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166360 



OSMANIA UNIVERSITY LIBRARY 

C!all No .*)/, , o I jf ft tA Accession No. 



*LIMA 

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<: <rt6\j^. /^t? 

This book should be returneii on or before the date ia^t marked' below. 



ATOMIC SPECTRA 



In two volumes 

VOLUME II 



LONDON 

Cambridge University Press 

FKTTER LANE 

NKW YORK TORONTO 
BOMBAY CALCUTTA MADRAS 

Macmillan 

TOKYO 

Maruzen Company Ltd 
All rigltts reserved 



ATOMIC SPECTRA 

AND TH*E VECTOR MODEL 



BY 

A. C. CANDLER 

Sometime Scholar of Trinity College, 
Cambridge 



'There is one thing I would be glad to ask you. When a mathematician 
engaged in investigating physical actions and results has arrived at 
his own conclusions, may they not be expressed in common language 
as fully, clearly and definitely as in mathematical formulae? If so, 
would it not be a great boon to such as we to express them so 
translating them out of their hieroglyphics that we also might work 
upon them by experiment.' 

Letter from MICHAEL FARADAY to CLERK MAXWELL 



VOLUME II 
COMPLEX SPECTRA 



CAMBRIDGE 

AT THE UNIVERSITY PRESS 
1937 



PRINTED IN GREAT BRITAIN 



CONTENTS 

VOLUME IT. COMPLEX SPECTRA 

Chap. XII. Displaced terms page 1 

XIII. Combination of several electrons 9 

XIV. Short periods 21 
XV. Long periods 45 

XVI. Rare earths 75 

XVII. Intensity relations 90 

XVIII. Sum rules and (jj) coupling 122 

XIX. Series limit 158 

XX. Hyperfine structure 166 

XXI. Quadripole radiation 215 

XXII. Fluorescent crystals 228 

App. V. Key to references 247 

VI. Bibliography 248 

A. Books of reference 248 

B. The spectra of the elements 248 

C. The hyperfine structure of the elements 261 

Subject index 267 

Author index 275 



LIST OF PLA-TES 

5. Fluorescent spectrum of a chromium 

phosphore and a multiplet from the 

iron arc facing page 62 

6. Absorption spectra of two samarium 

compounds 86 

7. Hyperfine structure of various lines 168 

8. Fluorescent spectra of samarium and a 

multiplet from the iron arc. 240 



CHAPTER XII 
DISPLACED TERMS 

1. The alkaline earths 

Only about half of the bright lines of the calcium arc spectrum 
are accounted for by the simple terms described in a previous 
chapter. Most of the remaining lines, however, can be explained 
by the ' dashed' or ' displaced' terms introduced by Gotze* in 
1921, terms which Russell and Saundersf were later to attribute 
to the activity of two electrons (Fig. 12*2). 
As an example of these terms consider the group of six bright 
lines occurring round 4300 A. 



Terms 


o 3p / 

L r 


2 3 P/ 


2 3 P/ 


2 3 P 




4289-363 (40) 
23306-96 








52-20 




2^ 


4307-738 (45) 
23207-53 47-23 


4298-989 (30) 
23254-76 86-77 


4283-008 (30) 
23341-53 






105-85 


105-87 


2 3 P 2 




4318-648 (45) 
23148-91 86-75 


4302-525 (60) 
23235-66 



Fig. 12-1. Wave-lengths and wave-numbers of the 2 3 P'- 
calcium. The numbers in brackets are intensities. 



2 3 P multiplet of 



The intervals 52-2 and 105-9 are recognised as the intervals of 
the well-known 2 3 P terms and these terms are therefore written 
in the left-hand column. The intervals 47-2 and 86-8 do not occur 
in the earlier analysis, but Lande's interval rule suggests that an 
empirical ratio of 1*84 should arise from a 3 P term, for the ideal 
interval ratios of 3 P and 3 D terms are 2 and 1-5 respectively. 

If the combinations not observed are those forbidden by the J 
selection rule, then the empirical terms must have J values of 
0, 1 and 2. Of the nine possible combinations, two are then for- 
bidden because they have A J = 2, and a third because the electron 

* Gotze, AP, 1921, 66 285. A key to letters used in referring to periodicals 
is given in Appendix iv. 

f Russell and Saunders, AJ, 1925, 61 38. The authors write the terms 1 3 P 
and 1 3 P' instead of 2 3 P and 2 3 F used here. 



2 DISPLACED TERMS [CHAP. 

would have to jump from J = to J = 0. The intersystem line 
TQ-^SQ is noticeably absent in the mercury spectrum. 



10,000 - 



10,000 - 




20,000 - 



30,000 - 



40,000 - 



50,000 



Fig. 12-2. Level diagram of calcium, extended to show the displaced terms. 
Even terms are shown by a circle, odd terms by a triangle. 

A critic might suggest that the above argument really only 
determines the values of /, but the Zeeman effect has also been 
examined and this, connecting as it does L, J and S, serves to 
fix L, when J and S are known. Every indication therefore 



XII] THE ALKALINE EARTHS 3 

suggests that the empirical terms should be written 3 P, or, since 
they are not of the usual 3 P series, 3 P'. 

So far no use has been made of the series laws, but five terms of 
the 3 P' series have been observed, and if these are fitted to a Ryd- 
berg formula, they indicate that the limit of the series is some 
13961 cm." 1 above the common limit of the earlier known series 
of the calcium atom. Indeed, the 4 3 P', 5 3 P' and 6 3 P' terms are 
all above the limit, and contain energies of 0-68, 1*03 and 1-24 
volts in excess of that required to ionise the atom. This sur- 
prisingly large energy content seems to be open to only one 
explanation. In the levels of this displaced series two electrons 
ase excited, and when the atom returns to one of the normal states 
both electrons jump and both contribute energy to a single 
quantum of radiation. 

This deduction may be still further refined. The second deepest 
term 1 2 D of the calcium ion is 13711 cm."" 1 or 1-72 volts above the 
basic 2 S term, and this is not very different from the amount by 
which the limit of the P' series is raised above the normal limit. 
If then the two optical electrons are assumed to have orbital 
moments I l9 1 2 , l must be assigned the value 2. 

The difficulty of explaining why the P' terms combine with 
normal P terms is then surmounted by the hypothesis that l x and 
1 2 combine vectorially to give a resultant L. L combines in the 
usual way with S, itself the sum of the s l , s 2 of the individual 
electrons, to give J; but the quantum transitions allowed depend 
on l x , 1 2 individually and only indirectly on L. The reasons already 
given for writing the unknown term 3 P' first determine J, and 
then require L to be 1, but 1 2 is still unassigned. If the old rule 
AL= 1 is to be written now AZ 2 = + 1, then the fact that the 
3 P' term combines with a P term shows that l z is or 2; and the 
former is ruled out, because if l x + 1 2 = L it is inconsistent with the 
previous allotment of L and l . 

Apply the same arguments to a so-called 3 D' term found by 
Russell and Saunders, which has the J properties of a D term but 
combines with 3 D, X S and X D. Clearly the J properties indicate 
L = 2, while the combining terms show that / 2 =1; and as the 
3 D' series has the same displaced limit as the 3 P' series, l is 2. 



4 DISPLACED TERMS [CHAP. 

When two electrons are excited, the atom as a whole can no 
longer be said to have a chief quantum number, though each 
electron has. Thus in the normal state of calcium, two electrons 
lie outside the closed shell of argon, and these occupy 4s orbits, so 
that the ground state is 4s 2 1 S . When one of these moves to a 
4p orbit the configuration becomes 4s4p 3 P; this is the 2 3 P 
term of the normal spectrum. In the lowest 3 P' term both 
electrons have moved to 3d orbits, so that the configuration 
is3d 23 P'.* 

Often the chief quantum number does not need to be stressed, 
and then 3d 2 3 P' is abbreviated to d 2 3 P' ; or if the two d electrons 
have different chief quantum numbers, as in 3d.4d 3 P', then we 
write d.d 3 P'. Again as there is only one 3d.nd 3 P series, the 
omission of the dash introduces no ambiguity, but in fact it is 
often retained as it gives a key to the transitions permitted. 

What are these ? Or in other words, what is the selection rule 
governing the combination of displaced terms? Heisenberg 
stated, on the basis of the quantum mechanics, that when two 
electrons jump simultaneously one is bound by the condition 
AZ X = 1 and the second by AZ 2 = or 2. Of this rule the 
transitions from the displaced to the normal terms of the alkaline 
earths offer a first example. 

A very important consequence of this selection rule is that 
when an atom emits or aljsorbs a quantum of radiation the sum 
of the orbital quantum numbers of the individual electrons SZ 
must change by an odd number; if the sum was even it must 
become odd, or if it was odd it must become even. Consequently 
all possible terms may be divided into two groups, an even group, 
written in accord with the suggestion of a number of physicists')" 
S, P, D, . . . , and an odd group, written S, P, D, . . . . A term of the 
one group can then combine only with a member of the other 
group. 

Another notation adopted for several years by many spectro- 
scopists differed somewhat from this. The even group of terms 

* The 3d 23 P' term is the 3 3 P' term of this description; though the 3 3 P', 
4 3 P' and 5 3 P X terms arise from 3d.nd configurations, the 2 3 P X term arises 
from 4p 2 ; it was wrongly assigned by Russell and Saunders. 

t Russell, Shenstone and Turner, PR, 1929, 33 900. 



XII] THE ALKALINE EARTHS 5 

was written S, P', D, F', ... and the odd series S', P, D', F, .... 
This notation wae convenient because it was in agreement with 
the notation of the earlier chapters of this book and could be 
extended. But to-day it seems more important to be able to 
distinguish odd and even terms at sight, for the group to which 
an empirical term belongs can easily be determined, and this the 
dashed notation does not facilitate. 

In simple spectra only one electron is excited, and for it the 
S, D terms have L even, while the P, F terms have L odd, and so 
to be quite accurate should be written P, F. Again, the displaced 
P', D' terms of Cai have the sum (Ii + l 2 ) equal to 4 and 3 re- 
spectively; so that they are d 23 P and p.d 3 D. 

Having dealt with two displaced series at considerable length, 
the other series found by Russell and Saunders, and written 
3 P", 3 D" and 3 F", can be considered more briefly. All the series 
have the same elevated limit and consequently in every state one 
electron must occupy a d orbit. The double dash signified that 
these terms, unlike 3 P' and 3 D', do not combine with the normal 
terms of the same letter. Thus 3 P", though it has the J properties 
of a P term, combines with 3 S, 3 D, 1 S, X D, so that L = I and Z 2 = 1. 
3 P" is therefore identical with d.p 3 P and may be written in the 
latter form. Similarly, 3 D" combines with 3 P, X P and therefore 
must be identical with d 2 3 D. Combinations of 3 F" are known only 
with 3 D and 1 D, for combinations with 3 S lie too far on the infra- 
red and 3 G is wholly unknown, but the energy of the term argues 
strongly in favour of d.p 3 F and against d.f 3 F, though the 
evidence here adduced allows the latter. 

Russell and Saunders in their analysis accounted for practically 
all the known lines of the three alkaline earths, though fhey 
hesitated to assign electronic states to all the terms which were 
suggested by the term differences, and whose energies were thus 
known. Wentzel,* however, has filled even this small gap, and 
the analysis of the visible and near ultra-violet region of calcium 
may be considered complete. 

2. Beryllium and magnesium 

In the spectra of beryllium and magnesium, and in the iso- 
* Wentzel, ZP, 1925, 34 730. 



6 DISPLACED TERMS [CHAP. 

electronic spark spectra B n to v and Al n to Cl vi, there occur 
a striking group of five lines; the separations are nearly equal, and 
four of the five lines are of equal intensity; the central line of the 
group, however, is noticeably stronger, and in some spectra it 
may be resolved into two close components. 

PP 3 P 2 - 



PP 3 P, 
PP 3 Po 



3 D 

sp P 2 - 



sp 



3pO_ 
r l 

3 D 

sp P - 



Fig. 12-3. Structure of a displaced triplet of magnesium; this arises in a 
3p2 sp_ >3s 3p apo transition. 

In 1925 Bowen and Millikan showed that these arise by the 
combination of the s . p 3 P term with a 3 P term, having so nearly 
he same intervals that the lines 3 P 2 -^ 3 P 2 and 3 P 1 -> 3 P 1 often 
coincide. According to Sommerfeld's intensity rule, this central 
line is due to chief lines having A/ = AZ, while the other four 
lines are satellites of the first order. A more accurate theory would 
predict the intensities shown in Fig. 12-3. Both are in good 
agreement with observation. 

The wave-lengths and wave-numbers of the central line in 
spectra isoelectronic with magnesium are shown in Fig. 12-4.* 

* Bowen and MiUikan, PR, 1925, 26 150. 



XII] BERYLLIUM AND MAGNESIUM 7 

The differences show how accurately linear is the progression of 
frequency with atomic number; and this means that the group 
of lines follows the irregular doublet law, which they can do only 
if the transitions take place between levels having the same chief 
quantum number. 

This argument applies as well to Be as to Mg, though figures 
are here adduced only for the latter. But in Be the jump ends in 
a 2s 2p orbit, so that it must start in a 2p 2 orbit; no other possi- 
bility exists, for there are no 2d orbits. The close similarity of 



Spectrum 


A 


V 


Diff. 


Mgi 


2780-64 


35962-96 










20727-9 


Alii 


1763-95 


56690-9 










20295-5 


Sim 


1298-93 


76986-4 










20050-7 


Piv 


1030-53 


97037-1 










19948-5 


Sv 


854-81 


116985-6 










19942-6 


ClVT 


730-31 


136928-2 





Fig. 12-4. The contra! line of displaced triplets in spectra isoelectronic with 
magnesium. 

the lines in Mg and Be suggests that in Mg too the 3 P term arises 
from the 3p 2 configuration; and this hypothesis is confirmed, 
when the frequency of the arc line p 2 3 P->s . p 3 Pis compared with 
the spark line p 2 P -> s 2 S ; the former is 35960 cm." 1 and the latter 
35760 cm.- 1 , so that both must surely arise in the same electron 
transition 2p->2s. 

A comparison of these displaced terms with those found in the 
alkaline earths shows that in Be and Mg the lines are produced by 
one electron jumping, whereas in Ca, Sr and Ba two electrons 
jump simultaneously. But in both alike the displaced terms arise 
from the second lowest term of the spark spectrum. 

3. Zinc, cadmium and mercury 

Displaced terms have also been identified in Cd by Ruark* and 
in Zn and Hg by Sawyerf; but instead of the six lines to be 
expected four only have been found, these being interpreted as 

* Ruark, JOSA, 1925, 11 199. f Sawyer, JO8A, 1926, 13 431. 



8 DISPLACED TEEMS [CHAP. XII 

the combination of the low s.p 8 P 0>lf2 terms with the displaced 
terms p 23 P 0>1 (Fig. 12-5). 

Whether the p 2 3 P 2 term is really missing or whether, as Foote, 
Takamine and Chenault* have suggested, it coincides wit 



-5000 


10000 
20000 
30000 
40000 



Fig. 12*5. Level diagram showing a PP' triplet of cadmium; this arises as 
5p a 8 P->5s 5p 3 P. 

so that in Cd the 2329 A. and 2268 A. lines are really narrow 
doublets, reihains a question still undecided. Certainly the in- 
tensities are somewhat irregular and the 2329 A. line is much 
stronger than the other lines. 

BIBLIOGRAPHY 

These displaced spectra are fully discussed by Grotrian, Oraphische Darstel- 
lung der Spektren, 1928, 1 188-210. 

* Foote, Takamine and Chenault, PR, 1925, 26 174. 




CHAPTER XIII 



COMBINATION OF SEVERAL ELECTRONS 

1 . Combination of unlike electrons 

The coupling of orbital and spin vectors, found to explain the 
displaced terms of the alkaline earths, gives also an adequate 
account of the terms of many more complex spectra. 

In this coupling the orbital and spin vectors of the electrons, 
commonly written l x , 1 2 . . . , s l , s 2 . . . , first combine to resultants L 
and S respectively, and then L and S combine to form J. The 
problem therefore is to determine all the values of L and S to 
which a given electron configuration can give rise; to solve this 



Electron 


State of ion 


added 


S 


P 


D 


F 


s 


S 


P 


D 


F 


P 


P 


SPD 


PDF 


DFG 


d 


D 


PDF 


SPDFG 


PDFGH 



Fig. 13*1. Atomic states resulting from the addition of an electron to an ion. 

* 

problem, consider the orbital and spin vectors separately. When 
a p and a d electron combine the 1 vectors are 1 and 2, so that their 
resultant must be 1, 2 or 3, values which correspond to P, D or F 
terms; further, each electron has a spin vector of |-, so that the 
atomic spin vector due to two electrons may be or 1, values 
which correspond to multiplicities of 1 and 3. Accordingly, a p 
and a d electron combine to form six terms: 1 P, *D, X F, 3 P, 3 D 
and 3 F. 

A similar train of reasoning will determine the terms produced 
when an electron combines with an ion; for if an s electron is to be 
added to an ion in the 4 F state, the orbital vectors to be combined 
are and 3, so that the resultant must be 3; while the s vectors 
are | and 1 J, so that the resultant may be 1 or 2; accordingly the 
terms produced are 3 F and 5 F. Fig. 13-1 summarises the results 
obtained in this way, for it shows the terms arising when an s, p 



10 



COMBINATION OF SEVERAL ELECTRONS [CHAP. 



or d electron is added to an ion in the S, P, D or P state, the 
multiplicity being omitted since it always increases and decreases 
by unity. 

When three or more electrons have to be combined together, 
the work must proceed by steps, two electrons being combined 
and then the third added to each of the terms produced by the two . 
Thus an spd configuration would give rise to the nine terms 
2 (PDF), 2 (PDF) and 4 (PDF). 

In the above discussion the word 'term' is used to denote a 
multiplet term, but in analysis each component of the multiplet 
appears as a separate empirical level or ( term ' . Theory thus states 
precisely how many levels will arise from a given configuration, 



\ M L 

m i\ 


-2 


1 





1 2 


I 


-1 





1 


2 3 





-2 


_ i 





1 2 


_ } 


-3 


-2 


-1 


1 


Term 
of 
atom 


F 


D 


P 





Fig. 13-2. Addition of a p electron to an ion in the D state, showing how P, D 
and F states result. 

and what their J values will be; and it is an outstanding achieve- 
ment of the theory that the empirical terms occur in just the 
number predicted and have the J values assigned. Sometimes, 
as might be expected, some of the levels are missing, but they are 
nearly always levels which would produce only lines of low in- 
tensity. In the great mass of spectra so far analysed, there is only 
a single level which seems to be adequately substantiated and is 
surplus to the theory; it is found in Pdi. 

Though the above method of combining two electrons is the 
simplest, another method due to Russell* is not without interest. 
Instead of combining the l x and 1 2 vectors of ion and electron, 
combine the m { and m l values; all combinations are permitted, 

* Russell, PR, 1927, 29 782. 



XIII] COMBINATION OF UNLIKE ELECTRONS 11 

so that a matrix of (2^ + 1) (21 2 + 1) values results, and this can 
be split into a number of, sequences by Breit's alleys, exactly as 
in the theory of the Paschen-Back effect. Fig. 13-2 shows the 
calculation when a p electron is added to an ion in a D state. 
The same method can be used to combine the ra, andra, of ion 

8 1 8 2 

and electron to obtain the multiplicity of the atomic terms. 

2. Combination of equivalent electrons 

Two electrons having the same values of n and I are said to be 
'equivalent'. 

When two equivalent electrons are to be combined, the above 
argument gives all the terms which might be produced, but it 
gives more than are produced, for the combination is restricted 
by Pauli's exclusion principle. Of this complication the simplest 
example is the combination of two electrons in the alkaline 
earths; thus in magnesium the two valency electrons must have 
n ^ 3, since the first two groups are full, and so the lowest terms 
may be expected to arise from the combination of two 3s elec- 
trons, s electrons, however, always have m^ = 0, so that if Pauli's 
exclusion principle is to be satisfied and the two electrons are not 
to occupy the same orbit, m s must be -f | for one and for the 
other. Consequently M 8 = and 8 = 0, showing that the lowest 
term is 1 S and that a 3 S term can appear only when the two s 
electrons producing it have different chief quantum numbers. 
Thus Pauli's exclusion principle clearly explains why the 1 3 S X 
term is missing in all the alkaline earth spectra and the 3 S t 
sequence begins with a 2 3 S X term. 



k I* 


m ll m l t 


m m c 

S l *2 


M L 


M 8 


Term 








i -4 








*S 



Fig. 13-3. Combination of two equivalent s electrons, showing that only a X S 
term results. 

