) = - -g fb T ...... (206). 

//t/O 

Mitchell [35] has used these formulas to calculate the mean 
lives of several excited states from already existing data for 
P (H) and tan 2^, and to see what error may have been made 
in r owing to the neglect of h.f.s. In carrying out the calcula 
tion, it is assumed that r is the same for any h.f.s. state of each 
isotope and is equal to the mean life of the atom in the excited 
state (n, I, j). This assumption has theoretical justification, 
although a direct experimental proof of it is lacking. Indirect 
evidence as to the validity of the assumption is, however, con 
tained in the fact that calculations made using the assumption 
are in accord with experimental facts, as will be evident from 
the following discussion. 

The calculation has been made for the 2537 resonance line 
of mercury, using the data given in Table LIII together with 
the value of T 1-08 x 10~ 7 sec. This value of r is that obtained 
by Garrett, and has been shown to be in agreement with 
absorption coefficient data by Zemansky and Zehden (see 
Chap. m). The values of P (/ 5 a ) given in the table are calcu 
lated with the help of Eq. (202). The results of the numerical 
calculation of P (H) and tan 2<f> are plotted in Fig. 79 and 
Pig. 80. The upper curve of Fig. 79 gives P (H) as a function of 
magnetic field obtained from Eq. (204). The lower curve is a 
hypothetical curve obtained on the assumption that the line 
2537 was due to isotopes having no nuclear spin and with a 
<7-value for the 6 3 P X state of 3/2, but that, for some unknown 
reason, the polarization in zero field was only 84-7 per cent. 
instead of the expected 100 per cent. Some experimentalists 
have made exactly this assumption in calculating r for mer 
cury and cadmium resonance radiation. The lower curve, 



298 



THE POLARIZATION OF 
TABLE Lin 



State 


*o(A a ) 


*<A") 


Even 






/-? 


0-754 


3/2 


199 






t = l/2 


0-000 





A =1/2 






199 






i = 1/2 


0-058 


1 


A =3/2 






201 






=3/2 


0-000 





A =1/2 






201 






=3/2 


0-016 


2/5 


201 






A=5/2 


0-020 


3/5 



100 

90 
< 
80< 






















































70 
60 
50 
40 
30 
20 

to 




kD 


\ 












___, L. 
-h 


A 

E M 


[fs.2537 r-l-OSxIO" 7 
lohfs. P -84-7% 
lson'sdata/J-84% 
lson'sdataP =79% 
.Keussler'sdataP -80% 






A 


N 
















.% 












~ 






\ 




















fc, 

tr-y 






S 2 


^ 


















<s 

ft. 








> 

ID 


H 


5>^ 




























^d 


) 

"^-B 


^!^- 


^^. 


^^2 


> 










H(gi 


n/5S) 









0-0 0-1 0-2 0-3 0-4 0-5 0-6 0-7 0-8 0-9 1-0 M 1-2 
Fig. 79. Polarization of 2537 as a function of weak magnetic fields. 



RESONANCE RADIATION 299 

therefore, shows the error in such a procedure for the case of 
2537; and it is seen to be quite small. The experimental points 
plotted for comparison with the theory are those obtained by 
Olson [37] and by von Keussler [49]. The circles represent experi 
ments made by Olson with his mercury arc operating under 
such conditions that the polarization in zero field is that given 
by theory. It will be seen that the points fit the theoretical 
curve, with r = 1-08 x 10~ 7 sec., within the limit of experimental 
error. Olson obtained a value for r of 0*98 x 10~ 7 sec. from a 
method of handling his results which did not involve the con 
sideration of h.f.s. The triangles on the diagram represent ex 
perimental points in which the exciting arc was run with 
higher current densities, while the squares give von Keussler's 
results. It is to be noted that, in this case, in zero field the 
experimentally observed polarization is not in accord with 
that predicted by theory. As the depolarizing field is increased, 
however, the points lie well on the theoretical curve. This is 
probably due to the self -reversal of the h.f.s. components in 
the arc operated at high current densities. 

In Fig. 80 the lower curve gives tan 2< as a function of the 
magnetic field H, calculated from Eq. (205). The upper curve 
is that obtained assuming that the entire radiation of the line 
2537 is due to non-spin isotopes having a ^-value 3/2. The 
experimental points are those of von Keussler, from which he 
calculated the value of r= 1-13 x 10~ 7 sec. The disagreement 
between experiment and theory is probably due to the 
intensity distribution in the source. 

Mrozowski [36] has measured the angle of maximum polariza 
tion as a function of magnetic field for certain separate h.f.s. 
components of the line 2537. In particular he has made 
measurements on the 0-0 and -hll-5mA. components to 
gether (each due to non-spin isotopes) and the 25'4mA. 
component. The latter component is due to the lines A and c 
coming from isotopes 199 and 201, respectively (see Fig. 12). 
The line c is, however, unpolarized, so that the contribution to 
the polarization, and hence to the angle of maximum polariza 
tion, is due entirely to the component A. The ^-value for the 
upper state corresponding to the 0-0 and -hll'5mA. com- 



300 



THE POLARIZATION OF 



ponents is 3/2, while that for the component A is 1. In these 
special cases Eq. (206) reduces to 






3-2 
2-8 
2-4 
2-0 
1-6- 
1-2- 






















vr 


}" nl 




















































y 


i; 45' 
























f 


IB 


























X^505' 


















E 


/ 




/ 






















/ 


f 


/ 










c^l 

e 














^^ 


/ 






















' 


/ 




















Q 


/ 


7 


























// 


























/ 


/ 
























/ 


/ 
























c 


'/ 






















0.x 






/ 


---Without Ms. (H;} T= H)8x10 7 
With hfs. J 
S von Keussler 






/ 


r 







E 


/ 


























,-6 












H (gauss) 













0-2 0-4 0-6 0-8 I'O 1-2 

Fig. 80. Angle of maximum polarization (2537). 

If one plots, therefore, tan 2<f> against H, for the components in 
question a straight line should result. If r is the same for both 
isotopes, the slopes of the lines should be in the ratio of the 
ff(fb ac ) ^ or ^ upper states, or in our case as 3/2: 1. Plots of 
Mrozowski's points for tan 2(f> against H do yield straight lines, 
and the ratio of the slopes for the central components to that 



RESONANCE RADIATION 301 

for the -25-4mA. component is 1-50. This value is in exact 
agreement with theory, and would appear to show that r is 
the same for both isotopes and is not dependent on which state 
/ or j is involved as the upper state. 

A similar calculation to that given above was made for 
cadmium by Mitchell. The results of a plot of P (H) against H 
give results in fair agreement with Soleillet's values, listed in 
Table XL VII, if r is taken to be 2-5 x 10~ 6 sec. 

8/. EFFECT OF LARGE MAGNETIC FIELDS; PASCHEN-BACK 
EFFECT OF HYPERFINE STRUCTURE. In our treatment of the 
effect of h.f.s. and polarization we have supposed, so far, that 
the vectors i and j are coupled together to form a resultant f , 
and that, in a magnetic field, this vector may have 2/+ 1 pro 
jections on the field direction, giving rise to the magnetic 
quantum number m f , which we have previously called simply 
ra. If now the magnetic field is sufficiently strong, the coupling 
between i and j will be broken, and each vector will orient itself 
in the field independently of the other. Such an effect is called 
the complete Paschen-Back effect of h.f.s. We may call these 
projections m % and m j respectively, and their vector sum m. 
The selection rules which now apply are : ( 1 ) m i does not change; 
(2) Am^O, 1. The polarization rules in this case are now 
given by the change in m^ (Ara ; - = 0, TT components ; Am^ = 1, 
a components). A schematic diagram for a line of the type 
^Q- 3 ?! with i = 1/2 is shown in Fig. 81, which should be com 
pared with Fig. 77, showing the same line in weak fields. It may 
be seen from Fig. 81 that, if an atom, situated in a very strong 
magnetic field, absorbs radiation which is polarized parallel to 
the field, the levels with m^ = will be reached. Since no tran 
sitions can occur to levels with m^ different from zero, TT com 
ponents will accordingly be re-radiated. One would expect, 
therefore, that a resonance line showing this type of structure 
would be 100 per cent, polarized if observed in a very strong 
magnetic field. From the above discussion it follows that the 
effect of h.f.s. on the polarization of resonance radiation dis 
appears if the experiment is carried out in very strong fields. 
This will be true for any resonance or fluorescent line, so that 



302 



THE POLARIZATION OF 



the degree of polarization calculated by means of the simple 
theory should be in agreement with experiment, provided the 
magnetic field is large enough. 

The strength of field necessary to obtain complete Paschen- 
Back effect of h.f.s. depends on the ratio of the separation of 
the h.f.s. levels in zero field to that due to the Zeeman effect on 
the multiplet level. When this ratio is large compared to unity, 
the Paschen-Back effect of h.f.s. will be complete. If, on the 
other hand, the ratio is of the order of unity, intermediate 
coupling schemes must be used. In this case formulas have 

m mi _ 

-\ -i 
*i 4 






: o 
>i 



7T 



M /-o 

Fig. 81. Paschen-Back effect of h.f.s. 



y-o 



been developed giving the transition probabilities for various 
TT and or components as a function of field strength*. 

This effect has been shown by various experiments. Von 
Keussler[49] showed that, whereas mercury resonance radia 
tion was about 80 per cent, polarized in fields ranging from to 
500 gauss, the polarization increased to about 100 per cent, 
in a field of 7900 gauss. Systematic determinations of the 
polarization of sodium resonance radiation as a function of 
magnetic field strength have been carried out by Larrickps]. 
In his experiment, the D lines were excited by polarized light 
and the resonance tube placed in a strong magnetic field 
parallel to the direction of the electric vector of the incident 

* See L. Pauling and S. Goudsmit, The Structure of Line Spectra, McGraw 
Hill Book Company, p. 219. 



