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

1 06 043