Fig. 13-3 shows the argument summarised in a table. A similar 
table for two equivalent p electrons appears in Fig. 13-4. 

In this table all possible combinations of m l and m l are in- 
cluded, but the two electrons are to be considered interchange- 



12 COMBINATION OF SEVERAL ELECTRONS [CHAP. 

able, so that m l = 1 and m l = is identical with m l and 
m l = 1. Further, the derivation of the erms, from the sums M L 
and M s needs to be explained. A 1 D term has L = 2 and $ = 0, so 
that it will give rise to a series of values of M L from 2 to 2 all 



h k 


m l t m l, 


m c m c 

<?1 S a 


J/j 


^ 


Terms 


1 1 


1 1 


i -i 


2 





*D 







* * 


1 


100 -1 


3p 




-1 


i i 





100-1 









* -i 








*S 




-.1 


1 i 


_ 1 


100-1 






-1 -1 


* -i 


-2 








Fig. 13-4. Combination of two equivalent p electrons, showing how the re- 
sulting terms are calculated. 

having M s 0. To work from M L and M 8 to L and 8 therefore, 
start with the highest value of M L available, namely 2 in the 
above figure, and cross out both a series of values of M L from 2 
to 2 and the corresponding values of M s , namely 0. When 
these values have been deleted, the table of Fig. 13-4 reduces to 
that shown in Fig. 13-5. 



M L 


M a 


Terms 


1 


-1 


1 -1 
I -1 


< 10-1 


3 P 

*S 



Fig. 13-5. A step in the elucidation of the previous figure; the M L and M s values 
which remain when the 1 D term has been removed. 

Now repeat the operation. The highest value of M L is 1, and 
the greatest corresponding values of M s also 1, so that the next 
term to be written in the margin must have L = 1 and S 1; and 
the values to be deleted are M L = 1,0, 1 and M s = 1,0, 1. 
Afterwards there remains only M L = when M s = 0, representing 
a *S term. 

The calculation of teripis arising from three equivalent p 
electrons introduces no new principles; the work, summarised in 
Fig. 13-6, shows that the terms to be expected are 2 D, 2 P and 4 S. 

The combination of four equivalent p electrons is worked out 



XIII] COMBINATION OF EQUIVALENT ELECTRONS 13 

in Fig. 13-7. The terms arising, be it noted, are those arising from 
two equivalent p electrons, and indeed this could have been 
predicted. For six p electrons form a closed group, in which 
every orbit permitted by the exclusion principle is occupied, and 
consequently M L = M S = Q. Therefore when there are four p 
electrons, the orbits left unoccupied will be precisely those 



J I, I, 


m l, m l 2 1 3 


w, m n rn 9 

s l o 2 s 3 


M L 


M a 


Terms 


1 1 1 




1 1 

-1 . 

1 

-1 
-1 -1 1 


1 -1 


4 -i 4 
i -4 4 
4 -4 4 
4 -4 4 
i -1 4 
i -4 4 
4 4 4 


2 
1 
1 
_ j 

-1 

-2 



4 

4 
4 
4 

4 
4 

4 4 4 14 


2 D 
2 F 

*S 



Fig. 13-6. Combination of three equivalent p electrons. 



k 1 2 I, k 


m l t m l t m l $ m l< 


m, m, m, m, 

1 2 S 8 S 4 


ML 


M B 


Terms 


1111 


1100 


4-4 4-4 


2 





iD 




-1 


4 -4 4 4 


1 


100-1 


3 P 




-1 -1 


4-4 4-4 








X S 




I -1 


4 -4 4 4 





100-1 






-1 -1 


4-4 4-4 


-2 









-1-110 


4 -4 4 4 


-1 


100-1 





Fig. 13-7. Combination of four equivalent p electrons. 



h l z Is I* k k 


MI MI MI MI m l mi 


m s m s m s m s m s m s 


ML 


M a 


Term 














111111 


1 1 0-1-1 


4 ~4 4 ~4 4 ~~4 








1 S 



Fig. 13-8. Combination of six equivalent p electrons. 

occupied by two electrons, and the values of M L and M 8 will 
be unaltered in magnitude. The change in sign will not affect 
the values of L and 8 or consequently the terms. For the same 
reasons five p electrons give rise to a 2 P term just as one electron 
does. 

The terms resulting from various numbers of p electrons are 
collected together in Fig. 13-9, while below are similar tables for 
d and f electrons. Of these, the first two were given by Hund and 



14 COMBINATION OF SEVERAL ELECTRONS [CHAP. 

bhe last by Gibbs, Wilber and White.* To save space terms of the 
same multiplicity are sometimes bracketed together, thus 4 P 4 F 
is abbreviated to 4 (PF); and the numberof times a particular term 
Dccurs is indicated by a figure written directly below the letter. 



Number of 
p electrons 


Terms resulting 


Oor 6 
1 or 5 
2 or 4 
3 


*S 
2 p 

^D 3 P 
2 P 2 D 


4 S 



Fig. 13-9. Terms resulting from the combination of equivalent p electrons. 



No. of d 
electrons 


Terms 


Oor 10 


1 S 




1 or 9 


2 D 




2 or 8 


^SDG) 


3 (PF) 


3 or 7 


2 (P1)FGH) 


4 (PF) 




2 




4 or 6 


MSDFGI) 


3 (PDFGH) 5 D 




22 2 


2 2 


5 


2 (SPDFGHI) 


4 (PDFG) 6 S 




322 





Fig. 13-10. Terms resulting from the combination of equivalent d electrons. 



No. of f 
electrons 


Terms 


Oor 14 


*S 








1 or 13 


2 F * 








2 or 12 


XSDGI) 


3 (PFH) 






3 or 11 


2 (PDFGHIKL) 

2222 


4 (SDFGI) 






4 or 10 


^SDFGHIKLN) 

24 423 2 


8 (PDFGHIKLM) 

3 243 422 


5 (SDFGI) 




5 or 9 


2 (PDFGHIKLMNO) 

45 7675532 


4 (SPDFGHIKLM) 

2 344332 


8 (PFH) 




6 or 8 


^SPDFGHIKLMNQ) 

4 648473422 


3 (P.DFGHIKLMNO) 

6 9796633 


6 (SPDFGHIKL) 

32322 


7 F 


7 


2 (SPDFGHIKLMNOQ) 

257 10 10 997542 


4 (SPDFGHIKLMN) 

22657 6533 


6 (PDFGHI) 


8 S 



Fig. 13-11. Terms resulting from the combination of equivalent f electrons. 
3. Deep terms of the short periods 

If the terms of low energy arise from electrons of low energy 
;hen the deep terms of the short periods must be derived from 

* Gibbs, Wilber and White, PR, 1927, 29 790. 



XIII] 



DEEP TERMS OF THE SHORT PERIODS 



15 



equivalent s and p electrons. Moreover, they can be read off from 
Fig. 13-9, for a closed shell contributes nothing to L or S, so that 
the terms which arise from an s 2 p n configuration are precisely 
those which would arise from p n . 

The elucidation of these deep terms is important, because a few 
terms often give the key to the whole spectrum, and transitions 
ending in deep terms yield the brightest lines. 



Outer electrons 


Ground 
term 


Other 
deep 
terms 


Some spectra in 
which these terms 
have been found 


Total 


3 


P 


1 
2 

4 


1 

2 
2 
2 


1 
2 


2 S 
J S 

2 P 

3p 


1 D^ 


Na i, Cs i, Ca n, Al in 
Mg i, Ca i, Al n, C in 
Al i, Tl i, C n, N in 
C i, Pb i, N n, O in 


5 
6 

7 
8 


2 
2 

2 

2 


3 
4 
5 
6 


4 S 

3p 
2|> 

J S 


2 D 2 P 
1 D*$ 


N i, Sb i, n, Cl in 
i, Se i, Cl n, A in 
F i, Cl i, A n, Na in 
Ne i, Kr i, Na n, Ca in 



Fig. 13-12. Low terms of the short periods. 

4. Two energy rules 

In the spectra of the short periods the deep terms are few in 
number, and so those predicted by theory are easily matched with 
those found empirically. But of the higher terms very many will 
arise from a single configuration, and to know which of these 
normally lie low and which high is a great help to the accurate 
labelling of the empirical terms. This problem was first studied 
by Hund, who solved it in two empirical energy rules. 

The first rule states that those terms lie deepest in which the 
electronic spin vectors are parallel to one another, and in which 
therefore S is a maximum. Thus in the alkaline earths, the triplet 
term arising from any electronic configuration lies deeper than 
the corresponding singlet term; while in the short periods 
Fig. 13-12 shows that of the terms arising from the simplest 
electron configuration that of highest multiplicity is the ground 
term. 

The second rule adds that of terms which have the same 
multiplicity, those lie deepest in which the electronic orbital 
vectors are also parallel, and in which therefore L is a maximum. 



16 COMBINATION OF SEVERAL ELECTRONS [CHAP. 

Accordingly, in carbon X D lies lower than 1 S, and in nitrogen 2 D 

lies lower than 2 P. 

t 

Thus of two terms arising from a set of equivalent electrons, 
that which lies furthest to the right in Pigs. 13-9-13- 1 1 lies deepest 
in the spectrum. These rules never fail to predict the ground term 
of a spectrum correctly, but among higher configurations many 
exceptions occur. 

5. Inverted terms 

When a group of electrons is more than half full the deep terms 
arising from it are inverted. Thus the 2 P ground term of All is 
erect, but the 2 P ground term of 01 1 is inverted; the 3 P ground 
term of silicon is erect, but that of oxygen is inverted. 

This fact is best examined in the light of a third energy rule, 
which asserts that the deepest components of a term arise when 
the orbital and spin vectors of the electrons are anti-parallel. 
When there are no restrictions this rule ensures that in the lowest 
component J will be a minimum and the terms will therefore be 
erect; but when the group is more than half full the restrictions 
imposed by the exclusion principle interfere. 

The ground terms of the elements of a short period may be 
built up graphically by adding one electron at a time. The first 
electron, having its 1 and s vectors anti-parallel, as shown in 
Fig. 13-13, gives rise to a 2 IJ| term. On adding the second electron 
the first energy rule makes s 2 parallel to s x , and would make 1 2 
parallel to l x if the exclusion principle did not interfere; but 
equivalent electrons may not have the same values of m l if they 
already have the same values of m s , so if m^ was 1, m /2 must be 
or 1, and of these will give the lower component since it will 
make the vectors more nearly anti-parallel; accordingly, in 
Fig. 13-13 the 1 2 vector is drawn horizontal. 

The addition of a third electron emphasises no new principle; 
but the fourth, if it is to produce the empirical term, must set its 
orbital vector 1 anti-parallel not to the resultant S but to the 
electronic vector s 4 . The lowest component then appears as 3 P 2 , 
and as the other components of the ground term are 3 Pj and 3 P 
the term appears inverted. 



XIII] INVERTED TERMS 17 

This theory, which can of course be applied also to d and f 
electrons (Fig. 13-14), explains well enough why the ground terms 



Configuration S 



J 



P 3 




Ground 
Term 



2 Pl 



2 P, 



Fig. 13-13. Vector diagram showing how the ground terms of a p shell may be 
derived with the help of the Pauli exclusion principle. 

of certain spectra are inverted, but it would not necessarily lead 
one to expect that many of the higher terms would also be 
inverted as in fact they are. A theory developed by Goudsmit,* 
serves however to bring out this point. 

* Goudsmit, PR, 1928, 31 946. Ruark and Urey, Atoms, molecules and 
quanta, 1930, 332. 



18 COMBINATION OF SEVERAL ELECTRONS [CHAP. 



Configuration S L 



J Ground 
| Term 



d 2 



d' 



d 4 



d 6 



Fig. 13 14. Vector diagram showing how the ground terms of a d shell may be 
derived. 



XIII] INVERTED TERMS 19 

Previously, the wave-number of a component of a multiplet 
term has been written v Q + r, ...... (4-1) 



where V G is the wave-number of the centroid. Let us assume that 
when several electrons are active the atomic displacement F is 
itself the sum of electronic displacements y x , y 2 > 7n 

In the vector model the energy of an electron having orbital 
and spin vectors l x , s l is assumed proportional to them and to the 
cosine of the angle between them, so that 

y\ = #1 li s l cos (li s x ) . ...... ( 1 3- 1 ) 

Now Z x precesses round L and s round S, so that 
y x = a x / x cos (l x L) s 1 cos (s l S) cos (LS), 
or summing for all the electrons, 

r = Sy 1 = cos(LS)Sa 1 Z 1 cos(! 1 L) 1 cos(s 1 S) ....... (13-2) 


In order to advance beyond this equation, Slater* had to make 

a further postulate; the electrons are to be divided into two groups 
according as their spin vectors are parallel or anti-parallel to 
the atomic spin vector; the resultants L' and L" of the corre- 
sponding orbital vectors are then ' action variables ', which inter- 
preted in terms of the vector model means that they must both 
be integral. 

Consider now the 3 P ground term of an element, such as oxygen, 
with four p electrons. Three of these will have s parallel to S, 
while one will be anti-parallel. Clearly then L" = 1, while L' might 
assume any value less than 3 did the exclusion principle not 
intervene, requiring that if all three electrons have the same value 
of m s then they can none of them have the same value of m ; ; 
consequently, when S' is 1|, the only possible value of L' is zero. 
Equation (13-1) now reduces to 

T = as cos (LS) (I/ -''), ...... (13-3) 

for if all electrons are equivalent a 1 = a 2 == ... = a n and all may 
be written a. 

This formula accounts for the empirical facts. So long as a shell 
is less than half full F will be positive and the terms erect; but 
* Slater, PR, 1926, 28 291. 



20 COMBINATION OF SEVERAL ELECTRONS [CHAP. XIII 

when there are present three p, five d, or seven f electrons, 
U = L" = 0, and the ground term will be an S term of multiplicity 
one greater than the number of electrons present. When a shell is 
more than half full U, but not L", is zero, so that F is negative 
and the terms are inverted. 

A very pretty confirmation of this theory is found in nitrogen, 
most of whose terms arise from the 2p 2 3 P configuration of N n 
and are consequently erect; two deep terms, however, a 4 P and a 
2 P, are inverted, and it seems clear that these have the electronic 
structure 2s. 2p 4 .* 

BIBLIOGRAPHY 

The consequences of Russell and Saunders' paper and the Pauli exclusion 
principle were first developed by Hund in Linienspektren und periodisches 
Systems der Elemente, 1927; more recent accounts appear in Ruark and Urey, 
Atoms, molecules and quanta, 1930; Pauling and Goudsmit, The structure of 
line spectra, 1930. 

Jompton and Boyce, PR, 1929, 33 147. 



CHAPTER XIV 

ELEMENTS OF THE SHORT PERIODS 
1 . Elements to be considered 

The seventh from last element of each period has a X S ground 
term, and this may be taken to mean that the configuration of 
each of these elements consists only of complete shells; the last 
six elements of each period shown in Fig. 14-1, are therefore 



Column 


III 


IV 


V 


VI 


VII 


VIII 


Configuration 


P 


P 2 


P 3 


P 4 


P 6 


P 6 


Elements 


B 


C 


N 





F 


Ne 




Al 


Si 


P 


s 


Cl 


A 




Ga 


Ge 


As 


Se 


Br 


Kr 


* 


In 


Sn 


Sb 


Te 


I 


Xe 




Tl 


Pb 


Bi 


Po 




Nt 


Ground term 


2p 


3 P 


4 8 


3 p 


2 P 


*S 


Prominent multiplicities 


2 


1,3 


2,4 


3,5 


2,4 


1,3 



Fig. 14-1. Elements arising from configurations of p electrons. 

formed by the entrance of six electrons into a new shell, the sixth 
electron completing the shell and forming the inert gas. As this 
shell must consist of p electrons in the first short period, it 
presumably consists of p electrons in the other periods. 

If this is true, then the partly filled shell of p electrons should 
produce the ground term of each spectrum, the terms being 
2 P, 3 P, 4 S, 3 P, 2 P, X S in successive columns, and in fact these are 
the terms found. Of the higher terms the great majority are 
formed by adding an electron to the ground term of the ion. 
Consider, for example, the spectrum of carbon in which there are 
only two p electrons ; the ground term of C 11 is 2 P, and accordingly 
C i should consist of singlets and triplets, the terms produced 
being *P and 3 P, ^SPD) and 3 (SPD), or *(PT>Y) and 3 (PDF), 
according as the second electron moves in an s, p or d orbit. And 
similarly in column VI the ground term of the spark spectrum is 
4 S, so that the arc spectrum should consist chiefly of the resulting 



22 ELEMENTS OF THE SHORT PERIODS [CHAP. 

triplets and quintets, though some less prominent terms may 
arise by the addition of an electron to the metastable states 
p 32 Pandp 32 Doftheion. 

2. Irregularities and their cause 

In the early days of spectrum analysis, spectroscopists were 
able to order only those spectra in which series are prominent, 
for a series was the only regularity which they had recognised. 
To-day, the spectroscopist who has analysed a spectrum into a 
complex of terms can name those terms only if they exhibit some 
regularity; and the regularities on which he chiefly relies are the 
selection rules, which serve to determine J, the magnetic splitting 
factor, and the intensity and interval rules. The three last are 
linked together, for when a spectrum fails to obey one rule, it 
often fails to obey all three; and in terms of the vector model this 
is taken to mean that the coupling of the vectors ceases to be that 
postulated by Russell and Saunders. 

What then are the influences which make a term irregular? 
Briefly they may be summarised as three; first is an increase in 
atomic number, carbon is more regular than lead, and neon than 
krypton; secondly, the column of the periodic table is significant, 
for the spectra of the elements on the left-hand side are more 
regular than those on the right, beryllium is more regular than 
nitrogen and nitrogen thanjieon; while third stands the height or 
energy of a term, for the higher a term lies the less likely is it to 
obey the simple rules, and particularly the interval rule. These 
influences are here stated as empirical rules; their explanation 
will be attempted only in a later chapter. 

3. The earth metals, s 2 p configuration* 

The spark spectra of the earth metals, like the spark spectra of 
the alkalis, have a *S ground term, so that the arc spectra should 
consist of doublets; and in fact a system of doublets has been 
found and analysed into principal, sharp, diffuse and fundamental 
series. Where the terms have been resolved they have been shown 

* Grotrian, Oraphische Darstellung der Spektren, 1928, 1 122 f. and 2 80, 
96. 



XIV] 



THE EARTH METALS 



23 



Volt 




0- 



--1-7 



-1-626 



-1493 



Fig. 14-2. Level diagram of thallium. (After Grotrian, Oraphische 
Darstellung der Spektren.) 



24 ELEMENTS OF THE SHORT PERIODS [CHAP. 

to be usually erect; in Pbn, however, the 2 D and 2 F terms are 
inverted. 

The ground term is clearly a P term, for the principal series 
extends into the infra-red and has a limit of much greater wave- 
length than the limits of the sharp and diffuse series (Fig. 14-2); 
in this the doublets of the earth metals may be compared to the 
triplets of the alkaline earths. Moreover, the absorption spectra 
confirm the ground term, for when the metallic vapour is main- 
tained at a low temperature, and illuminated with white light, 
the sharp and diffuse series are absorbed, but not the principal 
series. 



Al 


ii 




All 




1,1 2 


Term 


/3 


Terms 


h k I* 


3s 2 


*S 


3p 


2p 


s 2 p 






4s 

& 

4f 


2 S 
2 P 
2 D 

2F 


S 2 .S 

s 2 .p 

S 2 .d 
S 2 .f 


3s 3p 


3po 


3p 


4 P 2 (SPD) 


sp 2 






4s 
4p 
3d 


4po 2po 

*(SPD) 2 (SPD) 
4 (PDF) 2 (PDF) 


sp.s 
sp.p 
sp.d 


3p 2 


sp 


3p 


4 S 2 P 2 D 


p 3 



Fig. 14-3. Terms predicted in column III. 
* 

Above the ground term of Al i lies first an S and then a D term, 
and theory makes it clear that these arise by the addition of 4s 
and 3d electrons to the X S ground term of Alii. Terms of the arc 
spectrum may, it is true, arise from spark terms other than 1 S 9 but 
they do not belong to the simple doublet system; in practice 
these terms do not produce bright lines in the elements of column 
III A, but they appear lying quite low in all the spark and higher 
spark spectra, which are isoelectronic with this column, such as 
Si ii and Sb in. The structure of these terms is shown in Fig. 14-3. 