RESONANCE RADIATION 



303 



light. The polarization of both D lines together was measured 
by observing in a direction at right angles to the magnetic 
field and to the direction of the incident light beam. The results 
of the experiment, showing degree of polarization as a function 
of field strength, are given in Table LIV. It may be seen from 

TABLE LIV 
POLARIZATION OF D LINES IK STRONG MELDS 



H 


Pj>i+I>2 


Error 





16-48 


0-38 


10 


16-26 


0-30 


20 


21-37 


0-38 


50 


34-54 


0-33 


70 


38-86 


0-33 


90 


43 





170 


44-5 





315 


46-25 






the table that the degree of polarization increased from 16-48 
per cent, in zero field to 46-25 per cent, in a field of 315 gauss. 
Since we have shown that the degree of polarization of the two 
D lines together should be 50 per cent., if calculated on the 
basis of no h.f.s., it seems probable, from Larrick's result, that 
a field of 315 gauss has caused an almost complete Paschen- 
Back effect of the h.f.s. of the D lines. Larrick used the 
theoretical formulas for calculating the degree of polarization 
in the intermediate field range, and, by comparing theory with 
experimental results, has determined certain constants having 
to do with the nuclear spin of sodium. 

Heydenburg [25] performed a similar experiment on the 2288 
line of cadmium. He excited the resonance line with un- 
polarized light, applied strong magnetic fields in the direction 
of the incident light beam, and measured the polarization of 
the resonance radiation (observed in a direction perpendicular 
to the field) by the method of crossed Wollaston prisms. 
Table LV, taken from his paper, shows the results of the 
experiment. In column 1 is given the observed polarization for 
the lines from both even and odd isotopes, and in column 2 the 
observed data of column 1 have been corrected for angular 
aperture of the exciting light beam. By the methods given in 



304 



THE POLABIZATION OF 



this chapter, the degree of polarization for the odd isotopes 
alone was calculated from that observed for the total radiation. 
ByuseofEq. (188) P n for the odd isotopes was calculated from 
the data in column 3. The results show that the radiation from 
the odd isotopes is about 43 per cent, polarized (P H ) in a zero 
field and increases to about 90 per cent, in a field of 563 gauss. 
From the intermediate field data he was able to calculate the 
constants of Goudsmit's equation. 

TABLE LV 
POLABIZATION OF Cd 2288 IN STRONG FIELDS 



p 

observed 


*o 
corrected 


PJL odd 
isotopes 


Pjl odd 
isotopes 


H 

(gauss) 


% 


% 


o/ 
/o 


% 




76-3 


76-7 


27-3 


42-7 





76-8 


77-3 


28-8 


44-7 


73 


79-3 


79-9 


36-0 


53-0 


144 


81-9 


82-5 


43-4 


60-5 


200 


85-5 


86-2 


54-4 


70-5 


255 


88-5 


89-1 


63-4 


77-6 


315 


91*3 


92-1 


73-0 


83-7 


375 


94-0 


95-0 


82-6 


90-5 


563 



9. STEPWISE RADIATION 

9 a. POLARIZATION or STEPWISE RADIATION. The stepwise 
radiation of mercury (see Chap, n), notably the visible triplet 
63p oi2- 73 Si and the ultra-violet triplet b*P &-**&!> **** 
recently been shown to exhibit polarization if excited by 
polarized light from a mercury arc. The phenomenon of 
polarization of stepwise radiation was discovered in a rather 
striking way by Hanle and Richter[23], They sent light from 
a water-cooled quartz mercury arc through a calcite block, and 
focused the two images as beams in the resonance tube con 
taining mercury vapour and about 2 mm. of nitrogen. They 
noticed that the two beams, seen as fluorescence, were of 
different colours; the beam with electric vector parallel to OX 
being blue green, the other (parallel to OT) being yellowish 
green. They immediately recognized this phenomenon as being 
due to polarization. 



RESONANCE RADIATION 



305 



Quantitative investigations of the polarization of the visible 
lines were made by Hanle and Richter, and of both ultra-violet 
and visible lines by Mitchell [32] and Richter [41], The results of 
Richter's observations are given in Table LVL 

The calculation has been carried through by Mitchell [35]* 
using Eq. (203) and the h.f .s. analysis of the mercury spectrum 
of Schiller and Keyston. It will be sufficient to mention certain 
assumptions of the calculations. The main contribution to the 
intensity of the stepwise lines is due to the non-spin isotopes, 
since they constitute 70 per cent, of the mixture. Since the 
calculation involving h.f.s. is rather tedious, we may discuss 



4047 



4358 



5461 



7*5, 



o 






1 










i 
























i 


! 






i 


r 1 


T < 


r TT < 


r c 


r c 


r <. 


\ 
i 
i 

TTT C 

\ J 


i 
I 

71 


i 
1 
i 
rcrnc 

\ \ 


r 


1 
I 
1 

T7TC 

\ 

\ 
















i - I 


f 


\ I 




| 








j t_ 


< 






' 6 3 /ji 


i 


t 




| 








/ 3 p o .. 






* 


~ r * u 

1 ,. ..,. i . 








t 


- 






o /j u 








f 










A , 


I 


I \ 


I 2 2 


: 


> ; 


i : 


> 2 6 


3 1 


3 4 3 




3 6 



Fig. 82. Zeeman levels of visible triplet of Hg. (Even isotopes.) 

the problem first in terms of the non-spin isotopes and then 
make the necessary corrections to account for the h.f.s. 

The magnetic energy level diagrams for the various states 
of the even isotopes and the allowed Zeeman transitions for 
the several lines in question are given in Fig. 82. It will be 
noticed at once that the 6 3 P state is single so that, as far as any 
subsequent absorption process is concerned, the way in which 
the 6 3 P state was reached is of no consequence. The polariza 
tion of the original 2537 line, therefore, need not be taken into 
account, nor need the effect of the collision between the 6 3 P a 
mercury atom and the nitrogen molecule introduce any com 
plications. The 6 3 P level may then be treated as the ground 
level and the phenomenon resolves itself into a simple case of 

* Earlier calculations by Mitchell [34] and von Keussler [50] led to 
erroneous numerical values for the polarization due to incorrect methods of 
calculation. The correct values for the polarization are given in Table LVL 



306 THE POLABIZATIOST OF 

the polarization of line fluorescence. Since the 7 3 S 1 and 
levels have the same type of magnetic splitting, and since the 
three 3 P states are involved in either the visible or ultra- violet 
triplet, the polarization of the visible lines ending on the 
various 3 P states will be the same as the ultra-violet lines 
ending on the same states. 

Starting then with atoms in the 6 3 P state, illumination 
with 4047 (or 2967) (Electric vector parallel to the field, i.e. 
.EH OX\\H of Fig. 70) leads to the absorption of the IT com 
ponent of 4047 (or 2967), and to the population of the middle 
level of the 7 3 S X (6 3 D X ) state. From this state the TT component 
of 4047 (2967), two a components of 4358 (3131), and various 
TT and a components of S461 (3663), may be re-radiated. A short 
calculation shows that, under these circumstances, 4047 (2967) 
should be +100 per cent., 4358 (3131) -100 per cent., and 
5461 (3663) + 14*3 per cent, polarized, when observations are 
made perpendicular to the field and to the direction of the 
incident radiation (along OY of Fig. 70). These results also 
hold in the absence of a field. If the field is perpendicular to 
both the electric vector of the exciting beam and to the obser 
vation direction (|| OZ), then one would expect 100 per cent., 
33 per cent., 7 per cent, for the three lines 4047, 4358 and 
5461 respectively. A sufficiently strong field parallel to the 
observation direction should give zero polarization for all lines. 
In the above notation the ( + ) means polarization parallel to 
that of the exciting beam and ( ) perpendicular to it. 

In considering the effect of h.f.s. one sees immediately that 
there is more than one magnetic level connected with the 6 3 P 
state. The effect of the nitrogen on the transfer of atoms from 
the 6 3 P X to the 6 3 P state must therefore be re-investigated. 
If one assumes an equal mean radiation life for each h.f.s. state 
of the resonance line (2537), and that the chance of transfer to 
the 6 3 P state by collision with nitrogen is the same for all 
isotopes, it follows that the relative number of isotopes in the 
6 3 P state after the collision process will be the same as that 
in the ground state (6 a S ). It must be assumed further that 
collision with nitrogen leads to an equal distribution of atoms 
among the magnetic sub-levels of a given hyperfine state. 



RESONANCE RADIATION 



307 



Since 6 3 P has the same structure as the ground level, the dis 
tribution of atoms among the magnetic sub-levels may be 
taken to be the same as in the ground state. With these assump 
tions in mind, the Zeeman diagrams of the h.f.s. components 
of the various lines in question may be drawn and the calcula 
tion made with the help of Eq. (203). Table LVI shows the 
result of the calculation, together with Richter's experimental 
results, taken in zero field. 

TABLE LVI 





Polarization 


Mean life 


Line 


Obs. 


Calc. 


<j> (Obs.) 


T (Richter) 


T (Calc.) 


4047 


72 6 


84-7 


17 


4-8 x 10~ 8 


7-2 xlO- 


4358 


-49 6 


-67-0 


29 


4-6 x 10~ 8 


1-69 x 10- 8 


5461 


131 


8-6 


29-5 


1-7x10-' 


1-53 x 10~ 8 


2967 


67 7 


84-7 











3131 


-29 7 


-67-0 











3663 


42 4 


8-6 












H = 2-81 gauss. The minus sign ( - ) indicates that the line is polarized with 
its electric vector at right angles to the electric vector of the incident light. 