4. Column IV, s 2 p 2 configuration 

In the fourth column Hund's scheme predicts that the s 2 p 2 
configuration will produce five low terms 3 P ,i,2> 1 D 2 an( i 1 ^o i* 1 



XIV] 



COLUMN IV 



25 



that order proceeding from the ground term up; and empirically 
in carbon, silicon, germanium, tin and lead five low terms have 
been found. 





3p 3p 2 4 p level of Si 11 - 


( 4 P)np 3 D 3 P 'D 


unknown 




3s 2 . 3p. 2 P level of Si IK 




above 2 ? 


Volts 
8-12 


3pns 3 P 

3p up 3 D 3 P i 3 S 

r r i i 1 i > 


, 1 D 'P ,'S 

r I III 






3pnd 3 F 3 D 3 P 1 F 


I I 

'D 'P 


65,765 
cnt: 1 






- 


60,000 


7- 










3d A~^ -.-^ 


*-* 




6- 




y^ A. - 
^' / " 


50,000 


5- 


P 


/ 


40,000 






/ 

/ 








/ 




2_ 
1-91" 

1- 
0-77- 




A 


20,000 
10,000 


o- 


3p ^ 


- 






Fig. 14-4. Level diagram of silicon. In this and the following diagrams, even 
terms are shown by a circle and odd terms by a triangle. Terms produced by the 
same electron are joined by a broken line ; when the electron is an s electron the 
line is drawn , when a p electron and when a d electron . 

In the region extending from the red end of the spectrum 
down to 2000 A. the carbon arc produces only one line, 2478 A.; 
but when a trace of carbon dioxide is added to helium at a pressure 



26 ELEMENTS OF THE SHORT PERIODS [CHAP. 

of 20 to 30 mm. many lines occur which have been attributed to 
the neutral carbon atom. Analysis of the spectrum shows that the 
reason why the visible lines are difficult to excite is that they 
arise between high terms; the low terms produce lines in the 
ultra-violet, and these occur quite readily both in the arc and in 
vacuum tubes containing carbon compounds. 



On 


Ci 


W* 


Term 


h 


Terms 


/! ... h 


2s 2 . 2p 


2pO 


2p 


3 P iD X S 


s 2 p 2 


3s 
3p 
3d 


apo ipo 

3 (SPD) ^SPD) 
3 (PDF) ^PDF) 


s 2 p.s 
s 2 p.p 
s 2 p.d 


2s. 2p 2 


4p 

2 (SPD) 


2p 


5 S 3 (SPD) ^SD) 


sp 3 


4 P 


3s 
3p 
3d 


5p 3p 

6 (SPD) 3 (SPD) 
5 (PDF) 3 (PDF) 


sp 2 . s 

8p|.p 

sp 2 .d 


2 D 


3s 
3p 


3 D *D 
8 (PDF) ^PDF) 


Sp 2 .S 

sp 2 .p 


2p 


3s 
3p 


3 p ip 

3 (SPD) ^SPD) 


sp 2 .s 

8p 2 .p 


2 S 


3s 
3p 


3 S *S 

apo ipo 


sp 2 .s 
sp 2 .p 



Fig. 14*5. Tejpns predicted in column IV. 

The C i spectrum arises from the 2 P ground term of C n and has 
been analysed quite regularly into a number of triplets and 
singlets; in contrast Pbi has been analysed only into series. To 
understand this better, consider the changes which occur in the 
s 2 p 2 and s 2 p.s configurations with increasing atomic number. 
Thus in C i the 3 P ground term has nearly the ideal interval ratio 
of the Russell-Saunders coupling, while the extreme interval is 
small compared with the distance which separates the 3 P from 
the 1 D term. Prom this ideal the low terms of Sii, Gei and Sn i 
fall further and further away until in lead A 3 P 01 is greater than 
A 3 P 12 , while the extreme triplet interval A 3 P 02 is as great as the 
separation of the 3 P 2 and X D 2 terms (Fig. 14-6). 



XIV] 



COLUMN IV 



27 



Again examine the intervals of the s 2 p.s configuration which 
produces a 3 P and 1 P term; in carbon the extreme interval of the 
3 P term is only 60 cm." 1 , while 1500 cm.- 1 separates 3 P 2 from 1 P 1 ; 





C 


Si 


Ge 


Sn 


Pb 


3 P - 3 Pi 

3 P!- 3 P 2 

3F 2 -iD 2 
1 D 2 - 1 S 


14-8 
27-5 
10,150 
11,452 


77-1 
146-1 
6075-5 
9095-4 


557-1 
852-8 
5716-0 
9241-2 


1692 
1736 
5185 
8550 


7,817 
2,831 

10,818 
8,000 


A'P^/A'P,^ 


1-86 


1-90 


1-53 


1-02 


0-36 



Fig. 14-6. Column IV. Intervals in the ground configuration, s 2 p 2 . 

but in tin the triplet and singlet are transformed into two diads, 
having intervals of only 300 and 600 cm." 1 , but separated from 
one another by 4000 cm.- 1 (Fig. 14-7). 





C 


Si 


Ge 


Sn 


Pb 


3 P - 3 Pl 
3 P!- 3 P 2 
IV 1 ?! 


20 
40 
1589 


77 
195 
1037 


251 
1415 
903 


274 
3714 
628 


327 


A 3 P . 2 
A ^.^ of ion 


60 
64 


272 
287 


1666 
1768 


3988 
4253 


14,071 



Fig. 14-7. Column IV. Intervals in the lowest s 2 p.s configuration. 

These changes run parallel to the increasing interval of the 2 P 
ground term of the spark spectrum, and the relation between the 
two may be explained in terms of the vector model, provided that 
the separation of two terms is assumed roughly proportional to 
the strength of the coupling producing it. This assumption is 
indeed implicit in the description of regular terms already given; 
for if, to fix ideas, the two p electrons of C i are considered, the 
triplet and singlet terms are found widely separated, a fact 
which the vector model translates to read that the spin coupling 
(SiSg) is strong; or again the two singlet terms are also widely 
separated, and so the orbital coupling (l^) must also be supposed 
strong; but the intervals of the 3 P term are small and so the 
coupling responsible, namely (LS), must be weak. 

Consider then the addition of an electron to an ion specified by 
{ L, ^S and ^J; if the coupling is Russell-Saunders, the coupling of 



28 ELEMENTS OF THE SHORT PERIODS [CHAP. 

^L and ^S must be split when the electron is added, and only after 
iL has combined with 1 and ^S with s may their resultants L and 
S combine together to form an atomic resultant J. In symbols, 
the coupling then appears as 



And this theory may be expected to yield a satisfactory account 
of the facts, so long as the (^L^S) coupling is weak; that is, so long 
as the interval of the spark ground term is small, a condition 
satisfied in carbon but not in tin. In contrast, when ($1^8) is 
strong, we obtain a more satisfactory account of the term scheme 
by considering the ionic and electronic vectors permanently 
coupled to ^J and j respectively; then the splitting is produced by 
the strong coupling (^L^S) and the weak coupling (^J j), so that in 
Sn T the s 2 p . s configuration produces not a triplet and a singlet 
but two diads. 

This new coupling is commonly referred to as (jj) coupling, 
being written symbolically as 



It is characterised by strong inter-system lines ; and in fact these 
are easily discovered in lead and can be traced greatly weakened 
in intensity back to silicon, but there is still a little doubt about 
the three lines found by Jog* in C I, for if the lines found are those 
sought, the singlet term ^ a l ues assigned by Fowler must be 
changed by no less than 667 cm.- 1 

5. Column V, s 2 p 3 configuration 

Hund's theory predicts that in the elements of column V the 
ground term should be 4 S xi . and that above this should lie four 
metastable states 2 D 2 j,H an( ^ 2 ^ > U,i* J ^ Ln ^ empirically these five 
terms have been found in the arc spectra of nitrogen, phosphorus, 
arsenic, antimony and bismuth. 

Of these spectra only Ni and Pi have been fully analysed. 
Ni was not easily observed, for many of the lines lie incon- 
veniently far out in the infra-red or ultra-violet; moreover, when 
excited by an arc strong bands appear which are apt to mask the 

* Jog, N, 1929, 123 318. 



xiv] 



COLUMN V 



29 





o 33.0, , _ ^P'Mp 4 ? 2 ? 


Lino o^n 






I* IU xu)U 






1 above 3 ? 




92 2 1-rk 1 rvr 1 n f TVJ TT 












2s 2 .2p 2 3 P level of Nil , 






( 1 D)ns f 2 D 






t\ \ .1 " I 


Li*5 ^?n 


Volts 


( P)rm 4 P 2 P II 

/ITV^ 2r-k Z'r* 

PP'ivin ^Tl 4 P 1 4c ZTX 2p .ZoVDMp D P 
V rVnp U r i o JJ , r i p 

r i T i T^ 1 ! T 


! above 3 ? 

i 

117 ^d-'i 




( 3 P)nd ^ 4 P 2 D 2 P 


Mi. ?*r? 

cm:' 


14- 






* 








5g Q Q A"' 


nn nnn 






11U,UUU 




4 ? ~ "J7^ r ^'^ "^ J^~ A / 




n__ 



3d" O Q G / 






4 s ^t 




12- 


/ 
> ^A i / I 


-100,000 




3p A -^ x v/ / / 






y / 




11- 


/ ^ 


-90,000 




. y / 






3s <2r- / 




10- 


/ 


-80,000 


4- 


/ 




3-56- 




-30,000 


3- 


/ 




2-37- 




-20,000 


2- 






1- 


/ 


-10,000 


0- 


2p afif 


-0 



Fig. 14-8. Level diagram of nitrogen. 



30 ELEMENTS OF THE SHORT PERIODS [CHAP. 

ultra-violet lines, while more vigorous excitation only brings out 
the spark lines. Compton and Boyce have, however, excited tne 
ultra-violet lines with single electron impacts, a convenient 
technique because work on neon and argon shows that a single 
impact will not disturb more than two electrons, no lines of the 



Nil 






Ni 




I,l 2 ...k 


Term 


*5 


Term 


/i .- h 


2s 2 . 2p 2 


3p 


2p 


4 S o 2 D o 21 o 


s 2 p 3 






ns 
np 
nd 


4p 2]> 

4 (SPD) 2 (8PD) 
'(PDF) 2 (PDF) 


S 2 p 2 .s 
s 2 p 2 .p 
s 2 p 2 .d 




A D 


ns 
np 


2 D 
2 (PDF) 


S 2 p 2 .s 
sV-P 




\S 


na 
np 


2 S 

2po 


8 2 p 2 .8 

s 2 p 2 .p 


2s 2p 3 ' 


3}>o 


2p 


4 P 2 (SPD) 


sp* 



Fig. 14-9. Terms predicted in column V. 

second spark spectrum being produced even when the potential 
is more than adequate. 

In Pi many lines lie even further out in the infra-red than in 
N i, so far out in fact that the usual sensitiser neo-cyanine would 
not serve; recently, howevej, at the Bureau of Standards a new 
sensitiser has extended the range which can be photographed 
and a thorough analysis of P i has been made. 

In the three remaining elements few terms outside the ground 
configuration have been named, though the energies of many are 
known; the intervals of these five terms, however, still show them 
as a singlet and two doublets in Sb i (Fig. 14- 10), while in Bi i the 



Interval 


N 


P 


As 


Sb 


Bi 


'Sn-'Dii 
2 il-*V*l 
2 D 2 i- 2 Pi 

*p;-< 


19,202 
-8 
9,606 



11,366 
15 
7,346 
25 


10,591 
322 
7,272 
461 


8512 
1342 
6541 
2069 


11,418 
4,019 
6,223 
11,505 



Fig. 14-10. CoJumn V. Intervals of the ground configuration, s 2 p 3 . Note the 
change from LS coupling in nitrogen to jj coupling in bismuth. 



XIV] 



COLUMN V 



31 



sequence of J values is still unchanged, so that the terms may be 
named by analogy; in an atom of high atomic weight (LS) 
coupling is not to be expected. 

Of the higher terms little need be said; in Ni the lowest are 2 P 
and 4 P from the 2p 2 . 3s configuration, while very little higher lies 
the 2s. 2p 44 P term. The energy relations are shown in Fig. 14-8. 

Most of the term series of N i approach the 3 P ground term of 
N ii as limit, but experiment shows that different series approach 
different components of the limit; for if two components of a 
multiplet tend to the same limit the interval decreases very 
rapidly, roughly in fact as I/ft* 3 ; but in Ni the intervals of some 
tei v ms decrease only slowly or actually increase, this being true 
in particular of the 2p 2 .ns 4 P and 2p 2 .ml 2 D series. 







Ni 






Nn 




71 


3 


4 


5 


6 






4 Pf 4 Pl* 


33-8 


50-0 


44-3 


44-7 


3P _3p 

L o r i 


50 


4 Pli- 4 P 2i 


46-7 


68-7 


70-1 


72-0 


'JVP, 


84 


4 IV 4 I\i 


80-5 


118-7 


114-4 


116-7 


3 Po~ 3 P 2 


134 



Fig. 14-11. Intervals of the 2p 2 .ras 4 P series in N I. 

With large values of n the intervals of the 2p 2 . ns 4 P series may 
reasonably be supposed to approach the values of 50 and 84 cm." 1 , 
which are the intervals of the ground term of N n. And if this is 
true then 4 P^ must tend to the lowest or 3 P limit, while 4 P 2i must 
approach the highest or 3 P 2 limit. In Fig. 14-12 these facts are 
shown graphically, the separations being measured horizontally 
away from the middle terms, 4 P lt . in Ni and ^P l in Nn. Un- 
fortunately in most series only two or three terms are known, 
and though the intervals of these may be roughly constant, they 
do not establish the limits beyond doubt as the above series 
do. Even in the 2p 2 . nd 2 D series, of which five terms are known, 
one would hesitate to say whether the intervals tend to a limiting 
value of 50 or 84 cm.- 1 , though evidently they do not tend to 
zero (Fig. 14-13). 

The passage of the different components of a multiplet term to 



32 ELEMENTS OF THE SHORT PERIODS [CHAP. 

different limits often leads to wide departures from the interval 
rule, and these, like the departures due to increasing atomic 
number, may be described with the vector model. For consider 



Nil 



10,000 - 




20,000 - 



30,000 - 



Fig. 14-12. Intervals of the 5s. nd 3 D series of Sr I contrasted with those of the 
2p 2 . m 4 P series of N I ; in the first the different series converge to the same 
limit, in the second they converge to three different limits. 



n 


3 


4 


f> 


6 


7 


2 Dii- 2 r>2i 


23-5 


22-2 


18-3 


58-3 


42-6 



Fig. 14-13. Intervals of the 2p 2 .ral 2 D series of N i. 

the addition of an electron defined by n, 1, s to an ion defined by 
^L, ^S; then in the low terms the couplings (^Ll) and (^Ss) are 
strong, while (LS) and (Is) suffice only to produce the splitting of 
the multiplet term into its components; but (LI) and (Ss) decrease 
as the chief quantum number of the electron increases and 
actually vanish when n tends to infinity, while (LS) remains 
constant, so that when n is sufficiently large the latter becomes 



XIV] COLUMN V 33 

the more important and the splitting becomes that of the ionic 
ground term. 





c n^ ^P Introl /if O II - 1 


-120,000 
cm: 1 
above S 

above 4 S 
above 4 S 


D 2 V 2 P 1CVC1 Of 11 ^ ^ 3P 


2s 2 .2 P 3 . 2 Dlevelof OH ^ ( 2p ) ns ipL 


( 2 P)np'D 'S 
( 2 D)ns 3 D 'D 


( 2 D)np 3 D *P 1 D 'P 


Volts 
13-55- 
13- 


2s 2 .2p 3 . 4 S c levelof01K / 
( 4 s)ns 5 S 'Sf X^' T - 
( 4 S)np 5 P | *P | | / /^ X ^A""^ I 


120,000 

109,837 
cm". 1 


( 4 S)nd 5 D 3 i) X __gS j 


12- 


Q J // 7^ I 

T S y * 


100,000 


10- 
8- 


"-'^" j . 

^ s f ' 


80,000 


i 

1 




1 


60,000 


6- 


I 






i 




- 


;- 


40,000 


4-18. 
4" 


. 







- X 


20,000 


1-95 = 


.^ 




0- 


2p 3^'^ 






Pig. 14-14. Level diagram of oxygen. 
6. Column VI, s 2 p 4 configuration 

Bund's theory predicts in column VI five low terms, 3 P 2 ,i,o> 
1 D 2 and ^Q, and empirically the 3 P term has been identified in 



34 ELEMENTS OF THE SHORT PERIODS [CHAP. 

the spectra of oxygen, sulphur, selenium and tellurium; while the 
two singlet terms are still missing only in sulphur (Fig. 14-14). 
The most notable changes in the energies of these low terms with 
increasing atomic number are first the closing together of the five 
terms, and secondly the movement of the 3 P X term from its 
normal position one-third of the distance between 3 P and 3 P 2 up 
to and past 3 P , so that in tellurium the 3 P term is partially 
inverted (Fig. 14-15). 



Interval 


() 


8 


Se 


Te 


30 31> 
1 2~ t I 


158 


398 


1,989 


4,7 


3p 3I> 
*- 1 


67 


174 


545 




3 P - 1 ^2 


15,641 





7,042 


5,8 


'Dg-% 


17,925 





13,794 


12,6 



-44 



Fig. 14-15. Column VI. Intervals of the ground configuration, s 2 .p 4 . 

Beyond these low terms very little is known of Tei; while in 
Se i only a few quintet terms have been identified; but a list of the 
higher terms predicted for all spectra of column VI is given in 
Fig. 14-16. 



(3 ii 






Oi 




/!/,.-. h 


Term 


k 


Terms 


/! ... ^ 


2s 2 . 2p 3 


4go 


2p 
ns 
np 
/id 


3 P ^S 

5 S 3 S 

5p 3 p 

5 D* 3D 


s 2 p 4 
s 2 p 3 .s 
s 2 p 3 .p 
s 2 p 3 .d 




2 D 


m 
np 
nd 


3 D o IJL)0 

3 (PDF) UPDF) 
3 (SP.DFG) ^SPDFG) 


8 2 p 3 .S 

s 2 p 3 .p 
s 2 p 3 .d 




2po 


ns 
np 
rid 


apo lpo 

3 (SPD) l (SPD) 
3 (PDF) ^PDF) 


S 2 p 3 .8 
8 2 P 3 .p 

s 2 P 3 .d 


2s.2p 4 


_ 


2p 


3po ipo 


sp 5 



Fig. 14-16. Terms predicted in column VI. 

In Oi and Si series were identified by Paschen and Runge 
before the end of last century, and these are listed in Fowler's 
Report as singlets and triplets. Theoretically these series should 
be prominent, because the normal state of the ion is an S state; 



XIV] COLUMN VI 35 

but a 4 S ground term should produce systems of triplets and 
quintets, not of singlets and triplets. This discrepancy between 
experiment and modern theory was only resolved in 1923 when 
Hopfield identified series of lines arising from the combination of 
Fowler's 'singlet' S and D series with a 3 P ground term. The 
numerical values of the three components of the term are 109,833, 
109,674 and 109,607,* showing intervals of 159 and 67 respec- 
tively and an interval ratio of 2-4 : 1. In combinations of this term 
the line of shortest wave-length is the most intense, so that the 
3 P term must be inverted. 

As inter-system lines are seldom strong, the combination of 
this triplet term with a ' singlet' series suggested that the sup- 
posed singlets were really triplets too narrow to be resolved. 
True, the 3 P ground term also combines with Fowler's Is 'triplet ' 
term, but the lines are much weaker, and though the Is -> 3 P 2 and 
IS-^P! lines are quite clear, the ls-> 3 P line is missing in both 
O i and S i. If, however, the supposed triplets are really quintets 
the absence of this particular line is readily explained, for the Is 
term is then 5 S 2 , and the combination with 3 P is forbidden, since 
J would have to change by two units. This evidence alone seems 
conclusive, but in 1923 the argument from theory was of little 
weight and so Paschen and Landef felt bound to settle the ques- 
tion by measuring the Zeeman splitting of two quintet com- 
binations 7771 A., 3p 5 P 123 ->3s 5 S 2 and 3974A., 4p 5 P 123 -> 3s 5 S 2 . 

Above the 3 P term thus identified the metastable states X D 2 
and 1 S should lie, and recently combinations of these states with 
various higher terms have been identified in Oi; but history 
records that these lines were found only after McLennanJ had 
shown in a brilliant research that the green auroral line 5577 A. 
arises in a jump between these two states. As the transition is 
forbidden by two selection rules the evidence requires careful 
scrutiny ; it will be considered in a later chapter on quadripole 
radiation. 

* Hopfield, AJ, 1924, 59 114. 

t Laporte, Nw 9 1924, 12 598, attributes this work to Paschen and Land6, but 
the reference given is inaccurate and the paper does not appear under either 
name in Science Abstracts, 1922-24. 

J McLennan, PES, 1928, 120 327. 

3-2 



36 ELEMENTS OF THE SHOUT PERIODS [CHAP. 

7. The halogens, s 2 p 5 configuration 

According to Hund's scheme the p 5 configuration produces 
only an inverted 2 P term, and in fact this is the normal state of all 
halogen atoms. 

The higher terms may be divided into three groups according 
as they arise from the 3 P, X D or 1 S term of the spark spectrum. Of 
the predicted terms shown in Fig. 14- 1 7, a large number have been 



FII 


Fi 


M 2 .../ 6 


Term 


*7 


Terms 


I,. ..I, 


2s a .2p 4 





2p 


2po 


s 2 p 5 


sp 


718 

np 
nd 


fP 2 P 

4 (SPD) 2 (SPD) 
4 (PDF) 2 (PDF) 


s a p 4 .s 
s 2 p 4 .p 
8 2 p 4 .d 


*D 


ns 

np 

rid 


2 D 
2 (PDF) 
2 (SPDFG) 


s 2 p 4 .s 
s 2 p 4 .p 
8 2 p 4 .d 


*S 


ns 
np 
nd 


2 S 

2po 
2J) 


s 2 p 4 .s 
s 2 p 4 .p 
s 2 p 4 .d 



Fig. 14*17. Terms predicted in the halogens. 

found in the arc spectra of all the halogens, and in the spark spectra 
of neon, argon and krypton. In particular, Bakker, De Bruin and 
Zeeman* have made an extensive magnetic analysis of A n and 
have studied the spectrum very thoroughly; it provides much 
material for the study of irregular g values and of series limits, and 
will be referred to again in that context; the terms obey the 
normal multiplet laws badly, but the Rydberg formulae rather 
well.f In the lighter elements the empirical terms are easily 
named, for they approximate to the Russell-Saunders laws, but 
only the J values of the higher terms of 1 1 are known. 

Directly above the ground term come even terms from the 
p 4 . s and p 4 . d configurations. Of these the p 4 ( 3 P) s configuration 
should produce five terms, named according to the Russell- 
Saunders scheme 4 P 2 i,u, * anc ^ 2 -^u,i5 an< ^ i* 1 ^ ac ^ in F I the extreme 

* Bakker, De Bruin and Zeeman, K. Akad. Amsterdam, Proc., 1928, 31 780. 
t Rosenthal, AP, 1930, 4 80. 



XIV] 



THE HALOGENS 



37 



intervals of the two multiplets are less than 450 and 350 respec- 
tively, while they are separated by nearly 2000 cm." 1 In Ii, on 



Volts 
12-96 



11 



10 



3s 2 . 3p 4 .( 3 P) level of 

( 3 P) ns 
( 3 P) up 




( 3 P)nd 






4 P 



_3d 
5p 



4p 



4s 



-3p- 



I I I 

J F 2 D 2 P 



..-A 



A 



104,991 
cmT 1 

100,000 



90,000 



80,000 



70,000 



Fig. 14' 18. Level diagram of chlorine. 

the other hand, the division of the five terms into multiplets is not 
justified by their energies; as the sequence of J values is the 
same as in chlorine, the empirical terms may be named by 



38 ELEMENTS OF THE SHORT PERIODS [CHAP. 

analogy, but if this is done A 4 ?^ is 4800 cm." 1 while 2 P 1} - 4 P^ 
is only 900 cm.- 1 (Fig. 14-20). If the five terms are divided by 
their energies, they form two diads below and a monad above; 
thus the lowest terms form a diad and have J values of 2| and 1^, 



1 e , 

1 3r' 3 P a 1<WI r<P A III 












-114,000 








cm". 1 


3s i? .3p 4 . 'S level of A 111 - 


('C') ^ 2t; 






?s z .3p 4 . *D level of A III 


X^ ( 1 S)np 2 P | 


unknown 


"~\ * i ' [ 


Js 2 . 3p 4 >P level of A III^ ('p) ns ^ ? D ( ' S)nd ^ 








( ] D)np 2 FI 2 D , 2 P 

1 T 1 | 1 


unkncvwn 












( 3 P)n8 ^P 


2p 





Volts 

27-72 - 


(V)np ^ 4 P 4 S 

r iii 


" 2 ? 2 ? I'? 


224,721 
220,000 


J F 1 1 1 ~ 

P) nd iF jD ^P ^ F ^D ^P 






^O 
_^G---0 0" 


200,000 


24 - 




O - /-^ " ' ^ 






4d __ _-o G 


- U ~~O^" 






5s -^--^ o 


o-^=-ai 


180,000 


20- 


4p ^.^^~ 


--^-^-^^ ^^" - 


160,000 


16- 


4s H^^^Ho 


'_^^- -^^ 


140,000 






- 


120,000 


12- 




iQ 


100,000 






/' 


80,000 


8- 




s 


60,000 






/ 


40,000 


4- 




s 








f 


20,000 


0- 


,p 


X 






Fig. 14-19. Level diagram of A n. Note that the d levels lie deeper here than 
in the preceding figure, which shows the isoelectronic spectrum 01 i. 

being formed presumably by the addition of an s electron to the 
3 P 2 spark term; similarly, the next diad has J values of 1| and |, 
and so may be assumed to arise from the addition of the s electron 
to the s?! spark term ; and highest of all lies the single level with a 
J value of , arising as ( 3 P ) s. These energy values clearly justify 



XIV] 



THE HALOGENS 



39 



us in saying that the coupling in F i is Russell-Saunders, but in 
Iiis(jj). 

A comparison of the isoelectronic spectra Cl i and A n brings 
out one common effect of increasing the nuclear charge; in Cl i the 
succession of the configurations is apparently 4s, 4p, 5s, 5p, 3d, 





F 


Cl 


Br 


I 


Pi*- 4 plt 


275 


530 


1471 


1459 


PU-'P/ 


160 


338 


1977 


4803 


<?*-< 


1892 


1398 


300 


924 


2 pu- 2 pi 


325 


640 


1787 


4530 


A 3 P 02 of ion 


491 


991 









Fig. 14-20. Intervals of the p 4 ( 3 P) . s configuration, showing the change from 
LS to jj coupling. 

terms arising from all the configurations except 5s having been 
identified; but in An the succession is 4s, 3d, 4p, 5s, 4d, the 
increased nuclear charge having thus moved the d terms down 
relative to the s and p terms. Of this movement much more will 
be heard in the long periods. 

8. The inert gases, s 2 p 6 configuration 

The p 6 group, being a complete shell, produces only a *S term, 
and empirically this always lies so much deeper than any of the 
odd terms that the lines which result lie in the far ultra-violet. 
The ground term and the lowest configuration of odd terms have 
been identified in the arc spectra of neon, argon, krypton and 
xenon and also in the spark spectra Na n, K n, Rb IT and Cs n; of 
these neon was the subject of such a thorough study at a time 
when the structure of complex spectra was very little understood 
that it still deserves pride of place (Figs. 14-21, 22). 

The spectrum of neon consists of two parts, one in the visible 
analysed into series by Paschen in 1918,* and a few ultra-violet 
lines unknown to Paschen, but discovered by Lyman and 
Saunders in 1925*f and attributed at once to the deep 1 S ground 
term. The large number of series discovered by Paschen may be 



* Paschen, AP, 1919, 60 405; 1920, 63 201. 
t Lyman and Saunders, PR, 1925, 25 886 a. 



40 



ELEMENTS OF THE SHOET PERIODS [CHAP. 



3p 5 . % level of All 
3p 5 . % level of A II 

( 2 P)m 3 P 
V r/iib r 2l 




( 2 P)np 
( 2 P)nd 



Plo - 

6 te 



-p 5 



Volts 



15- 



14- 



13- 



12- 



P4-Pl 

4terms 



8 terms 



4 terms 



I 



5s 
3d 



4p 



4s 



o- 



3 P 



cm: 1 
-120,000 

-110,000 
-100,000 
- 90,000 



rO 



Fig. 14*21. Level diagram of argon; this differs from the level diagram of neon 
only in the energies of the terms. 



XIV] THE INERT GASES 41 

divided by the energies of their lowest terms into three groups; of 
these the lowest contains four terms, named from below up s 6 , s 4 , 
s 3 and s 2 , and identified in modern theory with the 2p 5 ( 2 P) 3s 
conguration. Above these lie ten terms called by Paschen p 
terms, and written from below up p 10 to p x ; these combine with 



Neil 


Nei 


1 1 2 ...1 7 


Terms 


IB 


Terms 


Paschen' s terms 


/!.../, 


2s 2 . 2p 5 


2p 


2p 


*S 


__ 


s 2 p 


na 
np 
nd 


3po ipo 

3 (SPD) ^SPD) 
3(PDF) HPDF) 


S 2 , s 3 , s 4 , s 5 

Pl-PlO 

Sj arid d 


S 2 p 6 .8 

sV-P 
S 2 p 5 .d 



Fig. 14-22. Terms predicted in the inert gases. 

the s terms and clearly arise from the p 5 ( 2 P) 3p configuration. 
Higher still appear twelve terms written some of them d and 
some s x ; these arise from the p 5 ( 2 P)3d configuration. All these 
terms were assigned J values by Lande* as the result of a mag- 
netic analysis (Fig. 14-23), and these J values agree precisely 
with those required by theory. 



/'dgS/'s/'" d 1 'd 4 ds 1 /// 




Fig. 14-23. Permitted combinations and / values of the empirical terms of neon. 

Though thus far agreement is so satisfactory the s terms alone 
come near to obeying the multiplet laws. By Hund's energy rules 



* Lande, PZ, 1921, 22 417. 



42 



ELEMENTS OF THE SHORT PERIODS 



[CHAP. 



these four terms should be 3 P 2 ,i,o ar *d 1 P 1 in order of increasing 
energy (Fig. 14-23); the empirical J values establish the 3 P 2 and 
3 P terms in the positions indicated; while for s 4 and s 2 Back* 



Terms 


{/ factor 


Limit 


Emp. 


Theor. 


Emp. 


Theor. 


Emp. 


Theor. 


S 2 

83 


5 


1-04 

o 
1-46 


1 




1-5 


Upper 
Upper 
Lower 


!p* 


85 


3 ^2 


1-50 


1-5 


Lower 


2p H 



Fig. 14'24. The 2p 6 .ws terms of neon; the empirical g values are those of the 
first or 3s term of the series. 

obtained g values of 1-46 and 1-03, in satisfactory agreement 
with the theoretical values of 1-5 for 3 P X and 1-0 for 1 P 1 . More- 
over, this allotment is confirmed by the ultra-violet combinations 
with the 1 S ground term, for the line of lower frequency s 4 -> 1 S 
is weaker than the line of higher frequency s 2 -> 1 Sf; and this 
agrees with the general rule that inter-system lines are weaker 
than combinations between terms of the same system. 

The p terms present much greater difficulties; a very brief 
examination shows that the interval rule is quite useless, while 
the Lande g formula is none too well obeyed. Accordingly, the 
matching proposed by HundJ (Fig. 14-24) must be regarded at 
best as the reasoned guesij of an expert; for a thorough study of 
the transition from Russell -Saunders to (jj) coupling is necessary 
before a satisfactory solution can be reached. Judging from 
H. N. Russell's success with the complex spectra of the iron row, 
a satisfactory solution might be expected from a careful study of 
intensities, but this does not seem to have been attempted yet. 

In ordering the high terms to series based on these low terms 
Paschen found clear evidence that the series might be divided 
into two groups, some tending to a lower limit and others to a 
limit 780 cm." 1 higher; these two limits appear in modern theory 

* Back, AP, 1925, 76 317. 

t Shenstone, N, 1928, 121 619. 

} Hund, ZP, 1929, 52 601. 

Pogany, ZP, 1935, 93 376 and chapter xvm, 7. 



XIV] THE INERT GASES 43 

as the two components of the 2 P ground term of Ne 11, now known 
to have an interval of 782 cm." 1 Of the s terms s 2 and s 3 tend to 
the upper limit, s 4 and s 5 to the lower limit; the limits of the p 
series are shown in Fig. 14-25. 



Empirical 


Theoretical 


Term 


J 


9 


Limit 


Term a 





Pi 





* 


Upper 


3 Po 





Pa 







or 


Lower 




* 


P 2 


1 


1-340 


Upper 


3p i 


1-5 


p 5 


1 


0-999 


Upper 


1 P 1 


1-0 


P 7 


1 


0-699 


Lower 


3D, 


0-5 


Pio 


1 


1-984 


Lower 


Si 


2-0 


P4 


2 


1-301 


Upper 


3p 2 


1-5 


P* 


2 


1-229 


Lower 


3 D 2 


1-167 


Ps 


2 


1-137 


Lower 


X I>2 


1-0 


P9 


3 


1-329 


Lower 


3 D 3 


1-333 



Fig. 14-25. The 2p 5 . 3p terms of neon. 
The naming of the terms is based on the most exiguous evidence. 



Interval 


Ne 


A 


Kr 


Xe 


3 P 2 - 3 P! 


417 


607 


945 


978 


3 Pl- 3 P 


359 


803 


4275 


8152 


^O^Pl 


1070 


846 


655 


988 



Fig. 14-26. Intervals of the p 5 ( 2 P).s configuration in the inert gases. 

The spectra of the heavier inert gases are very similar to neon, 
but as the interval of the ground term of the spark spectrum 
increases, its influence on the arc spectrum becomes increasingly 
evident; it appears, for instance, in the intervals of the four 
( 2 P) s terms, shown in Fig. 14-26; while in Kr I the p terms divide 
themselves into two groups with an interval of no less than 
5200 cm." 1 between them; the upper group consists of four terms 
and the lower group of six just as theory will be shown to require, 
but the chance of fitting the Russell-Saunders notation to these 
terms is more remote even than in neon. 

Indeed, the heavy inert gases centre in themselves three in- 
fluences which all conspire to break up the simple Russell- 



44 ELEMENTS OF THE SHORT PERIODS [CHAP. XIV 

Saunders coupling; first, increasing atomic number makes for 
loss of regularity; this was discussed particularly in columns 
IV and V, but it is visible in every column; secondly, the increas- 
ing separation of the ground term of the ion tends to divide the 
terms by limits rather than by multiplets; and lastly spectra grow 
less regular as one passes from left to right across the periodic 
table, neon is less regular than carbon and carbon less regular 
than sodium. 

BIBLIOGRAPHY 

The first systematic account was by Hund in Linienspektren und periodisches 
System der Elemente, 1927, and this is still standard. 

Term values are largely taken from Bacher and Goudsmit, Atomic Energy 
States, 1932. References to particular elements can be traced in the select 
bibliography of Appendix vi. 



CHAPTER XV 

LONG PERIODS 

1 . The ground terms 

In the short periods the s electron carries appreciably less energy 
than the p electron, and very little study suffices to show that the 
first two electrons enter an s shell and the last six a p. In the long 
periods however, while an s electron still carries less energy than 
a p, the s and d electrons carry roughly the same energy, so that 
a first glance shows one group of twelve elements instead of two 
groups of two and ten. 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


K 


Ca 


Sc 


Ti 


V 


Cr 


Mn 


Fe 


Co 


Ni 


Cu 


Zn 


Rb 


Sr 


Y 


Zr 


Cb 


Mo 


Ma 


Ru 


Rh 


Pd 


Ag 


Cd 


Cs 


Ba 


La-Lu 


Hf 


Ta 


W 


Re 


Os 


Ir 


Pt 


Au 


Hg 



Bohr's work on the periodic system showed that in the first two 
of these twelve elements the electron enters an s orbit, but that 
thereafter as the nuclear charge increases the d orbits grow more 
stable and the s less, until in the spark spectrum of a system of 
ten electrons all ten occupy d orbits, and produce the 1 S ground 
term characteristic of a complete shell. The eleventh and twelfth 
electrons then re-enter the s shell producing copper, zinc and 
their homologues. Thus in only eight of the twelve elements are 
the configurations still in doubt; these eight were enclosed by 
Bohr in a frame, and will be described in successive periods as the 
elements of the iron frame, the palladium frame and the platinum 
frame. 

Since only two electrons can enter an s shell, an atom with n 
outer electrons has the choice of only three configurations, 
d n , d n ~ l . s and d n ~ 2 . s 2 ; the chief quantum numbers will usually be 
omitted, in order to simplify the discussion, for the orbits are 
always 3d and 4s in the iron frame, 4d and 5s in the palladium 
frame and 5d and 6s in the platinum frame. 

The terms, which any configuration produces, can be calcu- 
lated ; and if the lowest term of each configuration is that with 



46 LONG PERIODS [CHAP. 

largest spin and orbital vectors, a list of possible configurations 
and the ground terms which they produce can be compiled, as 
Fig. 15-1 shows. But the ground term is the easiest of all terms to 
determine empirically, so that the argument which produced this 
table may be reversed, and the ground term used to decide which 
configuration produces the lowest term (Figs. 15-2-4). When 



No. of 


Configuration 


electrons 


d n 


d^.s 





l ti 




1 


2 D 


2 S 


2 


3 F 


3 D 


3 


4^ 


4 F 


4 


5 D 


5 F 


5 


S 


6 D 


6 


5 D 


7 S 


7 


4JF 


6 D 


8 


3 F 


5 F 


9 


a D 


4 F 


10 


\S 


3 D 


11 




2 S 


12 







3 F 
2 D 



Fig. 15-1. Ground terms of three configurations. 



No. of 


Arc spectra 


Spark spectra 


elec- 
trons 


Atom 


Ground 
term 


Con- 
figuration 


Atom 


Ground 
term 


Con- 
figuration 


1 


K 


2 S 


4 8 


Ca+ 


2 S 


s 


2 


Ca 


X S 


S 2 


Sc+ 


3 D 


d.s 


3 


Sc 


2 D 


d.s 2 


Ti+ 


4 F 


(d 2 .s) 


4 


Ti 


3 F 


d 2 .s 2 


V+ 


5 D 


d 4 


5 


V 


*F 


d 3 .s 2 


Cr+ 


6 S 


d 5 


6 


Cr 


7 S 


d 5 .s 


Mn+ 


7 S 


d 5 .s 


7 


Mn 


6 S 


d B .s 2 


Fe+ 


6 D 


d c .s 


8 


Fe 


5 D 


d.s 2 


Co+ 


3 F 


d 8 


9 


Co 


4 F 


(d 7 .s 2 ) 


Ni'- 


2 D 


d 9 


10 


Ni 


3 F 


d 8 .s 2 


Cu+ 


1 S 


d 10 


11 


Cu 


2 S 


d 10 .s 


Zn+ 


2 S 


d 10 .s 


12 


Zn 


*s 


d 10 .s 2 


Ga+ 


J S 


d 10 .s 2 



No. of 
elec- 
trons 

1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 



Fig. 15-2. Ground terms of the iron frame elements. 

In this and the two following figures, the ground term is given only when it is 
known empirically; a ? following the term shows that it is still open to doubt. 
A configuration enclosed in brackets cannot be deduced from the ground term 
alone, but is known from further study of the spectrum ; where a configuration 
is given in the absence of the ground term, reliance has been placed on the 
argument of 4 of this chapter. 



XV] THE GROUND TERMS 47 

there are 3, 6 or 9 electrons, two configurations produce the 
same ground term, and then further study is necessary to dis- 
tinguish between them; where a configuration has been obtained 
in this way, it is enclosed in brackets. 



No. of 


Arc spectra 


Spark spectra 


No. of 


elec- 
trons 


Atom 


Ground 
term 


Con- 
figuration 


Atom 


Ground 
term 


Con- 
figuration 


elec- 
trons 


1 


Rb 


2 S 


s 


Sr+ 


2 s 


s 


1 


2 


Sr 


*S 


s 2 


Y 


T S 


s 2 


2 


3 


Y 


2 D 


d.s 2 


Zr+- 


4jr 


d 2 .s 


3 


4 


Zr 


3 F 


d 2 .s 2 


Cb+ 


5 1) 


d 4 


4 


5 


Cb 


6 D 


d 4 .s 


Mo+ 


6 S? 


d 6 


5 


6 


Mo 


7 S 


d 5 .s 


Ma+ 





d 5 .s 


6 


7 


Ma 





d 5 .s 2 


Ru+ 


*F 


d 7 


7 


8 


Ru 


*F 


d 7 .s 


Rh+ 





d 8 


8 


9 


Rh 


*v 


(d 8 .s) 


Pd+ 


2 D 


d 9 


9 


10 
11 


Pd 

Ag 


*s 

2 S 


d io 
d 10 .a 


Ag+ 
Cd+ 


1 S 
2 S 


d 10 
d 10 .s 


10 
11 


12 


Cd 


A S 


d lo .s 2 


In+ 


J S 


d 10 .s 2 


12 



Fig. 15-3. Ground terms of the palladium frame elements. 