One may see from the table that the agreement between 
theory and experiment is not good. The phenomenon is a com 
plicated one, and further work must be done to clear up present 
existing difficulties. Such work is now in progress, and it is to 
be hoped that it will lead to a successful solution of the various 
difficulties. 



96. MEAN LIFE OF THE V^ STATE OF Hg. By applying 
small magnetic fields in the direction of observation and keep 
ing the nitrogen pressure constant, Richter measured the 
magnetic depolarization and rotation of the plane of polariza 
tion of the visible triplet. From the angle of rotation, <, 
Richter calculated the mean life of the 7 3 S X state as measured 
by 4047, 4358, 5461 to be r 4047 = 4-8 x 1Q- 8 sec., r 4358 = 4-6 x 10~ 8 
sec., T54 61 = 1-7 x 1Q- 7 sec. 

These figures are only qualitative, since the mean life was 
found to depend on the nitrogen pressure. The interesting 
thing, however, is that the mean life of the 7 3 S 1 state as 
measured by 4047 and 4358 at 1-77 mm. nitrogen pressure is 
the same, but as measured by 5461 is four times larger. 



308 THE POLARIZATION OF 

These results, if correct, would be in disagreement with 
present theories of atomic structure. One would expect, 
theoretically, the mean life of a given electronic state n to be 
a property of that state, since by definition r n = (LA nk )~ l . If 

k 

the mean life of a state n be measured by experiments, such as 
those described above, on individual lines coining from that 
state the result should be the same for all such lines. 

In making the calculation from the measured angular rota 
tion </>, Richter neglected the effect of hyperfine structure and 
also used incorrect formulas for the calculation, and further 
more made a numerical mistake in the computation. Mitchell 
has recalculated Richter's results with the help of Eq. (205) 
and the hyperfine structure data and has obtained results 
quite different from those given above. These are shown in the 
last column of Table LVI. It appears from the results that 
further measurements will have to be made in order to be sure 
of the mean life of this state. One must point out that the 
apparent confirmation of Randall's [39 a] results by Richter 
must be considered to be no confirmation at all, due to an 
erroneous method of handling the experimental data. 

10. DEPOLARIZATION BY COLLISION 
We have seen in the foregoing sections that the polarization of 
resonance radiation decreases when the vapour pressure in 
creases, and have ascribed this phenomenon to the disturbing 
effect of neighbouring particles on the emitting atom. Leaving 
aside the question of the depolarizing effect of high vapour 
pressure of an element on its own resonance radiation a 
problem which offers some difficulties it will be well to con 
sider first the effect of foreign gases on the polarization of 
mercury and sodium resonance radiation. 

In the first place, Wood measured the polarization of mer 
cury resonance radiation as a function of the pressure of added 
gas, using the character of the polarization fringes from a 
Savart plate arrangement as a measure of the polarization. He 
found that with 0-65 mm. of air in the resonance tube the 
polarization fringes were strong and with 1 cm. of air they dis 
appeared entirely; with 2 mm. of helium they were faint, while 



RESONANCE RADIATION 



309 



with 1 cm. of hydrogen they were strong. These results were 
only qualitative and showed the influence of added gases on 
the polarization. 

Quantitative experiments were performed by von Keus^ 
sler[49]. With the mercury vapour pressure at 2x 10~ 5 mm. 
( 21 C.) various pressures of several foreign gases (O 2 , H 2 , 
A, He, N 2 , C0 2 , H 2 0) were added and the percentage polariza 
tion measured as a function of the gas pressure. The results of 
the observations are given in Kg. 83, from which it will be 
100, 




i-O 1-5 2-0 

Foreign gas pressure (mm.) 
Fig. 83. Depolarization by collision. 

noticed at once that 2 and H 2 have the smallest depolarizing 
effect, while H 2 and C0 2 have the largest, with the other 
gases ranging in between in the order named above. 

In Chap, iv it was shown that H 2 and 2 are the most 
efficient in quenching mercury resonance radiation. Other 
gases are much less efficient in removing mercury atoms from 
the G 3 ?! state, and kinetic theory calculations showed that, in 
some cases, a number of collisions were necessary before the 
6^ state became depopulated. Qualitatively, the low de 
polarization action of H 2 and 2 results from the fact that when 
an excited mercury atom is struck by an H 2 or 2 molecule it 
practically always loses its power to radiate, and the remaining 
unstruck atoms, being practically undisturbed, can radiate 
light showing a high degree of polarization. With argon, on 



310 THE POLARIZATION OF 

the other hand, the excited mercury atom may endure several 
collisions without losing its power to radiate, but when it does 
emit radiation the polarization properties will have been 
destroyed by these collisions. 

The mechanism of depolarization is usually thought of in 
terms of the Zeeman levels. In small fields the Zeeman levels 
are not widely separated and the energy difference between 
them is small. A colliding atom may give or lose a certain 
amount of kinetic energy to the excited atom, transferring it 
from one Zeeman level to another and thus causing a decrease 
of polarization of the emitted radiation. An increase in the 
magnetic field, however, causes a greater separation of the 
Zeeman levels, and the colliding atom is then not so efficient in 
transferring excited atoms from one magnetic state to another, 
due to the greater energy required, so that the polarization is 
not decreased to such a great extent by the addition of a given 
pressure of foreign gas. This has been shown by Hanle[22] for 
the case of sodium resonance radiation and argon, neon, 
helium and hydrogen. In every case, it took a greater pressure 
of added gas to depolarize the resonance radiation a given 
amount when there was a field of 600 gauss on the resonance 
tube, than in zero field. 

The effect of collision on the depolarization of resonance 
radiation may be represented by a formula similar to the 
Stern-Volmer* formula, namely 

P = ...... < 207 >> 



where P is the polarization observed with foreign gas pressure 
p, P the polarization when no foreign gas is present, and rZ D 
is the number of depolarizing collisions per lifetime of the 
excited atom. Since in von Keussler's experiments the mer 
cury vapour pressure was kept very low (corresponding to a 
temperature 2= 21 C.), the effect of imprisoned resonance 
radiation may be neglected. It has been shown in 1 of 
Chap, iv that 



...... (208), 



RESONANCE RADIATION 



311 



where a D 2 can be regarded as an effective cross-section for 
depolarization. From von Keussler 's experimental results and 
the use of Eqs. (207) and (208) values of o^ 2 have been found 
and are given in Table LVIL By comparing these figures with 

TABLE LVII 
DEPOLARIZING CROSS-SECTION FOB Hg RESONANCE RADIATION 



Foreign gas 


<7 D 2 X 10 16 


2 


5-28 


H 2 


3-29 


CO. 


49-5 


H 2 


47-7 


N 2 


33-8 


He 


9-92 


A 


17-6 



cr Q 2 (Chap, rv, 8), it will be seen that there is no relation 
between the effective cross-section for depolarization and that 
for quenching. It may be seen from Table LVII that the 
values of a D are of about the same order of magnitude as the 
usual kinetic theory diameters. Abnormally large values of &$ 
(10 4 times the kinetic theory value) were found by Datta for 
the depolarization of sodium resonance radiation by potas 
sium. Usually, large values of a D are found for the depolariza 
tion of resonance radiation by atoms of the same kind as the 
emitting atom. 

The extremely large value of a D for the case of the depolar 
ization of sodium resonance radiation by potassium was of 
unusual interest to the chemist at the time the work was 
published. The chemist had been looking for evidence of the 
transfer of energy by collision over large distances in order to 
account for the rates of first order monomolecular reactions. 
That the large value of a D found by Datta is not really due to 
a transfer of energy by a kinetic theory collision was shown by 
Foote [15]. He noticed that most atoms such as argon do not 
lead to large depolarizing diameters for sodium resonance 
radiation, and that these atoms have closed outer electronic 
shells and consequently no magnetic moment. Potassium, on 
the other hand, has only one valence electron in the outer shell 



312 THE POLARIZATION OF 

and consequently shows a magnetic moment. From this re 
mark of Foote's, it is quite easy to explain the large depolar 
izing effect of potassium. Thus, from the fact that it has a 
magnetic moment, potassium acts like a small magnet and the 
magnetic field due to the potassium atom is quite considerable 
at small distances (1C" 5 to 10~ 8 cm.). With a zero applied field 
the sodium atom might find itself in the field of a potassium 
atom, which could have a random direction with respect to the 
electric vector of the exciting light and thus cause depolariza 
tion of the resonance radiation. With large applied magnetic 
fields the depolarizing effect of potassium on sodium resonance 
radiation decreases. This effect is undoubtedly due to the 
setting in of the Paschen-Back effect of hyperfine structure in 
sodium. 

In the case of the depolarization of resonance radiation by 
atoms of the same kind as those emitting the radiation, two 
factors come into play: (1) the effect of imprisoned resonance 
radiation; and (2) the effect of collisions. It is known that in 
creasing the vapour pressure of gas has a large depolarizing 
effect on its own resonance radiation. In the past this has been 
ascribed to a large effective cross-section associated with 
depolarizing collisions. In view of the unknown effect of 
imprisoned resonance radiation it is unwise at this time to 
make any definite statements until further experimental work 
is done. 

11. EFFECT OF ELECTRIC FIELDS ON 
RESONANCE RADIATION 

11 a. MEASUREMENTS ON FREQUENCY (STARK EFFECT). 
Two major accomplishments in the development of physics 
have been the discovery and explanation of the Zeeman effect 
and the Stark effect. The former has been extensively dis 
cussed in the preceding sections, and is concerned with the 
behaviour of emission and absorption lines in magnetic fields. 
Somewhat similar phenomena take place in strong electric 
fields, as was shown originally by Stark. The original experi 
ment consisted in showing that an emission line of an element 
splits into several components if the emitting source is placed 



RESONANCE RADIATION 313 

in a strong electric field, the separation and number of the 
various components depending on the line in question, and the 
strength and direction of the electric field. For light atoms, the 
separation of the Stark effect components is measurable with 
apparatus of ordinary resolving power. In the case of heavy 
atoms, such as sodium or mercury, the splitting is too small to 
be measured with the usual spectroscopic apparatus, even in 
the highest fields obtainable. For this reason indirect methods 
of measurement have been devised which depend on the 
properties of absorption lines discussed in Chap. in. 

Ladenburg[27] investigated the effect of electric fields up to 
160,000 volts/cm, on the absorption of the sodium D lines by 
sodium vapour. Light from a discharge tube containing sodium 
and an inert gas was sent through an absorption cell containing 
sodium vapour, which could be placed in a strong electric field, 
and was examined visually with a Lummer-Gehrcke plate and 
spectroscope. The light source was operated in such a way that 
the light intensity from it was continuous and uniform over 
each D line (breadth of line about 0-13 A.), i.e. it exhibited 
neither self -reversal nor hyperfine structure. Observations on 
the D 2 line with the absorption cell in place, but in zero applied 
field, showed an absorption minimum at the centre of the line. 
In fields of from 95,000 to 160,000 volts/cm, the absorption 
minimum shifted toward the red by an amount between 
0-009 A. and 0-025 A., increasing approximately as the square 
of the field strength. 

An attempt at a quantitative measurement of the Stark 
effect broadening of the 2537 line of mercury was made by 
Brazdziunas[i], who used the method of comparing the form 
of an emission line from a resonance lamp with that of the 
absorption line in an absorption vessel (see Chap, ni, 4A). 
A mercury arc excited radiation in a resonance lamp, and the 
light emitted therefrom was sent through an absorption cell, 
containing mercury vapour, and its intensity measured by 
means of a photoelectric cell. The resonance lamp was fitted 
with brass plates, to which could be applied a potential suffi 
cient to give a field of 160,000 volts/cm. The experiment con 
sisted in measuring the change of intensity of the resonance 



314 THE POLARIZATION OF 

radiation transmitted through the absorption cell as a function 
of electric field applied on the resonance lamp, and comparing 
this with results obtained by applying a magnetic field of 
known strength to the resonance lamp. Taking the Zeeman 
splitting as known, and neglecting complications due to hyper- 
fine structure, the Stark effect splitting was calculated. Braz- 
dziunas found a shift of 5-4 x 10~ 4 A. for the a components (those 
polarized at right angles to the electric field) in a field of 
100,000 volts/cm., and of 1-9 x 10~ 4 A. for the TT component in 
a field of 140,000 volts/cm. He further shqwed that the wave 
length shift was proportional to the square of the applied 
electric field strength. 

The results of the experiment are open to the criticism that 
the hyperfine structure of the 2537 line was not considered in 
making the calculation, Since the splitting due to Stark effect 
is less than the hyperfine structure splitting, and since the 
calculation was based on the assumption that the 2537 line 
splits into one TT and two a components in a magnetic field, the 
absolute values of the wave-length shifts obtained may be in 
error. 

The Stark effect of some of the higher states of mercury was 
investigated by Terenin[46]. He investigated the intensity of 
the stepwise radiation produced in mercury vapour by strong 
illumination as a function of an electric field applied to the 
resonance vessel. He found that the intensity of certain lines, 
coming from higher states, decreased when the electric field 
was applied to the cell. The explanation is, of course, that the 
position of a given absorption line of the vapour is displaced by 
the field to such an extent that excitation by the corresponding 
line from the arc is impossible, the intensity of the fluorescent 
line being thereby decreased. The lines showing this effect 
were 5770, 5790, 3650, 3655, 3663, 3126, 3131 and 2967. 

116. MEASUREMENTS ON POLARIZATION. Hanle[2i] made 
an investigation of the effect of electric fields on the polariza 
tion of mercury resonance radiation. The resonance vessel con 
sisted of a glass bulb into which were fitted two brass plates, 
which, when charged by an electrostatic machine, were capable 



RESONANCE RADIATION 315 

of producing an electric field, in the region between them, of 
100,000 volts/cm. The vessel was equipped with suitable quartz 
windows so that mercury vapour contained therein could be 
excited and the resonance radiation observed. 

With the incident light progressing in the Z direction, and 
the electric field paraUel to X (see Fig. 70), the following 
experiments were made: 

1. Observation parallel to Y. 

(a) Electric vector parallel to X. The resonance radiation 
was linearly polarized parallel to X independent of the presence 
of the electric field. 

(b) Electric vector parallel to Y. The radiation was weak 
and unpolarized in the absence of a field; strong and polarized 
parallel to Z in the presence of the field. 

2. Observation direction at an angle of 25 to the incident 
beam (in YZ plane). 

(a) Electric vector parallel to X. The resonance radiation 
polarized paraUel to X independent of the presence of the 
field, as in 1 (a). 

(b) Electric vector parallel to Y. Resonance radiation 
polarized paraUel to Y in zero field, and slightly strengthened 
by the presence of the field. 

(c) Electric vector at an angle of 45 to the X axis. In zero 
field the resonance radiation was polarized in a direction 
paraUel to the incident electric vector. In the presence of a 
field of 100,000 volts/cm, the radiation was entirely unpolar 
ized. In weaker fields the radiation was eUipticaUy polarized. 

The explanation of these experiments may be attempted on 
the basis of the Stark effect diagram for mercury (Fig. 84), 
Neglecting complications which may arise from hyperfine 
structure, the 6^ state of mercury splits into three levels in 
an electric field: viz. 7i 3 = 0; ^ 3 = 1; these last two coincide, 
however. From these states TT and a components may be 
produced by transitions to the 6 1 S state. 

If the electric vector is paraUel to the field, a mercury atom 
wiU absorb only the * component reaching the upper state 
% = and wiU hence radiate a -n component, so that the 
resonance radiation wffl be polarized as in experiment 1 (a). 



316 THE POLARIZATION OF 

Experiment 1 (b) is definitely not in agreement with the theory. 
In this case, the electric vector of the incident light is perpen 
dicular to the electric field, so that only <r components are 
absorbed, and the states % = 1 will be reached. These states 
have the same energy, but the radiation given off when the 
atom drops back to the ground state will be circularly polar 
ized about the field in either a right-handed or left-handed 
sense depending on the sign of n 3 . In the language of quantum 
mechanics we may say that, on the average, the atom has as 
good a chance of being in one of the two states as the other. 
The radiation emitted should then consist of two circularly 



0- 
1- 



TT 



Fig. 84. Stark effect for 2537. 

polarized components of the same frequency and equal in 
tensity, and these two components should be capable of inter 
fering with each other. If one observes the resonance radiation, 
as in experiment 1 (6), at right angles to the direction of the 
electric field, the theory predicts that the radiation should have 
exactly the same appearance as regards intensity and polariza 
tion as if no field were applied. This is in disagreement with 
experiment, which showed that both the intensity and the 
polarization increased on applying the field, the direction of 
polarization being parallel to Z. 

A similar experiment was performed oa sodium resonance 
radiation by Winkfer [52], who found the same type of effect as 
that found by Hanle, which in this case is again in disagree 
ment with theory. 



RESONANCE BADIATION 317 

The reason for the discrepancy between theory and experi 
ment is possibly that the theory may have to be altered to take 
nuclear spin into consideration. It is to be hoped that this 
point will be investigated in the near future. 

REFERENCES TO CHAPTER V 

[1] Brazdziunas, P., Ann. d. Phys. 6, 739 (1930). 

[2] Breit, G., Journ. Opt. Soc. Amer. 10, 439 (1925). 

[3] ibid. 11, 465 (1925). 

[4] Rev. Modern Phys. 5, 91 (1933). 

[5] Breit, G. and EUett, A., Phys. Rev. 25, 888 (1925). 

[6] Datta, G. L., Z.f. Phys. 37, 625 (1926). 

[7] Dirac, P. A. M., Quantum Mechanics, Oxford University Press. 

[8] EUett, A., Nature, 114, 931 (1924). 

[9] Journ. Opt. Soc. Amer. 10, 427 (1925). 

[10] Phys. Rev. 35, 588 (1930). 

[11] ibid. 37, 216 (1931). 

[12] EUett, A, and Larrick, L., ibid. 39, 294 (1932). 

[13] EUett, A, and MacNair, W. A., ibid. 31, 180 (1928). 

[14] Fermi, E. and Rasetti, F., Z.f. Phys. 33, 246 (1925). 

[15] Foote, P. D., Phys. Rev. 30, 300 (1927). 

[16] Gaviola, E. and Pringsheim, P., Z.f. Phys. 34, 1 (1925). 

[17] Granath, L. P. and Van Atta, C. M., Phys. Rev. 44, 60 (1933). 

[18] Gulke, R., Z. f. Phys. 56, 524 (1929). 

[19] Hanle, W-, Naturwiss. 11, 691 (1923). 

[20] Z. f. Phys. 30, 93 (1924); Ergeb. der Exakten Naturwiss. 4, 214 

(1925). 

[21] Z. f. Phys. 35, 346 (1926). 

[22] ibid. 41, 164 (1927). 

[23] Hanle, W. and Richter, E. F., ibid. 54, 811 (1929). 

[24] Heisenberg, W., ibid. 31, 617 (1926). 

[25] Heydenburg, N. P., Phys. Rev. 43, 640 (1933). 

[26] Heydenburg, N. P., Larrick, L. and EUett, A., ibid. 40, 1041 (1932). 