No. of 


Arc spectra 


Spark spectra 


No. of 


elec- 
trons 


Atom 


Ground 
term 


Con- 
figuration 


Atom 


Ground 
term 


Con- 
figuration 


elec- 
trons 


1 


Cs 


2 8 


s 


Ba+ 


2 S 


s 


1 


2 


Ba 


^ 


s 2 


La+ 


3 F 


d 2 


2 










Lu+ 


*S 


s 2 




3 


La 


2 D 


d.s 2 


Hf+ 


2 D 


d.s 2 


3 




Lu 


2 D 


d.s 2 










4 


Hf 


3tf 


d a .s a 


Ta+ 








4 


5 


Ta 





d 3 .s 2 


w-i- 








5 


6 


W 


5 D 


(d 4 .s 2 ) 


Re+ 








6 


7 


Re 


6 S 


d 5 .s 2 


Os+ 








7 


8 


Os 





d e .s 2 


Ir+ 


___ 





8 


9 


Ir 


2 D? 


d 9 ? 


Pt+ 


__ 





9 


10 


Pt 


3 D 


d 9 .s 


Au+ 1 ^ 


d 10 


10 


11 


An 


2 S 


d 10 .s 


Hg+ 


2 S 


d 10 .s 


11 


12 


Hg 


1 S 


d 10 .s 2 


T1+ 


J S 


d 10 .s 2 


12 



Fig. 15-4. Ground terms of the platinum frame elements. 

With only one exception the arc spectra of the iron frame 
(Fig. 15-2) have d n ~ 2 .s 2 as their ground configuration, while the 
spark spectra have d 71 " 1 ^ or d n , a contrast which shows how 
general is the tendency of the d electrons to sink relative to the s 
electrons as the nuclear charge increases; of this tendency an oft- 



48 LONG PERIODS [CHAP. 

quoted example is the descent of the s electron of K i and Oa n 
into the d orbit of Scin. In the palladium frame (Fig. 15-3) the 
tendency is again in evidence; the d n configuration produces the 
ground terms of six spark spectra, but only one arc. Com- 
parison of the iron and palladium frames shows that the d orbits 
are more stable in the latter; of the platinum frame (Fig. 15-4) 
not much is yet known, but there is some reason to think that in 
the early elements the d orbits are more stable still, but that after 
the intrusion of the f shell between lanthanum and lutecium, the 
d shell is less stable even than in the iron frame. Thus La n has a 
d 2 3 F ground term in contrast to the ds 3 D of Sc n and the s 2 X S 
of Y n, but the ground states of Lu n, Lu i, Hf i and Re i all seem 
to contain two s electrons, besides varying numbers of d electrons. 

2. Configurations and analysis 

In all three frames the s and d electrons have roughly the same 
energy, and this determines the general form of the spectra. 
A configuration which contains only s and d electrons outside the 
last closed shell will consist of even terms, and accordingly the 
low terms of all elements are even; they will usually arise from 
two different configurations, and as no combinations are per- 
mitted, the higher of the two is metastable. 

Above these low terms come a group of odd terms containing 
a p electron, and above those again a second group of even terms 
containing only s and d efectrons. Theory allows many higher 
terms, but in practice the lines involving these terms are weak 
or absent, so that series consist of only two or at most three 
terms. 

This means that the method of analysis differs from that 
applied to simple spectra*; the spectroscopist tries to find not 
series, but multiplets. As in other spectra constant differences 
between the frequencies of pairs of lines indicate terms, and these 
may be separated into odd and even, because an odd term com- 
bines only with an even. The ground term can usually be picked 
out because it gives rise to the raies ultimes and most of the 
absorption lines; the spark produced under water is also useful, 

* For an account of methods of analysis, see Russell, AJ, 1927, 66 348. 



XV] CONFIGURATIONS AND ANALYSIS 49 

for the spectrum consists of a few lines all ending in the ground 
term. 

The approximate energy of a term can be determined by 
examining the temperature class of the lines to which it gives rise. 
If it is of low energy content, then it will appear bright at a low 
temperature and in King's classification will belong to a low class. 
This and the division into odd and even terms will often determine 
the configuration to which a term belongs. 

Finally, the terms of a configuration may be divided into 
multiplets by examining the intensities of the lines to which they 
give rise, for when the coupling is not normal the intensities are 
far less seriously disturbed than either Land^'s interval ratios or 
the magnetic splitting factors. 

To suit these new methods of analysis, new ways of specifying 
the empirical terms have had to be developed; thus the analysis 
may succeed in finding terms, but be unable to divide them into 
multiplets; the terms are then numbered 1, 2, 3, ... beginning 
from the term of lowest energy, or if the J value is also known then 
this may be added as a suffix I 2i . Or again the terms may have 
been worked out, and then each term is specified by a small letter 
placed before its term symbol; in this notation the letters a to e 
are reserved for the low terms, z, y, x, ... for the middle or odd 
terms, and/, g, h, ... for the high terms; in each group the terms 
are lettered from low to high energy. 

3. Individual spectra 

The spectra of the long periods are most naturally classified by 
the number of electrons outside the last inert gas shell, and in this 
order they will be reviewed. 

The energies of all the low terms and a varying number of odd 
terms are'tabulated; the energy given for any multiplet is that of 
the component with greatest J, for this will produce the strongest 
lines; the energies are measured up from the ground term, and the 
ground term itself is in clarendon type. To avoid any misunder- 
standing the chief quantum number is added for spectra of the 
iron frame; to apply to the palladium and platinum frames it 
should be increased by one and two respectively. 



50 LONG PERIODS [CHAP. 

One electron. Ki, Rbi, Csi; Can, Srn, Ban, Ran; Scm, Yin, 
Lain, LUIII; Tiiv, Zriv, Ceiv. 

In the arc spectra of the alkalis and the spark spectra of the 
alkaline earths the ground term is always 2 S, the single electron 
occupying a 4s, 5s or 6s orbit. With further increase in the nuclear 
charge, however, the electron falls into a d orbit, for Sc in, Y in, 
Zriv, and Ceiv are all known to have a 2 D ground term. 

The introduction of a group of f electrons produces, however, a 
surprising change; LUIII, which differs from Lam only in having 
this group, has a 2 S ground term, so that the 6s orbit must have 
grown more stable than the 5d. 

Low terms 





K 


Rb 


Cs 


Ca ii 


Srn 


Ban 


Ran 


4s 2 S i 
3d 2 D 2i 




21,539 




19,355 




14,597 



13,711 




10,837 




5,675 




26,209 





Sc m 


Yin 


La HI 


Lu in 


Ti iv 


Zriv 


Ceiv 


4s 2 S+ 
3d 2 D 2i 


25,537 
198 


7460 
725 


13,590 
1,604 




8648 


80,379 
348 


' 38,258 
1,250 


5152 
3305 



Fig. 15-5. One electron. Energies of the low terms. 

Two electrons. Cai, Sri, Bai; Sen, Yn, Lan, Lun; Tim, 
Zrin. 

The ground terms of the arc spectra of the alkaline earths and 
the second spark spectra of column IV are respectively 1 S and 
3 F 2 , the first arising from the s 2 configuration and the second from 
the d 2 ; and this is natural enough, since the d orbit normally sinks 
relative to the s as the nuclear charge increases. Between these 
two extremes the singly ionized earth metals should provide a 
natural transition, and in some measure they do, for the ground 
term of Sc n is d . s 3 D and of La n d 2 3 F ; while if the f shell screens 
the outer electrons from the nucleus the s 2 1 S ground term of Lu n 
does not go unexplained. But that the ground term of Y n should 
be s 21 S is a striking anomaly, for the above scheme would 
predict it as arising either from d.s or d 2 ; moreover, the ground 
term of nearly every spectrum is derived by the addition of an 



XV] INDIVIDUAL SPECTRA 51 

electron to the ground term of the next higher spark spectrum, 
but Y ii forms an exception to this rule also, for the single electron 
of Yin occupies a d orbit. 

The other low terms which theory dictates are shown in 
Fig. 15-7; and just these terms are actually found in the spark 

Low terms 





Ca 


Sr 


Ba 


Sen 


Yn 


4s 2 % 











11,736 





3d. 4a 3 D 8 


20,371 


18,320 


9,596 


178 


1,45C 


*D 2 


21,849 


20,149 


11,395 


2,541 


3,296 


3d 2 8 F 4 











4,988 


8,743 


3 P2 


48,564 


32,625 


23,919 


12,154 


14,09H 


*G 4 











14,261 


15,683 


% 





= 


= 


10,945 


14,833 



La ii 


Lu ii 


Ti in 


Zrm 


7,395 











3,250 


14,199 


38,425 


19,533 


1,395 


17,332 


41,704 


16,122 


1,971 


32,504 


422 


1,487 


6,227 





10,721 


8,840 


7,473 





14,398 


2,534 


10,095 





8,473 


3,392 








14,053 


3,835 



Fig. 15-6. Two electrons. Energies of the low terms. 



Low terms 



Configuration 


Terms 


Triplets 


Singlets 


4s'- 
3d. 4s 
3d 2 


D 
PF 


S 
D 
SDG 



Middle terms 



Ion 


Atom 


'i 


Term 


1 2 


Terms 


1,1, 


3d 

4s 


2 D 

2 S 


4p 
4p 


3 (PDF) HroF) 

3p lp 


dp 

sp 



High terms 



Ion 


Atom 


/i 


Term 


k 


Terms 


1,1, 


3d 


2 D 


ns 
nd 


3 D iD 

MSPDFG) 


d.s 
d.d 


4s 


2 S 


na 
nd 


3 S ] S 
3 D *D 


s.s 
s.d 



Fig. 15-7. Terms predicted from two electrons. 



4-2 



52 LONG PERIODS [CHAP. 

spectra; d 21 S has been a little difficult to locate, but it has been 
found all right in Tim and Zrm. These low terms are in satis- 
factory agreement with Hund's energy rules; in the d . s configura- 
tion of Sen, for example, the 3 D term lies below X D, while in the 
d 2 configuration 3 F lies below 3 P; among the singlets, however, 
b X D is lower than a 1 G. Deviations such as this are common in all 
spectra. 

The middle and high terms have also been collected in Fig. 15-7; 
and the general relations of a typical spectrum are shown in 



60,000 
cm: 1 



40,000 - 



20,000 - 




Fig. 15-8. Simplified level diagram of Sc 11. 

Fig. 15-8, where the four groups of even terms, arising from the 
configurations 3d 2 , 3d . 4s, 3d . 4d and 3d . 5s, all combine with the 
central group of odd terms, but not at all with each other. This 
means, of course, that all terms of the 3d 2 configuration are 
metastable, for no direct return to the ground state is possible. 

In the high 3d . 4d configuration of Sc n the agreement with 
Hund's energy rules is much less satisfactory than among the low 
terms; among the triplets 3 F and 3 P lie close together, but some 
4000 cm." 1 above the 3 G, 3 D and 3 S levels; while among the 



XV] 



INDIVIDUAL SPECTBA 



53 



singlets, on the other hand, 1 F and X P lie some 4000 cm.- 1 below 
the 1 G, 1 T> and X S levels, each group being fairly compact. This 
curious alternating arrangement of energy levels finds a parallel 
in pentads of similar origin in other spectra, but it is quite con- 
trary to Hund's energy rules and has only recently received any 
theoretical explanation. 

All the triplet terms of Sc n are erect, and most of them obey 
the interval rule well (Fig. 15-9). 



Configuration 


Interval 


Interval quotient 


3d. 4s 


A 3 D t 2 67-7 
A 3 13 2) ' 3 109-9 


33-8 
36-6 


3d 2 


A 3 F 2 3 80-7 
A 3 F 3 [ 4 104-2 


26-9 
26-0 


3d 2 


A 3 P 0>1 27-4 
A 3 P ' 52-9 


27-4 
26-4 



Fig. 15-9. Interval rule in the low terms of Sc II. 

Three electrons. Sci, Yi, Lai, Lui; Tin, Zm, Ceil, Hfn. 

The ground terms of the arc spectra of scandium, yttrium and 
lutecium are d . s 2 2 D, while the usual subsidence of the d relative 
to the s orbit produces d 2 . s 3 F in the spark spectra of titanium and 

Low terms 





Sc 


Y 


La 


Lu 


Tin 


Zm 


Gen 


Hfn 


3d. 4s 2 2 D li 


168 


530 


1053 


1994 


25,193 


18,397 


420 





3d 2 . 4s *F,, 


11,677 


11,532 


4122 





393 


1,323 


1923 


V8362 


4 IV 





15,477 








10,025 


8,058 


1870 





^l 


20,237 


18,499 








15,258 


14,190 








a *W 


15,042 


15,864 





. 


4,898 


6,468 








"D/* 


17,013 


16,159 


- 





8,744 


4,505 





?3051 


'Pi* 





19,406 








16,625 


6,112 








'V 














21,338 


25,202 








3d 3 F 


33,90(5 


29,843 





- 


1,216 


3,758 








4p 2i 


36,573 


32,366 








9,518 


9,969 








"H 8 * 














12,775 


12,360 








2 GW 











. 


9,118 


8,153 








'** 














20,892 


19,433 








D.; 


36,330 











12,758 


14,733 








"D.* 





- 











14,163 








PI* 











. 


9,976 


20,080 









Fig. 15-10. Three electrons. Energies of the low terms. 



54 LONG PERIODS 

zirconium. It has been suggested that the ground term of Hf n is 
d 2 .s 2 D, but this irregularity still awaits confirmation. 

The low terms predicted by theory are collected in Fig. 15-10; 
every one of these terms has been found in Zr n, while all the odd 
terms have been found in Yi; thus once again the great power of 
Hund's theory is demonstrated. The greatly increased com- 
plexity of Sc i and Y i compared with Sc n and Y n is perhaps so 
obvious that it hardly deserves mention. 

Low terms 



Configuration 


Terms 


Quartets 


Doublets 


3d. 4s 2 
3d 2 . 4s 
3d 3 


PF 
PF 


D 
SPDGF 
PDFGH 

2 



Middle terms 



Ion 


Atom 


M 


Term 


'3 


Terms 


Jl/,1, 


4s 2 


*S 


4p 


2 P 


8 2 p 


3d. 4s 


3 D 

*D 


4p 
4p 


4 (PDF) 2 (PDF) 
2 (PDF) 


d.sp 


3d 2 


3 F 
3 P 
1 G 

*D 

*S 


4p 
4p 
4p* 
4p 
4p 


4 (DFG) 2 (DFG) 
4 (SPD) 2 (SPD) 
2 (FGH) 
2 (PDF) 
2 p 


d 2 .p 



Fig. 15-11. Terms predicted from three electrons. 

The lines due to transitions from high to middle terms are, in 
the spectrum of Y i, so much weaker when the terms are doublet 
than when quartet, that very few high doublet terms have been 
identified. 

Four electrons. Tii, Zn, Hfi; Vn, Cbn. 

The arc spectra of titanium, zirconium and hafnium all have as 
ground term 3 F 2 of the d 2 .s 2 configuration; but the d orbit 
evidently falls abruptly relative to the s at this point, for the 
spark spectra seem to have d 45 D as ground term. 



XV] INDIVIDUAL, SPECTRA 55 

The spectra of titanium and zirconium have been very 
thoroughly analysed at the Bureau of Standards by Russell and 
Kiess, and almost all the low terms from the d 2 . s 2 and d 3 . s con- 
figurations have been identified. In their analysis of hafnium 

Low terms 





Ti 


Zr 


Hf 


Vii 


Cbn 


3d 2 . 4s 2 3 F 4 


387 


1,241 


4568 








3 P 2 


8,602 


4,186 


8984 








*G 4 


12,118 


8,057 











^2 


7,255 


5,101 


5639 





. . 


1 S 


15,167 


13,142 











3d 8 . 4s 5 F 5 


6,843 


5,889 





3,163 


4147 


3 F 4 


11,777 


12,342 





9,097 





6 p 


14,106 


11,258 





13,741 





3T> 


18,912 


15,932 











8 H 6 


18,193 


15,120 





20,363 





1 J^5 


20,796 


18,739 











3 G 5 


15,220 


12,773 





14,655 





ir** 


18,288 


17,753 











3 F 4 





15,700 











1 F 3 


29,818 














3 D 3 


17,540 


14,697 











3D, 


20,210 


17,228 











3^ 


18,145 


17,143 


z 


z 


~ 


iy> 


20,063 














3d 4 5 D 4 





22,398 





339 


1225 


3 Hfl 



















36,201 








16,532 





3 F 4 











13,608 





3 *\ 

















3T> 
3T> 











11,908 






Fig. 15-12. Four electrons. Energies of the low terms. 

Meggers and Scribner had to rely on wave-lengths and furnace 
intensities only, but this has not prevented them from identifying 
seven even and 63 odd terms. From a study of the observed 
combinations, J values have been assigned and the suggestion put 
forward that the lowest three terms are d 2 .s 23 F. The J values 
would allow the next terms to be 1 D 2 and 3 P, and this allotment 
would make the low terms very similar to those of Tii; but 
further discussion must wait on the promised measurements of 
the Zeeman effect. 



56 



LONG PERIODS 



[CHAP. 

Among the odd terms those due to the configuration d 2 . sp lie 
lowest in the arc spectra, but terms from the two other con- 
figurations have been recognised. 

Numerous combinations have been found between both singlet 
and triplet terms, and between triplet and quintet terms, but very 

Low terms 



Configuration 


Terms 


Quintet 


Triplet 


Singlet 


3d 2 . 4s 2 
3d 3 . 4s 

3d 4 


PF 
D 


PF 
PDFGH 

222 

PDFGH 

2 2 


SDG 
PDFGH 

2 

SDFGJ 

22 2 



Middle terms 



Ton 


Atom 


I,. ..I, 


Term 


h 


'Perms 


1....1, 


3d 2 . 4s 


4 F 


4p 


5 ' 3 (DFG) 


d 2 .sp 




4 P 




5 . 3 (SPD) 






2 G 




V(FGH) 






SF 




^(DFG) 






2 D 




s.^PDF) 






2 P 




3 ' 1 (SPD) 






2 S 




3 f lp 




3d 3 


*F 


4p 


5 - 3 (DFG) 


d 3 .p 




4 P 




5 > 3 (SPD) 






2 H 




3 \( (~^ T-TT\ 

' ^VJTXJ-L^ 






2 G 




3 . 1 (FGH) 






2 D 




3 - 1 (PDF) 






2 D 




3 1 (PDF) 






P 




3 . 1 (S1 ) D) 




3d. 4s 2 


2 D 


4p 


3 ,'(PDF) 


d.s 2 p 



Fig. 15-13. Terms predicted from four electrons. 

few between singlets and quintets, and even these few are all 
susceptible of the same explanation. When two terms of the same 
configuration and the same J have nearly the same energy, they 
share both their intensities and their g values. Thus d 3 .p 1 D 2 
combines with the low even 5 D 3 term because the former lies very 
near to the 5 P 2 term of the same configuration; the empirical g 
values of the 4d 3 .5p 1 D 2 and 5 P 2 terms of Zn are both 1-42, 



XV] INDIVIDUAL SPECTRA 57 

whereas the Land6 values are 1-000 and 1-833 respectively; 
their respective energies are 34,850 and 34,761 cm." 1 

Five, electrons. Vi, Cbi; Crn, Moil. 

The ground term of these spectra starts as 4 F of the d 3 . s 2 
configuration in the iron row, changes to 6 D from d 4 .s in the 
palladium row, and settles down as d 5 6 S in both the spark spectra; 
these changes clearly conform to the general type. 

Low terms 





Vi 


Cbi 


Crn 


Mo ii 


3d 3 . 4s 2 *F 4i 


553 











4 P 2 


9,825 











3d 4 . 4s 6 D 4i 


2,425 


1050 


12,498 


known 


4 H 6 i 


15,063 





30,393 


- 


4 G 5 i 


17,242 





33,696 





*F 4 i 


15,770 





31,221 





4 D 3 i 


8,716 





20,025 


known 


*P' 


15,572 











21> li 








17,593 





3d 6 S H 











ground? 


4 G 5 i. 








20,514 





*F 4 i 








32,856 





4 l>3i 








25,035 





2 < 


__ 


__ 


21,824 






Fig. 15-14. Five electrons. Energies of the low terms. 

Of the other low terms little is known outside the Cr n spectrum, 
in which many quartet but only two doublet terms have been 
found; these doublets are conspicuous in breaking Hund's energy 
rules, for they lie among the lower of the quartet terms. 