[27] Ladenburg, R., Z.f. Phys. 28, 31 (1924). 

[28] Larrick, L. (Thesis). 

[29] Larrick, L. and Heydenburg, N. P., Phys. Rev. 39, 289 (1932). 

[30] MacNair, W. A., ibid. 29, 766 (1927). 

[31] p roc . Nat. Acad. Sci. 13, 430 (1927). 

[32] MitcheU, A. C. G., Phys. Rev. 36, 1589 (1930). 

[33] ibid. 38, 473 (1931). 

[34] ifcid. 40, 964 (1932). 

[35] ibid. 43, 887 (1933). 

[36] Mrozowski, S., Butt. Acad. Pol. Sci. (1930 and 1931), No. 6 A, p. 489. 

[37] Olson, H. F., Phys. Rev. 32, 443 (1928). 

[38] Pringsheim, P. and Gaviola, E., Z. f. Phys. 25, 690 (1924). 

[39] Rabi, I. I. and Cohen, V., Phys. Rev. 43, 582 (1933). 



318 POLARIZATION OF RESONANCE RADIATION 

[39 a] Randall, R. H., Pkys. Rev. 35, 1161 (1930). 

[40] Rayleigh, Proc. Roy. Sac. 102, 190 (1922). 

[41] Richter, E. F., Ann. d. Phys. 7, 293 (1930). 

[42] Schiller, H. and Briick, H., Z. f. Phys. 55, 575 (1929). 

[43] Schiiler, H. and Keyston, J., ibid. 67, 433 (1931). 

[44] Soleillet, P., Compt. Rend. 185, 198 (1927); 187, 212 (1928). 

[45] ^id. 187, 723 (1928). 

[46] Terenin, A., Z. f. Phys. 37, 676 (1926). 

[47] Urey, H. C. and Joffe, J., Phys. Rev. 43, 761 (1933). 

[48] Van Vleck, J. H., Proc. Nat. Acad. Sci. 11, 612 (1925). 

[49] Von Keussler, V., Ann. d. Phys. 87, 793 (1927). 

[50] Z. f. Phys. 73, 565 (1932). 

[51] Weisskopf, V., Ann. d. Phys. 9, 23 (1931). 

[52] Winkler, E., Z.f. Phys. 64, 799 (1930). 

[53] Wood, R. W., Phil. Mag. 44, 1109 (1922). 

[54] Wood, R. W. and Ellett, A., Proc. Roy. Soc. 103, 396 (1923); Phys. 
Rev. 24, 243 (1924). 



APPENDIX 

I. ABSORPTION COEFFICIENT OF A GAS. On the basis of 
the electron theory of dispersion, Voigt [Ref. 75, Chap, nr] 
showed that the absorption coefficient of a gas, when Doppler 
effect and natural damping are present, is given by 

ne * * bvy - dy ...(209), 



,, t 

v - 

2 / 



where n = index of refraction, 

UK- electron theory absorption coefficient, 
co = frequency at the centre of the line, 



&=- 



cV M 

v f = atomic damping constant, 
^= frequency distance from centre of line. 

In the notation of this book, the above quantities are as 

follows: 

^ JT i 
n i, 



- 

4-7T 



V = 



from which it is evident that 



= V&2==a [see Eq. (39)], 
2o Av 



and = - 0VE ^ =((j [see Eq> 



320 APPENDIX 

In the notation of this book, Voigt's formula then becomes 

k = / ?L ^ 2w 

v 77 AiAp V 77 me J o 

and in virtue of Eq. (35), namely 

2 /In2 rre*N 
AvpV 77 " me 
Voigt's formula becomes finally 



y 
-- 



Now it can easily be shown that 
arc tan 



, , 

-5 - 9 = arc tan - - - arc tan 
a 2 + co 2 - y 2 a a 



whence, Voigt's formula becomes 

k r f 2 <*> + / f a 

77 LJ o a Jo 

and upon integrating by parts 



.(210), 



fi-y*- 



l+ - 



1 , 
-ay 



e-^- 



d r 

77j _ a 2 



.(211), 



which is identical with Eq. (40). 



cos - 



Therefore 



and since 



= I e-^^ I 

'""JO J -oo 

& r 00 r 

= e-^coscoxfo 

77 J J - 

r*> _?! 

e~ y * cos o:i/ d2/ = VTT- e 4 5 

J -00 



v 

V 77 

which is the form given by Reiehe [Ref. 60, Chap. m]. 



(212), 



APPENDIX 321 

II. VALUE OF - 2 ** FOR SMALL VALUES OF a. 
Using Reiche's form of this integral and assuming that a ^ 0-01, 

T ! = ~ ~ e * coswxdx -7= I xe 4 cosa)xdx 

^0 A/77 J A/77 J 

2 f 2<z f" 3 

A/77 J A/77 J 

2 r 00 2^y r~ /* ~i 

= -7= e~' 2 cos 2wtdt ^=1 l-2a> er* sin 2a>tdt . 

A/77 Jo A/77L Jo J 

Using the formulas 

f v/ ^ 

Jo 6 " cos2a) ^ = T~ e "~ W2 

/*co /0> 

and e~^sin2cu^i = e~ a> e xZ dx=F(aj), 

Jo Jo 

the absorption coefficient assumes the form given by Eq. (41), 
namely 

Jc 2a 

= /? ^ 2 ri *>, ~w {/ \\\ (9.1 Q\ 

&0~~ A/7^ 

The following table of values of F (co) was obtained from the 
very complete table of W. Lash Miller and A. R. Gordon in the 
Journal of Physical Chemistry, 35, 2878 (1931). 

It is interesting to note that 



act) 
For small values of o> 



(2o>y (20,*)* 

nr3--i^5 + r3^7 



whereas for large values of c 



322 



APPENDIX 



CO 


I'M 


l-2o> F (<o) 


CO 


F(aj) 


l-2co F(u) 




Q 


0-0000 
1948 


1-0000 
9221 


6-0 
6-2 


08454 
08174 


01451 
- -01355 


Z 

4 . 
6 

.0 


3599 
4748 
5321 


7121 
4303 
1487 


64 
6-6 
6-8 


07912 
07666 
07435 


- -01268 
-01190 
-01118 


*o 

1-0 
1-2 
14 
1-6 
1-8 
2-0 
2-2 
24 
2-6 
2-8 
^0 


5381 
5073 
4565 
3999 
3468 
3013 
2645 
2353 
2122 
1936 
1783 


- -07616 
- -2175 

-2782 
- -2797 
-2485 
- -2052 
-1638 
- -1295 
-1033 
- -08389 
-06962 


7-0 
7-2 
74 
7-6 
7-8 
8-0 
8-2 
84 
8-6 
8-8 
9-0 


07218 
-07013 
06820 
06637 
06464 
06300 
06144 
05995 
05854 
05719 
05591 


- -01053 
- -009938 
- -009393 
- -008892 
- -008429 
- -008000 
- -007608 
- -007242 
- -006902 
- -006586 
- -006290 


O v 

3-2 
34 

3*6 


1655 
1545 
1450 


-05896 
-05076 
-04430 


9-2 
94 
9-6 


05467 
05350 
05237 


- -006014 
- -005757 
- -005516 


3-8 
4-0 
4-2 


1367 
1293 
1228 


-03908 
-03480 
-03119 


9-8 
10-0 
10-2 


05129 
05025 
04926 


- -005290 
- -005076 
- -004877 


44 


1168 


-02815 


104 


04830 


- -004688 


4-6 


1115 


-02554 


10-6 


04738 


- -004511 


4-8 


1066 


-02336 


10-8 


04650 


- -004344 


5-0 


1021 


-02134 


11-0 


04564 


- -004183 


5-2 

54 


09804 
09427 


-01963 
-01812 


11-2 
114 


04482 
04403 


- -004035 
- -003893 


5-6 
5-8 


09078 
08755 


-01678 
-01558 


11*6 
11-8 


04327 
04253 


- -003757 
- -003630 








12-0 


04181 


- -003510 



III. LIKE ABSORPTION A L . The line absorption A L is de 
fined as [see Eq. (58)] 



and is evaluated by means of the series 



where a n 



(n+l) 



APPENDIX 



323 



The following table was taken from the papers of H. Kopfer- 
mann and W. Tietze, Z.f. Phys. 56, 604 (1929), and B. Laden- 
burg and S. Levy, ibid. 65, 189 (1930). 



V 


AL 


kl 


A L 


k l A L 










- 


0-1 


-070 


1-1 


491 


2-1 -675 


0-2 


129 


1-2 


-516 


2-2 


685 


0-3 


181 


1-3 


538 


2-3 


695 


04 


232 


1-4 


562 


24 


706 


0-5 


284 


1-5 


-583 


2-5 


-715 


0-6 


327 


1-6 


602 


2-6 


724 


0-7 


366 


1-7 


619 


2-7 


732 


0-8 


401 


1-8 


634 


2-8 


-738 


0-9 


433 


1-9 


649 


3-0 


-750 


1-0 


465 


2-0 


662 


4-0 


-800 










5-0 


835 



IV. THE ABSORPTION A a . This is defined as [see Eq. (61)] 



f 

J -0 



The following table is the result partly of the use of the above 
series, partly of graphical integration and partly of graphical 
interpolation. 



Avtf 

~OL 

Av D 





0-5 


1-0 


1-5 


2-0 


2-5 


3-0 


V 

o 























25 


221 


200 


160 


-125 


102 


086 


0723 


50 


-393 


-360 


-291 


229 


188 


-159 


133 


1-0 


632 


588 


-486 


385 


316 


265 


-226 


1-5 


111 


736 


619 


494 


400 


336 


287 


2-0 


865 


832 


711 


575 


472 


400 


348 


3-0 


-950 


925 


820 


674 


564 


-476 


414 


4-0 


982 


967 


878 


740 


622 


-532 


461 


4-5 


989 


977 


897 


762 


640 


549 


480 



324 



APPENDIX 



V. THE FUNCTION 8. This is defined as [see 4/, Chap, in] 
1 



.-f .... 



= 1 - 



(V) 2 (M J 



2!\/2 ' 3IA/3 4! \/4 

The following table of values of S was obtained from the 
paper of R. Ladenburg and S. Levy, Z. f. Phys. 65, 189 (1930). 
A convenient relation exists between S and A L , namely 

2S(2k l) 

- 



V 


S 


k lS 


k l 


S 


k lS 





1-000 





1-2 


683 


820 


10 


964 


0964 


1-4 


646 


905 


15 


948 


142 


1-6 


616 


985 


20 


933 


187 


1-8 


584 


'050 


25 


917 


229 


2-0 


556 


112 


30 


902 


270 


2-2 


532 


170 


35 


887 


311 


2-4 


507 


218 


40 


872 


348 


2-6 


487 


267 


45 


859 


387 


2-8 


468 


311 


50 


844 


421 


3-0 


450 


350 


55 


831 


457 


3*2 


432 


385 


60 


818 


491 


3-4 


417 


415 


65 


806 


524 


4-0 


372 


1-488 


70 


793 


555 


44 


347 


1-530 


75 


780 


585 


5 


316 


1-580 


80 


768 


620 


6 


276 


1-656 


85 


757 


640 


7 


246 


1-720 


90 


745 


675 


8 


222 


1-778 


95 


734 


700 


9 


202 


1-820 


1-00 


725 


725 


10 


186 


1-860 


i 













(l_ e -V. 

I r J -co 



P (l-e-W 

J -00 



VI. THE ABSORPTION A' k<i , v . This is defined as [see 
Eq. (59)] 



From the definition of the function S, it is apparent that 

' 



APPENDIX 



whence expanding the expression ( 1 e~' 
making use of the function JL a , we get 

* I J /7 f\ toft & A 



325 

) in a series and 



The following table was obtained from the above series and 
with the aid of the reciprocal relation 

xS(x)A x '(y)=yS(y)A y '(x). 

VALUES OF A' k . r . 



\v 

v\ 





5 


1-0 


1-5 


2-0 


2-5 


3-0 


4-0 





























25 


160 


156 


153 


149 


147 


145 


144 


135 


50 


291 


285 


279 


273 


267 


-262 


258 


246 


1-0 


486 


475 


465 


454 


445 


437 


429 


419 


1-5 


619 


608 


597 


583 


573 


-562 


551 


540 


2-0 


711 


700 


687 


674 


662 


651 


642 


626 


3-0 


820 


811 


800 


789 


776 


764 


750 


740 


4-0 


878 


870 


861 


850 


839 


828 


817 


800 


4-5 


897 


889 


880 


869 


858 


848 


839 



















i 



VII. Kumsr's THEORY OF MAGNETO-ROTATIOK. [Ref. 32, 
Chap, m.] According to the classical dispersion theory, and in 
agreement with the quantum theory, the index of refraction n 
of a gas at the frequency v in the neighbourhood of an absorp 
tion line at the frequency v is given by [see Eq. (87)] 

e*Nf 
- ~- - 



If the gas be placed in a magnetic field and be traversed by 
a beam of plane polarized light travelling in the direction of the 
lines of force, there will result a rotation of the plane of polar 
ization, because of the difference in magnitude between the 
index of refraction for right-handed circularly polarized light 
and that for left-handed. 

In order to calculate the index of refraction for right-handed 
circularly polarized light travelling parallel to a magnetic field 



326 APPENDIX 

of strength H, it is necessary to take into account that, in 
place of the undisturbed absorption line at v , there are various 
right-handed circularly polarized Zeeman components with 
intensities j8 5 and at frequencies v + oca 5 , where the subscript s 
refers to the particular Zeeman component, a represents the 
normal Zeeman separation 

He 

a = - 



and oc s the splitting factor of the 5th component. The index of 
refraction for right-handed circularly polarized light at the 
frequency v is then given by 



From the principle of spectroscopic stability, the j8 s or 
relative intensities of the various Zeeman components satisfy 
the condition that 

S&=1. 

For left-handed circularly polarized light at the frequency v y 
the index of refraction is given by 



n 1= 

+ 



If x v denote the rotation of the plane of polarized light in 
traversing a layer of gas of thickness Z, then 



L 



v v aa 



2mc . (v-v ) 2 -a 2 oc s 2< '< 

If we limit ourselves to the edges of the absorption line, so that 



then we can write 

Xv _ Nfe^ 
I 2mc(v-v ) 2 7 *' 

A- * A 
and introduemg a= 



and ft = 27r(v v ), 



APPENDIX 



327 



there results 



which in comparison with Eq. (72) shows that 



(216). 



The quantity z indicates how much bigger the observed 
magneto-rotation will be in the neighbourhood of an absorp 
tion line with anomalous Zeeman effect (characterized by the 
splitting factors a s and the intensities & of the circularly 
polarized components) than the magneto-rotation in the neigh 
bourhood of a line of the same intensity but with normal 
Zeeman effect. Since the splitting factors and relative in 
tensities of the Zeeman components of aU normal multiplets 
are known, z can be easily computed. They are given in the 
following table: 



Line 


> 


A 


ou 


A 


8 


lg 21 p 


1 


1 








1 


IS* "'"p 1 


t 


1 
1 





z 


3 
i 


1S$-2P$ 


i 


J 


I 


i 


| 


i'P^-S'D,'', 


A 


1 


it 


i 


* 



The values of a s in the above table are strictly accurate only 
for values of the field strength H in the neighbourhood of 
1000 gauss or more. The experiments of Minkowski show, how 
ever, in the case of the sodium D lines that no error is introduced 
at 300 gauss, and even as low as 30 gauss a difference of only 
5 per cent, was noted by Weingeroff. This is due to the fact that, 
in the neighbourhood of 300 gauss, the Paschen-Back effect 
of the hyperfine-structure components sets in [see Chap. v]. 

VIII. EFFECT OF HYPERFINE STRUCTURE ON THE VALUE OF 
Xv . It was shown by Weingeroff [Ref. 81, Chap, m] that when 
a'spectral line consists of hyperfine-structure components of 
which the ith component is at the frequency v^ the magneto- 
rotation may be calculated by the method of Kuhn, provided 



328 APPENDIX 

one sums over all Zeeman components of all hyperfine- 
structure components. Therefore 



and the magneto-rotation is 



7 



At the edges of any component where 



we have Xv = _ 

and finally, if we denote by v the frequency of the centre of 
gravity of the hyperfine-structure components, we can write 
approximately 



where K^ is defined by the formula 

/>=*;/ 
and must satisfy the condition that 



In comparison with E<j. (72), it is apparent that, in this case, 

...... (217), 



which shows that z depends not only on the relative intensities 
j8^. and splitting factors <x s . of the Zeeman components, but 
also on the relative /-values of the hyperfine-structure com 
ponents, 



IX. VALTJE OF - -^ , y , 9 FOB LARGE VALUES OF 



a! . A series expansion was used to evaluate this integral for 
a' = 0-5, 1-0 and 1-5 according to a method due to T. H. Gron- 
wall and given in a paper by M. W. Zemansky, Phys. Bev. 36, 
919 (1930). The values for a! = 2 and 10 were obtained from a 
table in Born's Optik, p. 486. 



a'=0 



a> 


* 
*o 


-0 


1-0000 


2 


9608 


4 


8521 


6 


6977 


8 


5273 


1-0 


3679 


1-2 


2369 


1-4 


1409 


1-6 


0773 


1-8 


0392 


2-0 


-0183 


2-2 


0079 


2-4 


0032 


2-6 


-0012 


2-8 


0004 


3-0 


0001 



a'=l-5 



CO 


* 

*o 





3216 


-2 


3186 


4 


-3097 


6 


2958 


-8 


-2779 


1-0 


-2571 


1-2 


2349 


1-4 


2123 


1-6 


1902 


1-8 


-1695 


2-0 


1504 


4-0 


0487 


6-0 


0228 


8-0 


0131 


10-0 


0083 



APPENDIX 


of = 0-5 


CO 


1 


-0 


6157 


-2 


-6015 


-4 


-5613 


-6 


5011 


8 


4294 


1-0 


3549 


1-2 


2846 


1-4 


2233 


1-6 


1728 


1-8 


1333 


2-0 


1034 


4-0 


-0183 


6-0 


0081 


8-0 


004 


10-0 


003 



329 



a'=2 



CO 


kv 



-4 


257 
252 


8 


236 


1-2 


-212 


1-6 


178 


2-0 


148 


2-4 


123 


2-8 


101 


3-2 


0850 


3-6 


0708 


4-0 


0598 


4-4 


0505 


4-8 


0440 


5-2 


0378 


5-6 


6330 


6-0 


6291 


6-4 


0259 


6-8 


0231 


7-2 


-0208 


7-6 


0186 


8-0 


0169 






k v 
F 





-4276 


2 


4215 


4 


4038 


6 


3766 


8 


3425 


1-0 


3047 


1-2 


2662 


1-4 


2292 


1-6 


1954 


1-8 


1657 


2-0 


1402 


2-2 


120 


2-4 


102 


2-6 


088 


2-8 


-078 


3-0 


066 


3-2 


057 


3-4 


051 


3-6 


045 


3-8 


041 


4-0 


037 


6-0 


016 


8-0 


009 


10-0 


005 



a'=10 



CO 






2 


0561 
0541 


4 


0486 


6 


-0414 


8 


-0344 


10 


0283 


12 


-0232 


14 


0191 


16 


0159 


18 


0134 


20 


0114 


22 


00965 


24 


00835 


26 


00728 


. 28 


00637 


30 


00564 


32 


00502 


34 


00451 


36 


00406 


38 


00366 


40 


00333 



330 



APPENDIX 



X. DIFFUSED TRANSMITTED RESONANCE RADIATION. 
When a collimated beam of resonance radiation of frequency 
between v and v + dv and intensity K is incident in the positive 
x direction upon the face x = of a slab of gas whose absorption 
coefficient for this radiation is i, the intensity of the radiation 
emitted in the positive x direction from the face x = Z is given by 

irI+(x = l) = KG(kl 9 TZ Q ) [see Eq. (141)], 
where G(kl,rZ Q ) 



sinh2H 



/ 
N 



where r = lifetime of the excited state, 

Z Q = number of quenching collisions per second per 

excited atom. 