The odd terms are best developed by the addition of a p electron 
to the lowest terms of the parent spectrum; in this way a number 
of triads are formed, and these agree very satisfactorily with the 
terms found empirically. Thus in V i there occur a triad of sextet 
terms at 18,000 cm." 1 and a triad of quartet terms at about 
22,000 cm.- 1 ; the J values show that in fact these are the two 
triads 6 (DPG) and 4 (DFG) which should arise by the addition of 
a p electron to the low d 3 . s 5 F term of V n. 

Of all these five electron spectra Cm has been the most 
thoroughly analysed, and in it nearly all the terms both obey the 



58 LONG PERIODS [CHAP. 

interval rule reasonably well and have normal g values. The 6 D 
and 4 P terms of the d 4 .p configuration are irregular judged by 
either criterion; but a term which deviates from one rule, often 
deviates from the second as well. 

Low terms 



Configuration 


Terms 


Sextet 


Quartet 


Doublet 


3d 3 . 4s 2 
3d 4 . 4s 
3d 5 


D 

S 


PF 
PDFGH 

222 

PDFG 


PDFGH 

2 

SDFGJ 

22 2 

SPDFGHJ 

322 



Middle terms 



Ion 


Atom 


I,. ..I, 


Term 


h 


Terms 


/1-./5 


d 4 
d 3 .s 


6 D 

SF 


P 
P 


M(PDF) 
M(DFG) 


d 4 .p 
d 3 .sp 



Fig. 15' 15. Terms predicted from five electrons. 

Six electrons. Cri, Moi, Wi; Mnn. 

The analysis of these spectra has hardly extended beyond the 
septet and quintet systems, only a few triplets having been found, 
and no singlets though these undoubtedly occur. The arc spectra 
of chromium and molybdenum and the spark spectrum of man- 
ganese all have d 5 . s 7 S as ground term ; in contrast the ground term 
of tungsten is probably 5 D, but the analysis is so little advanced 

Low terms 





Cri 


Moi 


Wi 


Mn ii 


3d*. 4s 2 5 D 4 


8,307 


12,346 


6219 





3d 6 . 4s 7 S 3 




7,593 
20,519 




10,768 
16,828 


2951 




9,473 


1 


24,282 
21,841 


18,229 








3d 6 5 D 4 











14,324 



Fig. 15*16. Six electrons. Energies of the low terms. 



XV] INDIVIDUAL SPECTRA 59 

that this cannot be surely assigned to the d 4 . s 2 as against the d 6 
configuration. 



Low terms 



Con- 






Terms 




figuration 


Septet 


Quintet 


Triplet 


Singlet 


3d 4 . 4s 2 
3d 5 . 4s 
3d 6 


D 

S 


D 
SPDFG 
D 


PDFGH 

2 2 

SPDFGHJ 

2433 

PDFGH 

2 2 


SDFGJ 

22 2 

SPDFGHJ 

322 

SDFGJ 

22 2 



Middle terms 



Ion 


Atom 


/!...*. 


Term 


h 


Terms 


l,...l. 


3d 3 . 4s 2 
3d 4 . 4s 
3d 5 


*F 

D 

6 S 


4p 
4p 
4p 


5 ' 3 (DFG) 
? . 5 (PDF) 

7p 5p 


d 3 .s 2 p 
d 4 .sp 
d 5 .p 



Fig. 15*17. Terms predicted from six electrons. 

The list of low terms is complete, but the middle terms are developed from the 
low terms of the spark spectrum ; a complete list would be so long as to give no 
guidance at all. 

Seven electrons. Mm, Rei; Fen, Run. 

The ground term of the arc spectra of manganese and rhenium 
is d 5 . s 2 6 S, but it changes first to d 6 . s 6 D and then to d 7 4 F in the 
spark spectra of iron and ruthenium respectively; thus once 
again the d orbit is seen to sink relative to the s orbit, when we pass 
from one period to the next or from an arc to a spark spectrum. 

Low terms 





Mn 


Re 


Fen 


Ru ii 


3d 5 . 4s 2 6 S 








23,318 





3d 6 . 4s 6 D 4i 


17,052 


11,754 





9,151 


4 G 6 i 








25,429 





4 F 4 i 








22,637 





4 D 3 i 


23,297 





7,955 


19,379 


*^2i 


._ 





20,830 





3d 7 *F 4i 








1,873 





*P 2 , 








13,474 


8,257 


2 F 3i 










22,289 



Fig. 15*18. Seven electrons. Energies of the low terms. 



60 



LONG PERIODS 



[CHAP. 

The ground term of Mm has been recently confirmed by showing 
that all the resonance lines arise from jumps ending in the 6 S 
state.* 



lor 


I 




Atom 




I,. ..I. 


Term 


I, 


Terms 


I,...l 7 


d 6 .s 


7 S 


8 
d 


6 S 
D 


d 5 .s 2 
d 6 .s 




5 S 


8 
d 


6 S (as above) 
6 D (as above) 4 D 


d 6 .s 2 
d 6 .s 


d*.s 2 


5 D 


d 


6 S (as above) *(PDFG) 


d 5 .s 2 



Fig. 15-19. Low terms of Mn i developed from the low terms of Mn n. 



Configuration 


Terms 


Sextets 


Quartets 


Doublets 


3d 5 . 4s 2 
3d 6 . 4s 
3d 7 


S 
D 


PDFG 
PDFGH 

222 

PF 


SPDFGHJ 

322 

SDFGJ 

22 2 

PDFGH 

2 



Middle terms 



Ion 


Atom 


I,. ..I. 


Term 


1 7 


Terms 


I^..l 7 


d 5 .s 


7 S 
5 S 


* P 
P 


8p 6p 
6p 4p 


d 5 .s.p 


d 4 .s 2 


5 D 


P 


6 ' 4 (PDF) 


d*.s 2 .p 


d 


5 D 


P 


6,4(PDF) 


d.p 



Fig. 15-20. Terms predicted from seven electrons. 

With the increasing number of electrons, even the low terms 
become so complex that they are not easily identified; to meet this 
difficulty the low terms may be developed from the lowest terms 
of the spark spectrum, just as the odd terms have been developed. 
Thus in Fig. 15-19 there are only a few terms where in Fig. 15-20 
there is a huge mass. 

* Fridrichson, ZP 9 1930, 64 43. 



xv] 



INDIVIDUAL SPECTRA 



61 



Since the ground term of the spark spectra of Mn and Re is 7 S, 
series are to be expected in the arc spectra; and in fact Catalan* 
did first analyse Mm into a number of series. The lowest terms of 
the odd series are shown in Fig. 15-20. 

The terms of these spectra are nearly all inverted; while those 
of Run show very regular g values. 

Eight electrons. Fei, Rui; Con. 

The ground term of the arc spectrum of iron is d 6 . s 2 5 D, but the 
ground term changes in the normal way to d 7 . s 5 F and then to 
d 8 3 F in the arc spectrum of ruthenium and the spark spectrum of 
cobalt respectively. 

Low terms 





Fei 


Rui 


Con 


3d 8 . 4s 2 6 D 4 





? 7,483 





3d 7 . 4s 5 F 5 


6,928 





3,350 


5 P 3 


17,550 


? 8,771 


17,771 


3 F 4 


11,976 


6,545 


9,813 


3 ^ 2 


22,838 








3d 8 3 F 4 


. 


? 9,120 





T, 





?10,623 






Fig. 15-21. Eight electrons. Energies of the low terms. 



loi 


i 




Atom 




1....1, 


Term 


'a 


Terms 


l,...l, 


d 6 .s 


6 D 


s 
d 


5 D 
(PF) 


d e .s 2 
d 7 .s 




4 D 


s 

d 


5 D (as above) 3 (PDFG) 
6 (PF) (as above) 3 (PDFG) 


d 6 .s 2 
d 7 .s 


d 7 


*F 


s 
d 


5 F 3 F 

3 (PF) 


d 7 .s 
d 8 




4p 


s 


5p 3p 


d 7 .s 






d 


3 (PF) (as above) 


d 8 



Fig. 15-22. Low terms of Fe i developed from the low terms of Fe n. 

Hund's theory predicts for the d 6 . s 2 configuration one quintet 
and seven triplet levels besides a number of singlets. In the iron 
* Catalan, Phil. Trans. K.S., 1922, 223 127. 



62 LONG PERIODS [CHAP. 

arc the 5 D term is inverted and follows the interval rule fairly 
well, as the following table shows (Pig. 15-24). 

Low terms 



Configuration 


Terms 


Quintet 


Triplet 


Singlet 


3d 6 . 4s 2 
3d 7 . 4s 
3d 8 


D 
PF 


PDFGH 

2 2 

PDFGH 

222 

PF 


SDFGJ 

22 2 

PDFGH 

2 

SDG 



Middle terms 



lor 


i 




Atom 




l L ...l, 


Term 


*8 


Terms 


/!.../8 


d.s 


6 D 


P 


7 - 5 (PDF) 


d fl .s.p 




4 D 


P 


.'(PDF) 


d.s.p 


d 7 


4 F 


P 


5 ' 3 (DFG) 


d 7 .p 




4 P 


P 


5 ' 3 (SPD) 






Fig. 15-23. Terms predicted from eight electrons. 



Term 


Interval AE/ch 


A 


6 A> 








89-9 


89-9 


D, 








184-1 


92-1 


2 


288-1 


96-0 


D. 


415-9 


104-0 



Fig. 15-24. Intervals of the d 6 . s- 5 D term of Fe I. 

Of the triplet levels, only four have been found; these are all 
inverted and obey the interval rule about as well as the 5 D term. 
Goudsmit's theory of the displacement sum predicts that the 3 D 
term will be erect, but the term is still unidentified. 

The other low configuration of the iron arc is d 7 .s, the four 
terms so far identified being clearly produced by an s electron 
adding itself to the d 7 4 F and 4 P terms, for the derivation is in- 



PLATE V 

1. Fluorescent spectrum of chromium in A1 2 O 3 at 186 C. At the right- 
hand or blue end of the spectrum a strong principal doublet appears, a 
thousand times over-exposed. Next to these are the subsidiary lines, 
weaker but sharp, while on the left are still weaker bands. The line near 
the centre is the 7032 A. of neon. (After Deutschbein, PZ, 1932, 33 875.) 

2. DF septet from the iron arc. This multiplet arises as 3d . 4s ( 8 D) 5s 7 D -> 
( 6 D) 4p 7 F. (Lent by Prof. H. Dingle.) 



flateV 




XV] 



INDIVIDUAL SPECTRA 



63 



dicated both by the energies and the intervals of the terms. In 
the spark 4 F lies 11,000 cm.- 1 below 4 P, and in the arc 5 F and 3 F 
lie about the same distance below the corresponding 5 P and 3 P 
terms. Again, 4 F obeys the interval rule well, while the derived 
5 F and 3 F terms do not deviate much (Fig. 15-25). But the ionic 
4 P term is quite irregular and so are the derived terms of the arc 
spectrum; even the irregularities are similar (Fig. 15-26). 



Term 


M/ch 


A 


Term 


M/ch 


A 


Term 


AA'M 


A 


6]^ 




















168-9 


84-5 








4 Fji 






*F ? 






3 F<> 








279-6 


111-8 




257-7 


85-9 




407-6 


135-9 


4 F 2 4 






5 F 3 






3 ^a 








407-7 


116-5 




351-3 


87-8 




584-7 


146-2 


4 F 3 i 






6 F 4 






3 F 4 








557-6 


123-9 


F 5 


488-5 


97-7 








4FH 







Fig. 15-25. Intervals of the d 7 ( 4 F).s B 3 F terms of Fe i and the d 7 4 F term of 
Fen. 



Term 


kEjch 


A 


Term 


M/ch 


A 


Term 


Mich 


A 


5 i\ 


200-4 


100-2 


Vo 


104-9 


104-9 


4T> 


231-7 


154-5 


5 I*2 






3 i>i 






4 l\i 






*l\ 


176-8 


58-9 




108-5 


54-2 


4p 


198-7 


79-5 



Fig. 15-26. Intervals of the d 7 ( 4 P).s 5 ' 3 P terms of Fe i and the d 7 *P term of 
Fen. 

A very large number of odd terms have been identified and 
named in the spectra of Fe i and Co n, for the terms satisfy the 
simple laws; their intervals are regular, and almost without 
exception they are inverted. But the terms of Ru i are much less 
regular, so that a thorough Zeeman analysis was necessary before 
the terms could be named, and even now only a J value has been 
assigned to very many; the interval law is only roughly satisfied. 

Nine electrons. Coi, Rhi; Nin, Pdn. 

The ground term starts as d 7 .s 24 F in the arc spectrum of 
cobalt, changes to d 8 . s 4 F in the arc spectrum of rhodium and 
finishes as d &2 D in the spark spectra of nickel and palladium; 



64 



LONG PERIODS 



[CHAP. 



Low terms 





Co i 


JRhi 


Nin 


Pdn 


3d 7 . 4s 2 A F 4i 




15,184 


12,733 








2 ^u 


20,501 











3d 8 .( 8 F)4s 4 F 4i 


3,483 
7,442 




5,691 


8,393 
13,549 


25,081 
32,278 


( 3 P)4s 4 P H 


13,795 
18,390 


9,221 
11,968 


25,035 
29,069 


36,281 
43,648 


('G) 4s *G 4i 
( 1 D)4s 2 D 2i 

( 1 S)4s a St 


16,468 
16,778 


16,018 
13,521 


32,498 
23,107 
24,825 


44,506 
41,198 


3d 9 2 D 2i 


21,920 


3,310 









Middle terms 





Co i 


Rhi 


Nin 


Pd ii 


3d 7 .4s( 5 F).4p 6 G H 


25,138 











6 *W 


23,612 











6 *V> 


24,628 











4 G 5i 


28,845 











4 *W 


28,346 











4 D 3i 


29,294 











( 3 F)4p HJ U 


41,528 











FH 


41,225 





91,797 





4 D3i 


39,649 











2 < 


31,700 


___ 








*W 


31,871 





93,525 





2 D 2i 


33,463 











3d 8 .(F)4p 4 G 5i 


32,431 


29,105 


53,495 


68,611 


4 *4i 


32,842 


29,431 


54,556 


69,878 


4 < 


32,027 


27,076 


51,557 


65,247 


2 G 4 ; 


33,440 


31,614 


55,299 


72,285 


'^3* 


35,451 


32,004 


57,079 


73,327 


2 D 2i 


36,092 


32,046 


57,419 


72,733 


(P)4p 4 D 3i 





36,787 


70,776 


83,056 


4 ^ 2 | 





35,334 


66,569 


76,767 


* S H 








74,299 


86,280 


l>i 








71,770 


83,802 


'Pi* 








72,984 


85,151 


s,- 








74,282 


85,071 


( 1 G)4p H 5i 








75,719 


85,593 


2 G H 








79,923 


89,982 


**H 








?75,916 


86,043 


(^D)4p P si 








67,693 


79,708 


2 D 2 ^ 








68,634 


82,057 


2 ^ii 








68,864 


80,956 


(!S)4p 2 P U 








60,502 






Fig. 15'27. Nine electrons. Energies of the low and middle terms. 



XV] 



INDIVIDUAL SPECTRA 



65 



moreover, whereas the ground 2 D term is only 8000 cm." 1 below 
the next lowest term in Nin it is 25,000 cm." 1 in Pdn. These 
changes are in the usual order. 

The energies of the low and middle terms are always related, 
but no group of electrons shows these relations more clearly than 
the group of nine here considered. In Coi the ground term is of 
the 3d 7 . 4s 2 configuration and the lowest odd terms are derived 

Low terms 



Configuration 


Terms 


Quartet 


Doublet 


3d 7 . 4s 2 

3d 8 . 4s 
3d 9 


PF 
PF 


PDFGH 

2 

SPDFG 
D 



Middle terms 



lor 


i 




Atom 




/>.../ 


Term 


*. 


Terms 


/!.../, 


d 8 


3 F 


P 


4 - 2 (DFG) 


d.p 




3 P 


P 


4 > 2 (SPD) 




d'.s 


F 


P 


6 4 (DFG) 


d 8 .sp 




5 P 


P 


6 ' 4 (SPD) 





Fig. 15-28. Terms predicted from nine electrons. 

from 3d 7 . 4s . 4p; on the other hand, when the ground term is from 
d 8 . s as it is in Rh i or from d 9 as in Ni 11 and Pd 11, practically all 
the known odd terms are from d 8 . p. Again, in Ni n the energies of 
the even and odd terms run strikingly parallel; of the 3d 8 . 4s con- 
figuration 2 D and 2 S lie exceptionally low, and this is matched 
among the odd terms by the anomalous positions of 2 (PDF) and 
2 P from 3d 8 . p. Presumably these two irregularities have a 
common cause in the d 81 D and d 81 S terms of Nini, but un- 
fortunately the latter spectrum has not yet been analysed. 

In Ni n all but one of the low even terms are inverted, but of 
the odd d 8 . p configuration eight terms are erect or only partially 
inverted. In Pdn the intervals are rather irregular. 



66 



LONG PERIODS 



[CHAP. 

Ten electrons. Nil, Pdi, Pti; Gun, Agn, AUII; Cdin, Hgin; 
In iv, Tliv. 

The ground term of all the spark and higher spark spectra is 
d 101 S; but the arc spectra exhibit two irregularities. Thus the 
ground term of nickel is 3d 8 . 4s 2 3 F, although the ground term of 
Ni ii is 3d 9 2 D and the ground term of an arc spectrum is usually 
obtained by adding an electron to the ground term of the spark; 
the only other exception to this rule seems to be Yn. Again, if 
the ground terms of nickel and platinum are respectively d 8 . s 2 4 F 
and d 9 . s 4 F, the ground term of palladium might be expected to 
be one or the other of these, whereas in fact it is d 10 X S. 

Low terms 





Nil 


Pdi 


Pti 


Gun 


Agn 


AUII 


3d 8 . 4s 2 3 F 4 




15,610 
22,102 
13,621 


25,101 
37,952 


824 
6,567 
21,967 
26,639 








__ 


3d 9 . 4s 3 D 3 


204 
3,410 


6,564 
11,722 




13,496 


21,925 
26,261 


39,164 
46,045 


15,036 
29,618 


3d 10 % 


14,729 





6,140 












Fig. 15-29. Ten electrons. Energies of the low terms. 



Low terms 



Configuration 


Terms 


Triplet 


Singlet 


d 8 .s a 
d 9 .s 
d 10 


PF 
D 


SDG 
D 

S 



Middle terms 



Ion 


Atom 


1....1, 


Term 


*10 


Terms 


Ji-iib 


d 9 


2 D 


P 


^(PDF) 


d 9 .p 


d 8 .s 


4 F 

2 F 


P 
P 


5 3 (DFG) 
^(DFG) 


d 8 .sp 



Fig. 15-30. Terms predicted from ten electrons. 



XV] INDIVIDUAL SPECTRA 67 

The changes in the arc spectra in passing from row to row are 
also instructive; in Nil the term separations are wide and the 
multiplets overlap; but, though complex, the spectrum is ad- 
mirably regular; all the even terms and nearly all the odd terms 
are inverted, and the intervals conform to Lande's rule; so simple 
was the analysis indeed that the Zeeman effect has not been 
studied. In the Pdi spectrum the wide interval, 3512 cm." 1 , of 
the 2 D ground term of Pdn begins to exert an effect; as some 
triplet series tend to the lower and some to the higher limit, the 
interval ratios change rapidly with the serial number. And the 
terms of Pti are even less regular than those of Pdi; in analysis 
the interval rule is useless, and the intensity rules can be treated 
only as approximations; the measurements of g, too, depart from 
Lande's values, but they suffice with the J selection rule to 
determine the J value of all the empirical terms. The deter- 
mination of the orbital and spin vectors is, however, far more 
difficult, for the failure of the simple rules is a sure sign that the 
coupling is no longer Russell-Saunders. However, all the low 
terms predicted from d 8 .s 2 , d 9 .s and d 10 seem to have been 
identified, save only d 8 . s 2 1 S, which has not yet been found in any 
spectrum. Names have also been assigned to some of the odd 
terms arising from the d 8 .sp and d 9 .p configurations. 

In Gun and Agn the terms are generally inverted, but the 
interval rule is very badly satisfied; in Ag n irregular g values are 
also indicated. 

In the analysis of Pd I there is a surplus level, known as k , 
which is of interest chiefly as being the only level which fails to 
fit into the Hund scheme. The level is determined by five exact 
combinations, but the lines due to k are all listed as diffuse and 
differ in this from all other lines of the palladium spectrum; the 
level can hardly be a hyperfine component, for no other levels 
show a similar structure, and the interval separating it from the 
nearest normal level is over 3 cm.- 1 

Eleven electrons. GUI, Agi, Aui; Znn, Cdn, Hgii. 
As the d level can hold only ten electrons, the elements copper, 
silver and gold, which have eleven electrons outside the last inert 

5-2 



LONG PERIODS 



[CHAP. 

gas shell, should exhibit the simple alkali spectra provided only 
that d 10 is firmly bound. In fact all three elements do exhibit 
doublet series and they all have a 2 S ground term. But besides 



Low terms 





Cu i 


Agi 


An i 


Znii 


Cdn 


Hgn 


3d'.4s a 2 D 2i 
3d 10 . 4s a S i 


11,203 






9161 



62,721 



69,259 



35,514 




Fig. 15*31. Eleven electrons. Energies of the low terms. 

this simple system, which was discovered in very early days, the 
last decade has revealed in copper and gold other quartet and 
doublet terms; in silver these terms have not been found, though 
all the lines of Agi have been classified.* 



Ci 


1+ 




C 


yii 


/i-./io 


Term 


*u 


Terms 




3d 10 


*S 


8 


a 








P 


2 P 


Alkali-like systems 






d 


2 D 




3d 9 . 4s 


*D 1 D 


4s 


2 JD 


Deep even term 




3 I) 


4p 

. 4 


4 (PDF) 
2 (PDF) 


Middle group of odd 




A D 


4p 


2 (PDF) 






3 D 


ns 


4 D 2 D 








nd 


4 (SPDFG) 
2 (SPDFG) 


High even terms 




1 D 


ns 


2 D 








nd 


2 (SPDFG) 





Fig. 15-32. Terms predicted in copper. 

The lowest term of Cun is d 101 S; and from it arise by the 

addition of s, p and d electrons the alkali -like system; from the 3 D 

and higher 1 D terms of Cu n arise all the other known terms ; those 

predicted are shown in Fig. 15-32, while those actually found are 

* Blair, PR, 1930, 36 1531. 



XV] 



INDIVIDUAL SPECTRA 



69 



arranged to their proper ionic limits in Fig. 15-33. In both the 
( 3 D) us 2 D and the ( 1 D) ns 2 D series two terms are known, and the 





CD)I 2 2 o 






1A 9 Ac.'r\}t>\tP\ nf full > \ / P , , V 


26^00 




PD)ns 4 /D 4 2 ^ot^n^GFD 2 P^S 

^94. c 3p 1 ^, 1^r,,TT( iD / n P__ rT I r Pl l ... P ? 2 9! 2 . P 


above 

'S 
21,900 




( 3 D)nd 4 GFD 4 P 4 S 2 GF 2 D 2 P 2 S 


above 






'S 




(.. .. 
y 






0- .. .---..^ 




VOLTS 


/ 

3d 10 'S. level of Cull / ,--' *^" 




7-68 


2 S 2 P 2 D , p. 


62,308 




/ / 


cm: 1 


7 


. ' / /'""" 

6p A / / 7 


60,000 


6 


-n^--^/ jV / 


50,000 


5 


!! "^ Xv- y " 


40,000 


4 


- 




3-75 


. 4p 


30,000 


2 


- 


20,000 


1-38 


^tf> 




1 


. 


10,000 





^^'"^ 






Fig. 15-33. Level diagram of copper. The even terms are shown by circles, the 
odd terms by triangles. 

Rydberg formula then determines the height of the 3 D series 
limits above the X S limit as 22,200 cm." 1 

In gold the deep 2 D term has been found and also some higher 
terms, but as the coupling is roughly of the ( jj) type only the five 
lowest terms can be named. 



70 LONG PERIODS [CHAP. XV 

The contrast between copper and gold on the one hand and 
silver on the other appears not only in their spectra but also in 
their chemical properties. Both copper and gold can be mono- 
valent, but copper is commonly divalent and gold may be 
trivalent, showing that the lower electron group is not as firmly 
established as in the alkali metals; silver on the other hand is 
always monovalent. 

4. The three rows compared 

The structure of a spectrum is primarily a function of the 
number of electrons; but it is also affected by the relative positions 
of the low terms, for they will determine which multiplets appear 
bright and which faint. Usually the ground term changes from 
frame to frame, and when this happens in a spark spectrum, even 
the prominent multiplicities of the arc spectrum change. In the 
Pel spectrum triplets, quintets and septets are known, but in the 
homologous Rui only triplets and quintets; Coi has doublets, 
quartets and sextets, but Rhi only doublets and quartets; Nil 
has singlets, triplets and quintets, but Pdi only singlets and 
triplets. And the reasons for these differences are not far to seek; 
the ground term of Fe iris d 6 . s 6 D, but of Ru n d 7 4 F; and if the 
ground terms of Ni n and Pd n are identical, as presumably are 
also the ground terms of Co 11 and Rh n, though Rh n has not yet 
been analysed, the d 8 . s 4 I* term lies so much lower in Ni n than 
in Pd ii that terms derived from it appear in one arc spectrum and 
not in the other. 

Since the energies of the three low configurations are of such 
importance, they are worth detailed consideration. Relative 
energies alone are known, and we therefore elect to consider the 
energies of the s 2 .d n ~ 2 and d n configurations relative to s.d n ~ l , 
since the last has been identified in more spectra than either of 
the other two. Many figures are still missing from the tables, but 
a fair sequence of s 2 . d n ~ 2 is available in the arc spectra of the 
iron and palladium rows, while rather less complete sequences for 
d n are found in the spark spectra of the same rows; accordingly 
(s 2 .d n - 2 -s.d n - 1 ) and (s . d* 1 " 1 - d n ) are plotted against n for the 
arc (Fig. 15-34) and spark (Fig. 15-35) spectra respectively. That 



-200 



Sr Y Zr Cb Mo Ma Ru Rh Pd 



spectra Sr Y Zr Cb M M * Ru 
of \ Ca Sc Ti V Cr Mn Fe 




Fig. 15-34. The energy difference of the s 2 . d n ~ 2 and s . d n-1 configurations in the 
arc spectra of the iron and palladium frames, n is the number of electrons out- 
side the inert gas shell. Due to a slip in drafting the energy scales of this and 
the two succeeding figures read down instead of up. 



- 100 - 



Energy difference 
sd n-i _ d n 

in 100cm' 1 




Fig. 15-35. The energy difference of the s.d n-1 and d n configurations in the 
spark spectra of the iron and palladium frames. 



72 LONG PERIODS [CHAP. 

the curves for the iron and palladium rows would resemble one 
another might have been anticipated, but the resemblance 
between the (s 2 .d n - 2 -s.d 71 - 1 ) and (s.d n ~ l -d n ) differences is 
altogether surprising; true the first curve is displaced a step to the 
right relative to the second, but closer examination reveals that 



-400 



- 300 - 



-200 - 



- 100 - 




+ 100 



+200 



-HOO 



Fig. J5-36. The energy difference of the d m ~ l and d m configurations, m is here 
n 1 in the arc and n in the spark spectra; n is still the number of electrons 
outside the inert gas shell. 

the (s 2 . & n ~ 2 - s . d 71 " 1 ) curve for the iron row arc actually resembles 
the (s . d n-1 d n ) curve of the iron row spark more closely than it 
resembles the (s 2 .d n ~ 2 s.d n ~ l ) curve of the palladium row arc. 
The fourfold magnification which occurs in all simple spectra does 
not affect these low terms at all, though it does still affect the 
ionisation potentials. 



XV] THE THREE ROWS COMPARED 73 

To make these facts stand out, write m = (/fc 1) in the 
(s 2 . d n ~ 2 - s . d"- 1 ) difference and m = n in (s . d n ~ l - d n ), and then 
plot both the differences (s 2 . d m ~ l - s . d m ) and (s.d m ~ 1 -d m ) 
against m (Fig. 15-36). That the four curves are so very similar can 
only mean that they all measure essentially the difference between 
the configurations d m ~ l and d m , the number of s electrons being of 
little moment. 

The regularity thus revealed enables us to fill up certain gaps 
in our knowledge; thus in the palladium row, there now seems 
little doubt that the ground terms of Mai, Man and Rhu the 



100 



Energies of s?d n ' 2 and s.d 11 " 1 
measured from their mean value. 




Ca Sc Ti V Cr Mn Fe Co Ni 
Arc spectra of Fe frame 



Fig. 15-37. Arc spectra of the iron frame. The energies of the s 2 .d n ~ 2 and 
s.d 11 " 1 configurations measured from their mean value. 

only spectra whose ground terms are not known must be 
d 5 .s 2 6 S, d 5 .s 7 S and d 8 3 F respectively; while if in the platinum 
row the ground term of W i is 5 D as has usually been supposed, 
then it must arise from the d 4 . s 2 configuration and probably the 
ground configuration of every arc spectrum from Lui to Os i is 
of the d n ~ 2 .s 2 type. The supposed 2 D ground term of iridium 
must be accepted with extreme reserve, for it would necessitate 
a d 9 configuration in the normal atom. 

The similarity of the four (d m ~ l d m ) curves further excites a 
desire to explain at least their more striking features; and in fact 
Hund has already done this, for if the energies of the s 2 . d n ~ 2 and 
s.d 71 " 1 configurations are measured from their mean value 
(Pig. 15-37), the sharp rise of the (d- 1 - d m ) curves at m = 5 and 



74 LONG PERIODS [CHAP. XV 

the precipitate drop at m = 6 are revealed as both due to the low 
energy of the d 5 configuration compared with either d 4 or d 6 . 

BIBLIOGRAPHY 

As for the short periods, the only systematic account seems to be by Hund in 
Linienspektren und periodisches System der Elemente, 1927. 

The values of energy levels are taken largely from Bacher and Goudsmit, 
Atomic Energy States, 1932. Other statements about particular elements are 
based on the select bibliography appearing in Appendix vi. 



CHAPTER XVI 
THE RARE EARTHS 

1 . In the periodic system* 

Bohr's theory explains the intrusion of fourteen rare earths into 
the sixth period as due to the filling of a shell of 4f electrons. Now 
Bohr's theory also explains the increase in metallic properties 
which occurs in descending a column of the table as due to the 
valency electrons occupying orbits of successively higher quan- 
tum numbers; while the decrease in metallic properties which 
occurs in passing across the table from left to right he ascribed to 
the firmer binding of the electrons as the nuclear charge increases. 
If these predictions are general, they should be valid in the rare 
earth elements. Yttrium should be more metallic than scandium, 
and lanthanum than yttrium, but in passing through the rare 
earths from lanthanum to lutecium the elements should grow 
steadily less metallic. 

The firmness with which the valency electron is bound is best 
measured by the ionisation potential; but for most of the rare 
earths the potential has only been estimated from the con- 
ductivities of the oxides in a flame, t and many have felt that the 
values are not so sure as those obtained by more direct methods. 
In the last two years this view has been confirmed by the analysis 
of the spectra of lanthanum and cerium; the ionisation potentials 
thus obtained are 5-59 and 6-54, which compare with the flame 
values of 5-49 and 6-91 voLfcs. 

For confirmation turn first to the molecular volume of homo- 
logous compounds, and then to two chemical reactions. The more 
firmly the valency electrons are bound, the smaller should be the 
volume of the compound, and in fact this prediction is fulfilled 
in the sesqui-oxides and sulphates. The sesqui-oxides of the rare 
earths exist in three crystalline forms, which Goldschmidt named 
A, B and C. A is stable at high temperatures, C at low, but the 

* Von Hevesy, Die seltenen Erden, 1926, 21 f. 

f Rolla and Piccardi, PM, 1929, 7 286, and Fig. 10-13 of Volume I. 



76 



THE RARE EARTHS 



[CHAP. 

transition temperature changes from element to element, rising 
from lanthanum to lutecium; so that at room temperature the 
form A is stable in lanthanum and the form C in lutecium. The 
hexagonal crystal A has been measured in four elements between 
lanthanum and neodymium, the pseudo-trigonal crystal B in four 
between neodymium and gadolinium, and the regular crystal C 
in scandium, yttrium and in all the elements which succeed 
samarium (Fig. 16' 1). These measurements show that in the sixth 





Sc 


Y 


La 


Ce 


Pr 


Nd 


11 


Sm 


Eu 


(A 
Sesquioxide \ B 
(C 


35-53 


45-13 


50-28 
c. 57 


47-89 


46-65 


46-55 
c. 51? 





46-9 

48-38 


46-5 

48-28 


Sulphate octahydrate 
Element 





240-8 


22-6 


21-0 


253-9 
21-8 


252-4 
20-7 





247-9 


247-3 




Gd 


Tb 


Dy 


Ho 


Er 


Tu 


Yb 


Lu 
42-25 


( A 
Sesquioxide \ B 

\c 


c. 43 

47-58 


46-38 


45-49 


44-89 


44-38 


44-11 


42-5 


Sulphate octahydrate 
Element 


246-4 





242-8 


241-1 


239-3 





235-1 
19-8 


234-7 



Fig. 16-1. Molecular volumes of some rare earth compounds. 

period the molecular volume of all three crystal forms decreases 
as the atomic number increases, while in travelling from scandium 
through yttrium to lanthanum there is a considerable expansion. 
These two variations are in the directions predicted by Bohr; 
together they bring yttrium out with very nearly the same 
atomic volume as holmium, an interesting coincidence, as a com- 
parison of chemical properties would assign yttrium the same 
place in the rare earth sequence; the four elements which succeed 
holmium are thus actually less metallic than yttrium, though still 
much more metallic than scandium. 

When the rare earth sulphates crystallise as the octahydrates, 
all except cerium are isomorphous. Their densities, which have 
been measured by Auer von Welsbach, show that once again the 
molecular volume decreases in passing from praseodymium to 
lutecium, and once again yttrium appears next to holmium. 



XVI] IN THE PERIODIC SYSTEM 77 

There are also chemical methods by which the decreasing 
basicity may be demonstrated. If one measures the iodine 
liberated in the reaction 

E 2 (SO 4 ) 3 + 5KI + KI0 3 + 3H 2 = 2E(OH) 3 + 3K 2 S0 4 + 3I 2 , 
increase in the iodine is a sign of decreasing basicity. The order 
in which this reaction places the elements is identical with that 
obtained from the molecular volumes, while the difference between 
samarium and europium is abnormally small here as there. 

Another method is to warm a solution of the sulphate with an 
exactly equivalent weight of sodium carbonate, and to measure 
the rate at which carbonic acid is liberated. The order obtained is 
again the same as that of the molecular volumes: Pr, Nd, Sm, Eu, 
Gd, Tb, Dy, Y, Tu, Yb. 

2. Valency 

If the periodic system was based solely on chemical grounds, 
there would be no choice but to crowd all the fifteen elements 
between lanthanum and lutecium into column III; elsewhere in 
the periodic system the valency changes by one when the atomic 
number changes by one, but all fifteen rare earths are trivalent 



S 4 ~ 


. 


Sm Eu Tu Yb 


* La Ce Pr Nd 4 11 1 

cd 

> 2- 




Gd Tb Dy Ho Er 


w 
Lu 



Fig. 16-2. Valencies of the rare earths; all are trivalent, and the size of the 
point shows the relative stability of the ion, Me 3 +; the appearance of quadri- 
valent compounds is shown by a line running up, and of divalent compounds by 
a line running down ; the lengths of these lines give a rough measure of stability. 
(After Jantsch and Klemm, Z. /. anorg. u. allg. Chem. 1933, 216 80.) 

and so similar in other ways that chemists have been able to 
separate them from one another only by such laborious methods 
as fractional crystallisation of their salts and fractional decom- 
position of their nitrates. Six of the rare earths however form 
compounds, in which they exhibit a second valency. Cerium, 
praseodymium and terbium can all be quadrivalent; samarium, 
europium and ytterbium divalent (Fig. 16-2). 



78 THE RARE EARTHS [CHAP. 

Eive of these deviations can be linked up with the theories of 
atomic structure developed in earlier chapters. The more electrons 
a shell contains the less willing is it to part with one of them; 
sodium is more reactive than magnesium, and aluminium than 
silicon; if then the 4f shell obeys the same laws, it should be easier 
to remove an electron from cerium in which only one is present 
than from succeeding elements in which there are several. And in 
fact the first two elements are quadrivalent, while cerium becomes 
quadrivalent much more readily than praseodymium, for com- 
pounds of the latter readily oxidise cerous compounds to eerie; 
further, only one quadrivalent compound of praseodymium has 
been isolated pure, whereas a whole series of eerie compounds 
are known. 

The divalency of europium and the quadrivalency of terbium 
are due to quite another cause. Both the p and d shells show that 
they are more stable when they are just half full than when they 
contain one electron more or less; nitrogen with three p electrons 
has a higher ionisation potential than either carbon or oxygen, 
while the examination of the low terms of the frame elements, 
carried out in the last chapter, shows that the d 5 configuration is 
more stable than d 4 or d 6 ; the difference is not so great as between 
d 9 and d 10 , but the evidence is too clear to admit of doubt. Now 
the f shell is half full in the Gd 3+ ion, which contains seven elec- 
trons, and one might reasonably expect the elements on either 
side of gadolinium to try to assume this configuration, europium 
which precedes gadolinium by keeping an extra electron and 
being divalent instead of trivalent, and terbium which succeeds 
gadolinium by parting with an extra electron and becoming 
quadrivalent. 

The divalency of ytterbium exhibits the tendency to form the 
closed shell of fourteen f electrons; but the divalency of samarium 
remains unexplained, for there is no reason to think the f 6 con- 
figuration much more stable than the f 5 ; in the d shell d 4 is more 
stable, but not much more stable, than d 3 . But we must not make 
too much of this failure, for SmCl 2 is definitely less stable than 
EuCL. 



XVI] ARC AND SPARK SPECTRA 79 

3. Arc and spark spectra 

The paramagnetic susceptibilities of the rare earths have 
already been cited as strong evidence that in the trivalent ions, 
which occur in crystals and in solution, all electrons outside the 
xenon core occupy f orbits. But to obtain evidence of the struc- 
ture of the elements themselves, appeal must be had to the arc 
and spark spectra. These exhibit an exceptional number of lines ; 
in the spectrum of dysprosium, for example, over 3000 have been 
measured. This naturally makes the identification of small 
amounts of the rare earths very difficult, for if one finds the weak 
yttrium line 3468-0 A., one cannot distinguish it from four other 
lines, 3467-4 A. of Gd, 3467-8 A. of Cd, 3468-2 A. of Tb or 3468-4 A. 
of Th, unless one can measure the wave-length to a few tenths of 
an angstrom. To surmount this difficulty spectroscopists have 
been driven to use the * residual lines ', that is, the lines which are 
the last to fade when the proportion of the element in the mixture 
is steadily reduced. For example, if the line measured as 3468-0 A. 
is really an yttrium line, then the strongest yttrium line 3710-3 A. 
must appear much stronger than 3468-0 A. on the same plate; 
moreover, as 3710-3 A. is a residual line, it must be the last to 
vanish as the material examined is diluted. 

As long ago as 1922 Bohr* stated that the atom in which an f 
electron first appears is cerium, and that the f shell is full in 
ytterbium; this statement he based on chemical properties and 
on a mathematical comparison of the stabilities of alternative 
orbits. Since then many spectra of elements lying just before and 
just after the rare earths have been analysed; while within the 
rare earth frame the low terms of Ce i, Sm i, Eu i and Gd I are 
now known. f 

The fifty-fifth electron occupies the 6s shell in Cs i and Ba n, 
and sinks into a 5d orbit in Lam; on Bohr's authority it was 
commonly expected to sink into a 4f orbit in Ce iv, but when the 

* Bohr, Theory of Spectra and Atomic Constitution, 1922, 110. 

t Recent analyses of rare earth spectra are: Ce I, Karlson, ZP, 1933, 85 482; 
Ce III, Kalia, Indian Journ. Phys., 1933, 8 137; EuII, Albertson, PR, 1934, 
45 499 a ; Eu I, Russell and King, PR, 1934, 46 1023 ; Sm I and Gd I, Albertson, 
PR, 1935, 47 370. 



80 



THE BABE EABTHS 



[CHAP. 

Ceiv spectrum was analysed the ground term was found to be 
2 D.* Thereafter it seemed rather improbable that any of the 
three electrons required to produce neutral cerium would enter a 
4f orbit; but apparently Bohr was correct after all, for the ground 
term of Cei is 3 H and this arises in the 4f . 5d. 6s 2 configuration. 