The following table of values of G was obtained from a paper 
by M, W. Zemansky, Phys. Rev. 36, 919 (1930). 

VALUES OF G (U, rZ Q ). 



\rZ Q 
*\ 





05 


10 


20 


333 


50 


0-5 


194 


175 


164 


143 


125 


107 


1-0 


290 


260 


236 


198 


160 


128 


1-5 


332 


282 


244 


195 


150 


118 


2-0 


344 


273 


227 


168 


124 


092 


2-5 


334 











0968 





3-0 


320 


219 


163 


106 


0704 


0488 


3-5 


300 








_ 


0504 





4-0 


280 


158 


104 


0590 


0351 


0224 


4-5 


260 











0241 





5-0 


243 


108 


0628 


0308 


0163 


00968 



XI. SAMSON'S EQUIVALENT OPACITY. The equivalent 
opacity, H, is defined by Samson as follows [see Eq. (142)]: 



J 



APPENDIX 



331 



where I is the thickness of the absorbing layer. The following 
values were obtained by graphical integration. 



V 


kl 








1 


0-665 


2 


1-241 


3 


1-715 


4 


2-104 


9-7 


3-29 


144 


3-76 


19-9 


4-15 



XII. KENTY'S EQUIVALENT OPACITY. The equivalent 
opacity Id is defined by Kenty as follows [see Eq[. (158)]: 



where 



) = e-< z 

Jo 



The following table was obtained with the aid of the table 
of values of F (o>) given in Appendix II. 



w 


H 


V 


kl 


1-5 


3-05 


100 


21-2 


2 


2-76 


200 


31-4 


3 


2-97 


500 


54-2 


4 


3-31 


1000 


77-8 


5 


3-70 


2000 


114 


10 


5-39 


3000 


142 


15 


6-85 


4000 


166 


20 


8-10 


5000 


186 


30 


10-4 


6000 


205 


40 


12-3 


7000 


223 I 


50 


14-1 


8000 | 240 



XIII. POLABIZATION OF RESONANCE RADIATION EXCITED 

BY UNPOLABIZED LIGHT. In making experiments on the 
polarization of resonance radiation, it is sometimes convenient 
to use an unpolarized exciting source, on account of the gain in 
light intensity thereby afforded, and to be able to convert this 
data into a form which will be comparable with the expressions 



332 APPENDIX 

developed in Chap. v. Suppose that a parallel beam of exciting 
light is progressing in the Z direction (Fig. 70) and that obser 
vations of the polarization of the resonance radiation are to be 
made along T . In this case the electric vectors of the exciting 
light lie in the XT plane. Three interesting cases arise for 
computation. 

(1) Strong Magnetic Field in Direction of Incident Beam. 
In this case the electric vectors all lie perpendicular to the 
field so that = 7r/2, and the polarization is P . 

(2) Strong Magnetic Field at Bight Angles to Incident Beam 
and Observation Direction. With the field parallel to X we may 
resolve the incident light into two polarized components. One 
polarized parallel to the field ( J||) and one perpendicular to this 
(/ ). To calculate the polarization, we write down the following 
equations, which follow from Eq. (182): 



The polarization is now P > defined by 



Remembering that I\\ = I, and using Eq. (187), a short 
calculation shows that 



where P\\ is the polarization observed with the incident light 
polarized parallel to the field H which is also parallel to X. 

(3) Zero Magnetic Field. If the resonance tube is situated in 
a zero magnetic field, we must make an application of the 
Principle of Spectroscopic Stability. Let the incident beam be 



APPENDIX 333 

resolved into two components polarized at right angles to each 
other, the one parallel to X, the other parallel to F. Let their 
intensities be I x and I 7 respectively. Consider first the reso 
nance radiation due to excitation by the component polarized 
parallel to X . On account of spectroscopic stability we must 
assume, in this case, that the resonance tube is situated in a 
small magnetic field parallel to X. This will give rise to reso 
nance radiation one component of which will be polarized 
parallel to X, and which we shall call x (I x ). The other com 
ponent will be circularly polarized about the field, but we shall 
see only the projection of this, since we observe in a direction 
perpendicular to the field. This radiation will be polarized 
along Z and will be called 77^ (J^). For excitation by I 7 , how 
ever, we must assume a small field parallel to the observation 
direction. The emitted resonance radiation will then consist of 
a part linearly polarized along Y, which will not be seen by the 
observer, and a part which will be circularly polarized about Y. 
This latter may now be resolved into two components of equal 
intensity polarized parallel to X and Z, respectively, which we 
may call r) x (I 7 ) and T\ Z ( J r ). Furthermore, it is obvious that 



The intensities of the components polarized parallel to X and 
Z, respectively, may be called 



and ^ 

The polarization is then given by 



If, on the other hand, we had measured the polarization (in zero 
field) of resonance radiation, excited by light of intensity I x 
polarized in the X direction, we should have found a com 
ponent polarized parallel to X, f *(/*), and components 
circularly polarized about X, of which we see only the projec 
tion f] z fix)' The polarization in this case is 



p jcj:-^ (22Q) 

~ ...... ( 



334 APPENDIX 

From Eqs. (219) and (220) it follows that 



Tn using the above formulas it is convenient to associate a plus 
sign with radiation partially polarized parallel to X and a 
minus sign with that polarized parallel to Z. In applying the 
formulas the signs of the polarization must be considered. For 
example, if P = +0-5, then P = + 0-333; or if P = -0-5, 
P =-0-20. 



INDEX 



Absorption, 118, 323 ff. 

by excited atoms, 44 

in magnetic field, 127 

of hyperfine structure components, 
126, 127 

of resonance radiation, 165 

stimulated by collisions, 113, 114 
Absorption coefficient, 92, 93, 97, 
99ff., 117, 128, 130,319 

area under the, 116, 117 

at the centre of a resonance line, 117 

at the edges of a resonance line, 128 

equivalent, 200, 201 
Absorption line, 92 

central region of, 102 

form of, 185 

half breadth of, 93 

shift of, 174 
Angle of maximum polarization, 267, 

297, 299, 300 
Angular momentum, 4 
Anomalous dispersion, 141 ff. 
Arcs with circulating foreign gases, 25 

with stationary foreign gases, 22 ff. 

without foreign gases, 21 
Argon, metastable atoms of, formation, 
243 

metastable atoms of, lifetime, 240 
As, fluorescence of, 17 
Asymmetric broadening, 174 
Asymmetry of a line, 180, 182 

Ba, resonance line of, anomalous dis 
persion, 144 
Bi, fluorescence of, 17 
Breadth of the absorption line, 93 
Broad line excitation, 289 
Broadening of an absorption line, 98 

Ca, resonance line of, anomalous dis 
persion, 144 

Cario-Lochte-Holtgreven lamp, 26, 27 

Cd, absorption coefficient of, 124 
energy levels of, 55 
excitation curve of, 149, 150 
hyperfine structure of, 291 

Cd arc, 22 

Cd excited atoms, mean life, 280 
quenching by collisions, 225 

Cd hydride, 79, 80 

Cd lines, magnetic depolarization of, 

279, 280 
polarization of, 304 



Cd resonance line, /-value, 135 

half lifetime, 135 
Cd resonance radiation, 15 
polarization of, 279, 280 
quenching of, 190 
Cd stepwise radiation, 54 
Central region of the absorption line, 

102 

Classification of the states, 4, 5, 6, 7 
Collision, connected with photo-ioniza- 

tion, 215 
involving the enhancement of spark 

lines, 217 
meaning of, 154 
of the first kind, 57 
of the second kind, 57, 59, 156 ff., 

220 
of the second kind, cross-section, 

214 

of the second kind, efficiency of, 66 
perturbing, 156 
stimulated emission and absorption, 

113, 114 

Conservation, of angular momen 
tum, 78 

of multiplicity, 69, 70 
Cross-section, depolarizing, 311 
effective, 155 

for Lorentz broadening, 170, 171 
of metastable atoms, 247, 249, 253 
of quenching, 206, 210, 211, 213 
of second kind collisions, 214 
Crossed spectra, 17 
Cs, photo-ionization by collisions, 215, 

216, 217 
polarization of the resonance line, 

143 

Cs fluorescence, 19, 20 
Cs resonance line, /-value, 135 
half lifetime, 135 

Damping, 186 

Decay constant of resonance radia 
tion, 229 ff . 

Decay of metastable atoms, 238, 239, 
251, 253 

Decomposition by excited atoms, 83- 
86 

Degenerated levels, 269 

Degree of polarization, 267, 271, 275, 
288, 289 

Depolarization, by collision, 308, 309 
magnetic, 270, 271 



336 



INDEX 



Diffuse bands associated with resonance 

radiation, 89 
Diffuse series, 5 
Diffusion of metastable atoms, 246 ff. 

cross-section, 247, 249, 253 
Dispersion electrons, 96 
Dispersion formula, 140 ff. 
Dissociation, of ILj by excited atoms, 
72 ff., 80 

of Nal, 204, 205 
Doppler breadth, 99 
Doppler broadening, 160 
Doppler line, transmission of, 201 
Doublet spectra, 6 

Edges of the absorption line, 103, 104 

Einstein A coefficient, 94 ff., 110 

Einstein B coefficient, 94 ff. 

Einstein theory of radiation, 93 ff. 

Electron excitation function, 149 

EUett tube, 22 

Emission, of a resonance lamp, 106 
stimulated by collisions, 113, 114 

Energy discrepancy, 220, 221, 225 

Energy level diagrams, 8 

Enhancement of spark lines, 217 

Excitation curve, 150 

Excited atoms, absorption by, 44 
rate of destruction (quenching), 198 
rate of formation, 196, 197 

Excited state, mean life of, 10, 11 

Fluorescence, 11 

effect of foreign gases on, 47 ff. 

sensitized, 67 

sensitized, intensity relations in, 68 
Flux of radiation, 196 
Franck-Condon curves, 176 
Fiichtbauer's experiment, 45, 46 
/-value, 96, 146, 147 



reaction by excited Hg 
atoms, 82 

HZ+ CO reaction by excited Hg atoms, 
82 

reaction by excited Hg 
atoms, 2 

formation by excited Hg atoms, 
81 

A reaction by excited Hg atoms, 
74 

Half breadth, natural, 161, 180 
Half lifetime, 123, 135 
He metastable atoms, formation, 244, 

245 
lifetime, 240 



Hg, absorption coefficient of, 123, 126 

energy interchange with molecules 
of, 221, 222 

energy levels of, 8, 9 

excitation curve of, 149, 150 

hyperfine structure of, 292 

index of refraction, 141 
Hg arc, 21 
Hg excited atoms, 71 

activation of Hj by, 76 

chemical reactions effected by, 74, 
81, 82, 83, 84 

decomposition by, 85, 86 

half lifetime, 123, 307 

quenching by collisions, 223, 224 
Hg hydride, 77, 78, 79 
Hg 2537 line, depolarization, 298 

hyperfine structure, 37-39, 294 

hyperfine structure, Zeeman levels, 
293 

polarization, 262 

pressure broadening, 162, 163 

Stark effect, 313, 314 

Zeeman effect, 268, 269 
Hg 2656 line, 52 
Hg metastable atoms, 235 

diffusion cross -section, 253 

formation, 250 
HgO formation, 83 
Hg quenching cross-section, 204 
Hg-rare gas bands, 87, 88 
Hg resonance line, anomalous disper 
sion, 143 
Hg resonance radiation, 14, 15 

Lorentz broadening by A, 169 

quenching of, 188 

quenching curve, 95 
Hg stepwise radiation, 44 ff., 304 

hyperfine structure of, 52 
Hg Zeeman levels, 305 
Holtsmark broadening, 183 

theory of, 183 ff. 
Hook-method, 142 
Houtermans' lamp, 25 
Hyperfine structure, 34 

absorption of, 126, 127 
Hyperfine structure pattern, 37 
Hyperfine structure of resonance radia 
tion,, 39-42 

Hyperfine structure of stepwise radia 
tion, 52 
Hyperfine structure quantum number 

(/), 35 
Hyperfine structure Zeeman levels, 286 

Index of refraction, 96, 325 



INDEX 



337 



Intensity, of a line, 11 

of a resonance line, 115, 116 
Interval rule, 8 
Isotopic shift, 37 

J-selection rule, 6 

K. resonance line, anomalous disper 
sion, 143 
/-value, 135 
half lifetime, 135 

Larmor precession, 267, 270, 271 

Li resonance radiation, 14 

Lifetime measurements, 110 ff., 146 ff. 

Lifetime of excited atoms, 94 

Lifetime of metastable atoms, 236-238, 
240 

Light sources for exciting resonance 
radiation, 20 

line, intensity of, 11 
self -reversed, 194 

Line absorption, 118 ff., 322 

Line fluorescence, 16 ff. 

Line spectra, 2 

Lorentz broadening, 158 ff. 
effect on quenching, 193 
frequency distribution, 182 
quantum theory of, 175, 177 ff. 

Lorentz half-breadth, 160 

Z-selection rule, 4 

Magnetic depolarization, 270, 271 

effect of hyperfine structure on, 296 ff . 
Magneto-rotation, 133 ff., 325 
Mean life of an excited state, 10, 11 
Mercury, see Hg 
Metastable atoms, 65 

decay of, 238, 239, 251, 253 

diffusion of, 246 ff . 

lifetime measurement, 236-238 
Metastable states, 10 
Monochromatic light, 20 
Multiplets, 7 
Multiplicity, 7 

Na, energy levels of, 11, 12 

excited atoms of, quenching, 226, 

227 

Na D line, Stark effect of, 313, 314 
Na flame, Lorentz broadening of, 

170-173 

Na fluorescence, 18, 19, 62 
Na lines, polariz&tion of, 302, 303 
Na metastable atoms, formation, 241 

lifetime, 240 



Na quenching cross-section, 209 
Na resonance line, anomalous dis 
persion, 143 

asymmetric broadening, 175 
Na resonance radiation, 12, 14 

Lorentz broadening of, 164, 166 

polarization of, 272 ff. 

quenching of, 189, 206 
Na sensitized fluorescence, 62, 67 
Na Zeeman levels, 272 
Nal, optical dissociation of, 204, 205 
Narrow line excitation, 289 
Natural broadening, 160 
Natural damping, 100 
Natural damping ratio, 101 
Natural half-breadth, 161 
Normal state, 8 
Nuclear spin, 35, 36 

Os-formation, 82, 83 

Opacity, 199, 233, 234, 330, 331 

Paschen-Back effect of hyperfine 

structure, 301, 302 
Pauli-Houston formula, 150 
Pb fluorescence, 17 
Photo-ionization by collisions, 215 
Photosensitized reaction, 71 
Photosensitizer, 71 
Pirani's lamp, 24 

Polarization of the resonance radia 
tion, 259 ff., 331 ff. 

effect of an electric field on, 314, 315 

effect of hyperfine structure on, 
284 ff. 

effect of pressure on, 276, 277 

theory of, 264 ff. 
Potassium, see 3 
Pressure broadening, 98, 161 
Principal series, 5 
Principle of microscopic reversibility, 

56 
Probability of transition, 11 

Quantum mechanical resonance, 66 
Quantum number/, 35 
Quantum number t, 35 
Quantum number j 9 5 
Quantum number Z, 3 
Quantum number m, 268 
Quantum number n, 4 
Quantum number s, 5 
Quantum weight, 8 
Quenching, 33 

Stern- Volmer formula, 192 
Quenching ability, 191 



338 



INDEX 



Quenching collisions, number of, 208 

theory of, 218 ff. 
Quenching cross-section, 202, 204 
dependence on velocity, 210, 211, 

213 

Quenching curve, 188, 201 
Quenching of excited atoms, 198 
Quenching of resonance radiation, 

187 ff. 
Quenching of sensitized fluorescence, 

65 

Radiation, scattered, 199 
Radiation density, 94 
Radiation diffusion, 196 ff. 
Radiation intensity, 94 
Rb resonance line, anomalous disper 
sion, 143 
Reactions sensitized by excited metal 

atoms, 86 

Resonance, quantum mechanical, 66 
Resonance bulb, 32 
Resonance lamp, 28, 29, 30, 31, 107 
Resonance line, intensity of, 115, 

116 
Resonance radiation, 12, 16 

absorption of, 165 

decay constant, 229 ft. 

hyperfine structure of, 39-42 

polarization of, 264 ff . 

quenching of, 187 if. 

secondary, 106-108 
Ritz combination principle, 3 
Rydberg constant, 3 

Satellites, 34 
Sb energy levels, 18 
Sb fluorescence, 17 
Scattered radiation, 199 
Schuler tube, 23 
Selection rules, 4, 6, 35 
Self-reversal, 21, 194 
Sensitized fluorescence, 59 ff . 

intensity relations in, 68 

quenching of, 65 
Sharp series, 5 



Shift of the absorption line, 174, 180 

Sodium, see Na 

Specular reflection, 31, 32 

Spin, 5 

Sr resonance line, anomalous disper 
sion, 144 

Stark effect, 312 ff. 

Stepwise excitation, 44 ff . 

Stepwise radiation, 45 

Stern- Volmer formula for quenching, 
192 

Subordinate series, 5 

Sum rule, 8 

Tl, sensitized fluorescence of, 61 
Tl energy levels, 16, 212 
Tl excited atoms, quenching by colli 
sion, 228 

Tl fluorescence, 16, 61 
Tl line fluorescence, 280, 281 
Tl resonance line, /-value, 135 

half lifetime, 135 
Tl vapour, quenching by, 65 
Tl Zeeman levels, 281 
Total absorption, 130 
Total angular momentum j, 5 
Transition probability, 11 
Transmission of a Boppler line, 201 

Vector model, 35 
Wave number, 8 
Xenon, excited atoms, 80 

Zeeman effect, 268 

Zeeman levels, hyperfine structure of, 

286 

Zeeman transition probability, 273 ff . 
Zn arc, 22 

Zn excitation curve, 149, 150 
Zn hydride, 80 

Zn resonance line, polarization of, 280 
Zn resonance radiation, 15, 16 
Zn sensitized fluorescence, 63, 64 
Zn stepwise radiation, 56 



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