No. of 
electrons 


Atom 


Ground 
term 


Configuration 


1 


Csi 
Ban 
Lain 
Ceiv 


2 S 
2 8 
2 D 
2 F 


s 
s 

d 
f 


2 


Bar 
La ii 
Gem 


*S 
3 F 

3F 


s 2 
d 2 
d 2 


3 


La i 


2 L> 


d.s 2 


4 


Co i 


3 H 


f.d.s 2 


8 

9 
10 


Smi 
Eun 
Eui 
Gdr 


7 n 

% 
^ 

D* 


f 6 .s 2 
f 7 ( 8 S).s 
f 7 .s 2 
f 7 .d.s 2 


15 


Tin 
Yb ii 
Lu in 


2 S 


f 14 .s 


16 


Ybi 
Lu n 


j s 


f 14 .s 2 


17 


Lu i 
Hfn 


2 D 

2 D 


f 14 .d.s 2 
f 14 .d.s 2 



Fig. 16-3. Ground terms of the arc and spark spectra with the configurations in 
which they arise. 

At the other end of the rare earth frame the ground terms of 
LUIII and Lun are 2 S and 1 S respectively, showing that the 4f 
shell is. complete when the nuclear charge is 71, for these terms 
must arise from the configurations f 14 .s and f 14 .s 2 ; but as the f 
shell is bound to grow more stable, when the nuclear charge in- 
creases, like the d shell of preceding periods, these results do not 
prove that the f shell is complete in ytterbium. Thus the spectra 
which have been analysed since 1922 are not inconsistent with 
Bohr's hypothesis, but they have not yet banished doubt. 

* Gibbs and White, PR, 1929, 33 157. Lang has since found a lower 2 F 
term. PR, 1936, 49 552a, 



XVI] ABSORPTION SPECTRA 81 

4. Absorption spectra 

As there are no specific chemical tests for any of the rare earths 
except cerium, the chemist relies on optical tests instead. Of 
these at least six are available; the arc and spark spectra, the 
absorption and phosphorescent spectra of a crystal or solution, 
and X-ray lines and absorption edges. Any of these can be used 
to identify an element, but of them all the absorption spectrum 
is often the simplest, for many of the trivalent ions are brightly 



Pr 59 
Nd 60 
II 61 
Sm 62 
Eu 63 
Gd 64 
Tb 65 
Dy 66 
Ho 67 
Er 68 
Tu 69 
Yb 70 
Lu 71 



II I III IH1 I II II II II III 



I i I 



444U-U-. .1 .1 



~i i i i i i i i r i i i i i r~ 



\ i i i r~i rn r i 



,11, If ,,,,,,,, ,",', , , , '.',', , 'I , ,".", , ,' , 



II II III 111 



7000 6500 6000 5500 5000 4500 4000 A 



Fig. 16-4. Absorption spectra of the rare earth ions. (After Hevesy, Die 
seltenen Erden, 1926, 39.) 

coloured. Praseodymium is green, neodymium red-violet, sama- 
rium yellow and element 61 probably yellowish green; dyspro- 
sium and holmium are both yellow, erbium is rose and thulium 
green; of the rest, four, cerium, gadolinium, ytterbium and lute- 
cium, are quite colourless, while europium and terbium show 
little trace (Fig. 16-4). Thus the elements near the ends of the 
block, and those round gadolinium, show little or no colour; this 
can be explained as depending on the depth of the ground term. 
Thus the 8 S ground term of the gadolinium ion, calculated by 



82 THE RARE EARTHS [CHAP. 

Hund and confirmed by the paramagnetic susceptibility, should 
be peculiarly stable, since it arises in an f 7 configuration; and in 
fact the absorption bands of gadolinium lie in the ultra-violet. 

When the absorption spectrum is more carefully examined, it is 
found to consist of surprisingly narrow bands; many indeed are 
only 1 or 2 A. wide, whereas the absorption bands of the coloured 
ions of earlier periods often cover 100 A. or more; indeed the rare 
earth bands are better described as 'lines more or less diffuse' 
than as bands. Thus if one dilutes the solution of a rare earth salt 
until all trace of colour disappears, the stronger absorption lines 
still appear in the spectroscope, though if a solution of potassium 
permanganate is similarly diluted, the lines disappear with the 
colour; and this difference is to be attributed to the sharpness of 
the rare earth bands. 

Do these bands arise in the molecule like the bands of a gas in 
a discharge tube, or are they atomic lines broadened by the 
varying fields of a crystal? In the band spectra of compounds, 
and especially of complex ions such as uranyl, homologous groups 
of lines recur at regular intervals, being due to atoms oscillating 
within the ion; but in the crystals of the rare earths no group of 
lines recurs. Again, the rare earth absorption lines split in a 
magnetic field, though the band spectra of uranyl compounds 
do not.* Moreover, at temperatures as low as 1-7 A. some are 
still bright, though a molecule could not vibrate at so low a tem- 
perature and could not therefore absorb radiation. True, the 
intensities of the lines change as the temperature falls, for while 
some remain bright, others fade; but the lines which fade are 
easily explained as arising from levels above the ground state, 
levels in which the Boltzmann distribution allows very few atoms 
at low temperatures.! 

The positions of the bands are largely independent of the anion 
and are the same in the solid as in solution. This alone is strong 
evidence that the lines are atomic in origin, and arise in a shell 

* Becquerel, le Radium, 1907, 4 328; K. Akad. Amsterdam, Proc. 1929, 32 
749. 

f Becquerel, L ivre jubiliare de Kamerlingh Onnes, 1922, 288; Ehrenfest, ibid. 
362. 



XVI] ABSORPTION SPECTRA 83 

which is well screened from the forces of other ions, as the 4f shell 
may be supposed screened by the 5s and 5p shells. 

If the rare earth lines arise within the atom, it should be pos- 
sible to identify the levels by the methods which have been so 
successful in arc spectra. The magnetic susceptibilities of the rare 
earths are strong evidence that the ground terms of the trivalent 
ions all arise in an f n configuration and are those predicted by 
Hund's energy rules. Do the absorption spectra confirm this 
hypothesis ? 

As long ago as 1 907 Becquerel showed that the absorption bands, 
narrow at room temperature, become narrower still as the tem- 
perature is reduced, until at the temperature of liquid hydrogen 
some bands are almost as sharp as the lines of gaseous spectra.* 
Becquerel and his co-workers however used minerals, which con- 
tained several rare earths, and perhaps also other ions in solid 
solution; these irregularities in the crystal lattice would produce 
strains which might well blur the absorption lines. Further 
advance waited until 1929, when Freed and Speddingf resorted 
to synthetic crystals; while the following year SahaJ suggested 
that the principal lines of a crystal may arise in forbidden tran- 
sitions of the ion. Of this suggestion Deutschbein and Tomaschek 
have made full use, though thus far work has been largely con- 
fined to gadolinium and samarium. 

5. Gadolinium 

The gadolinium ion exhibits the simplest spectrum of all the 
rare earths, and produces sharp lines even at room temperature; 
both the multiplets and their components are well separated from 
one another. The basic level 8 S is known to be very little dis- 
turbed in electric fields, || and as experimental evidence shows that 
all lines arise from it, the lines constitute in effect an energy level 
diagram. The only misfortune is that so many lines lie in the 
ultra-violet. 

* Becquerel, le Radium, 1907, 4 328; K. Akad. Amsterdam, Proc. 1929, 32 
749. 

f Freed and Spedding, PR, 1929, 34 946. J Saha, N, 1930, 125 163. 

See chapter XXH on Fluorescent crystals. 
|| Spedding, PR, 1931, 38 2080a. 

6-2 



84 THE RARE EARTHS [CHAP. 

Freed and Spedding* worked first with the chloride, GdCl 3 . 6H 2 O , 
which crystallises in colourless plates. The spectra were taken 
along the principal axis, that is, perpendicular to the faces, 
but tests made perpendicular to the principal axis showed 
that within the limits of measurement the spectrum is indepen- 
dent of the direction in which the light passes. Moreover, in 
solutions of varying concentration, photographs show that the 
positions and general spacing of the multiplets are similar to 
that found in the crystal, except that the lines are rather more 
blurred and the multiplets are shifted slightly towards higher 
frequencies. 

When the absorption spectrum of the chloride is compared with 
that of other gadolinium salts, the negative ion is seen to produce 
little change in the positions of the multiplets, though it changes 
the number of lines and their positions within the multiplet. 
Accordingly, the multiplets must arise from electronic transitions 
of the Gd 3 + ion, but the splitting of these levels must depend on 
the forces exerted by the surrounding atoms. These forces seem 
to depend more on the crystal symmetry than on the negative 
radical; the spectra of monoclinic Gd 2 (S0 4 ) 3 . 8H 2 0, GdCl 3 . 6H 2 Ot 
and GdBr 3 .6H 2 0{ are almost identical, but different from hexa- 
gonal Gd(C 2 H 5 SO 4 ) 3 . 9H 2 and Gd(BrO 3 ) 3 . 9H 2 O; while work on 
the triclinic acetate suggests still a third type, but only one band 
of the acetate has been ^examined, so it is perhaps unwise to 
generalise. 

As the temperature is reduced little change appears in the 
spectrum; true the multiplet intervals increase slightly, and the 
whole spectrum shifts slightly towards the red, but this move- 
ment averages only some 4 cm." 1 in a change from the laboratory 
to liquid hydrogen. These two changes are primarily due to the 
contraction of the crystal, which brings the ions closer together, 
and therefore makes the electric field more intense. 

* Freed and Spedding, PR, 1929, 34 945. GdCl 3 .6H 2 0; Gd 2 (S0 4 ) 3 .8H 2 0. 
t Spedding and Nutting, PR, 1931, 38 22940. 

j Spedding and Nutting, Am. Chem. Soc. J. 1930, 52 3747. GdBr 8 .6H 2 0. 
Spedding and Nutting, Am.Chem.Soc.J. 1933, 55 503. Gd(C 2 H 5 SO 4 ) 3 .9H 2 O 
and Gd(BrO 3 ) 3 .9H 2 O. 



XVI] SAMARIUM 85 

6. Samarium 

At room temperature the absorption spectrum of samarium 
consists of diffuse lines and bands, lying chiefly between 3000 and 
5000 A. As the temperature is reduced the lines sharpen, until 
when the crystal is in liquid hydrogen the lines are very fine; the 
lines also change in intensity, and this change is much more 
striking in samarium than in gadolinium; at low temperatures 
some lines disappear, while new lines make their appearance*; 
and this is to be expected, since Hund's theory makes the ground 
term f 56 H, and at low temperature lines arising in the higher 
components of this term must be very weak. 

The Boltzmann distribution law indeed makes it certain that 
any absorption lines which appear below room temperature must 
arise in a level lying less than 500 cm." 1 above the ground level. 
The visible spectra of crystals of chloride and bromate thus arise 
between half a dozen levels lying below 500 cm.- 1 and other levels 
lying between 17,000 and 27,000 cm.- 1 In order to follow the 
changes in intensity more closely, the absorption spectrum of the 
chloride, SmCl 3 .6H 2 0, was photographed at five temperatures 
between 293 and 20 A., first with a single crystal and then with 
powdered crystals!; the latter method brings out the weak lines, 
though it blurs the strong, as multiple internal reflection 
lengthens the path. Comparison of these photographs suggests 
the division of the lines into two groups; one consists of lines 
which increase in intensity as the temperature is lowered, many 
only appearing when the temperature has already fallen to 
195 C., while in the other group the lines decrease in intensity 
as the temperature falls, many being absent at 20 A. These two 
groups are conveniently referred to as 'low temperature lines' 
and 'high temperature lines'. Many of the fainter low tempera- 
ture lines appear on the violet side of a multiplet, while the high 
temperature lines seem to congregate on the red side. 

The intensities of both groups of lines depend in part on the 
populations of the lower levels, and this in turn is governed by 

* Freed and Spedding, N, 1929, 123 526. 

t Spedding and Bear, PR, 1932, 42 58, 76. SmCi 3 .6H 2 0; single crystal and 
powdered crystal. 



86 THE RARE EARTHS [CHAP. 

Boltzmann's law; if three low levels exist, separated by intervals 
of 150 cm.- 1 , and all are of equal weight, the numbers of atoms in 
these levels at 20 and 78 A. are those given in Fig. 16-5. Thus in 



^"^^^^ Level 


cm." 1 


150 cm.- 1 


300 cm." 1 


20 A. 

78 A. 


1 

1 


8-3.10- 6 
2-4.10- 2 


6-9. 10~ n 
5-7. 10~ 4 



Fig. 16*5. Normal fraction of atoms existing at any time in three low levels. 

liquid hydrogen the number of ions lying in levels above the 
ground level is small, and there seems little doubt that the low 
temperature lines may be attributed to the ground level, while 
the high temperature lines arise in a group of levels lying between 
100 and 300cm.- 1 

These predictions are very satisfactorily confirmed by a 
search for constant intervals between lines of the low and high 
temperature groups (Fig. 16-6). In the crystals of SmCl 3 .6H 2 O 



Low temperature line 


High tem- 
perature line 


Av cm." 1 


A A. 


v cm. l 


v cm."" 1 


5592-6 
5582-5 
4988-2 
4899-6 
4513-2 


17875-8 
17908-0 
20042-5 
20404-5 
22151-8 


17730-6 
17763-1 
19897-0 
20259-0 
22006-0 


145-2 
144-9 
145-5 
145-5 
145-8 


5592-6 
5582-5 
4988-2 
4899-6 
4866-0 


17875-8 
17908-0 
20042-5 
20404-5 
20544-8 


17716-3 
17748-6 

19882-7 
20246-0 
20386-0 


159-5 
159-4 
159-8 
158-5 

158-8 



Fig. 16-6. Doublet intervals of 145 and 159 cm.- 1 found in the absorption 
spectra of SmCl 3 .6H 2 at low temperatures. 

these differences reveal levels at 145, 160, 204, 217 and 300 cm.- 1 
above the ground level. Some of these levels are probably com- 
plex, the 300 cm." 1 level in particular consisting perhaps of 
components at 295 and 315 cm." 1 , for the spread varies with the 



PLATE VI 

1. Single crystal absorption spectrum of SmCl 3 .6H 2 O at four different 
temperatures. The photographs were taken at the temperatures shown on 
the left, these being the boiling points of the substances shown on the right . 
All the lines grow sharper as the temperature is reduced, but the intensity 
may increase or decrease. 

2. Conglomerate absorption spectrum of Sm(BrO 8 ) 3 . 9H 2 O at four different 
temperatures. A conglomerate or mass of small crystals has a longer 
optical path than a single crystal, so that it brings out the weak lines, but 
it blurs the stronger multiplets. 

(Photographs lent by Prof. F. H. Spedding.) 



Plate VI 




o 

CM 

S3 





CO 



8 



fi 

o 

o 



ffi 

CM 




00 



o 

Ci 
CO 



o 

00 



O 

O 



XVI] SAMARIUM 87 

height of the level from 2 to 30 cm." 1 , and these involve errors 
rather greater than might be reasonably expected. 

Turning again to the photographs, the lines which originate in 
the 300 cm." 1 level are found entirely absent at - 195 C., while 
those arising in the 204 and 217 cm." 1 levels fade rapidly as the 
temperature is further reduced. 

Examined by the same methods hexagonal crystals of the 
bromate, Sm(Br0 3 ) 3 .9H 2 0, behave very much like the crystals 
of the chloride until the temperature falls to 78 A.; the shift in 
position and widening of the multiplets may perhaps be slightly 



Tem- 
perature 


Low tempera- 
ture line 


Satellite A 


Av A 


Satellite B 


Av 


78 A. 


17847 


17809 


38 


17783 


64 




18857 


18817 


40 


18790 


67 




19987 


19949 


38 


19920 


67 




20382 


20342 


40 


20315 


67 




28125 


28087 


38 


28055 


70 


Tem- 
perature 


Low tempera- 
ture line 


Ai 


AVA, 


An 


Av All 


Bi 


Af,t, 


Bn 


Av BlI 


20 A. 


178474 (11) 


. 


_ 


17802-5 


44-9 








17780 


67 




17857-2 (n) 


_. 





18812 


45 
















17949 (i) 


17912 


37 








17867 


82 










19985-6(t,ii) 


19949-7 


35-9 


19941 


45 


19904 


82 


19919 


67 




20385-9 (i) 


20348-9 


37-0 



















28125-2 (ii) 








28080 


45 








i 



Fig. 16-7. Low temperature lines and their high temperature satellites in the 
absorption spectrum of Sm(Br0 3 ) 3 .9H 2 0; this shows how the energy levels 
split as the temperature is reduced from 78 to 20 A. 

greater, but only slightly; between 78 and 20 A. however most 
of the lines split into two components, of which the red one is 
almost certainly complex (Fig. 16-7). Thus above 78 A. the 
temperature variation of the lines and a search for constant 
intervals reveals levels at 39 and 68 cm." 1 above the ground level, 
with perhaps other levels between 100 and 230 cm.- 1 ; but at a 
temperature of 20 A. the levels revealed are at 0, 37, 45, 67 and 
82cm.- 1 (Fig. 16-8). 

Moreover, the transitions observed at 20 A. suggest that these 
levels form two independent sets; 0, 37, 82 combine with one 
group of high levels, and 0, 45, 67 with another (Fig. 16-8). That 



78 K 20 K 




20117 


20110 << 
2002,3 -^ 










-20032-9 
20027-6 


20009 
19987 


















0007-7 
9985-6 

8882-9 




























79*9 


1794-0 ^ 




























7939 

7875-fe 






























7*47-4. 


t 


ii mi 

*P\ CVJv*. 


? 
^ 
Si 


!i 


H 


9> O 

1 5 

I- ooe 


-* <^ 

3^ 5 

si s 


M-O 



sss 


8 * 

S 
CO O 


t! 

:s 






- 


II 


1 




32 


i! 


^? 
srS 


3SS 

SE 


s t~ e>Me*v\<o r~ . 

^ O*OO<T>O^O C 
h <jv 0>00 O^O * 


















co -/~ 
































, - 57 






























- - 4$ 


a 
























- 37 
O 



Fig. 16-8. Energy levels of Sm(BrO 3 ) 3 .9H 2 O at 20 A., with the lines arising in 
transitions between them. The figures are wave numbers. (After Speckling 
and Bear, PR, 1933, 44 290.) 





78 K 20 K 

20117 


20023 










20009 
19987 








' 1??B3-b 












18882-9 


















i^ 7 5 l6 


















1MW-2 
17949 






















*=^ 179 39 


17^7 1 


1 ll I 


















^ . 17847-4 


1 


till 


















^- 17844-9 



II 



1 






















1 
































































. 82 






















^ 45 






















7 



Fig. 16-9. Energy levels of Sm(BrO 3 ) 3 .9H 2 O at 78 A. (After Spedding and 
Bear. PR, 1933, 44 290.) 



CHAP. XVI] SAMARIUM 89 

the ground term appears in both groups means nothing, for in 
fact the method, by which the splitting of the low levels is cal- 
culated, automatically reduces any real interval to zero; if all the 
low levels developed the same interval, one would be free to 
ascribe this splitting entirely to the high levels.* 

The existence of more than three low levels in the samarium 
salts makes it probable that in Sm 3+ there is a second electronic 
level lying close to the 6 H 2 ^ term predicted by Hund, for in an 
electric field this term splits into only three components; and this 
fits in well with the magnetic susceptibility which does not agree 
with the value predicted, if 6 H 2J is the only low term.f 

BIBLIOGRAPHY 

The last three sections of this chapter should be read with chapter xxu. 
Spencer, J. F., The metals of the rare earths, 1919, is a very thorough study with 
full references ; but it was written before Bohr had outlined the electronic 
structure of the elements. Hevesy, Die seltenen Erden, 1926, makes full use of 
Bohr's theory. 

* Spedding and Bear, PR, 1933, 44 287. Sm(Br0 3 ) 3 .9H 2 0. 
t Spedding, Am. Chem. Soc. J. 1932, 54 2593. 



CHAPTER XVII 
INTENSITY RELATIONS 

1 . Experimental 

For rough estimates of intensity the spectroscopist has often 
relied on his eye; but the eye is subjective and far from accurate, 
so that in recent years much attention has been paid to methods 
of estimating the density of a photographic plate. In general if 
the intensity of one component of a multiplet is expressed as a 
percentage of the brightest line, then these methods ensure that 
the percentage is correct to the nearest integer; but this statement 
is subject to a few restrictions, of which the most important is 
that the lines must not be too far apart, for no one knows quite 
how the sensitivity of a photographic plate varies with wave- 
length. 

This is not the place to indulge in a description of experimental 
procedure, especially as it is fully described elsewhere;* but the 
wedge method may be briefly reviewed as illustrating the chief 
points of interest. As the density of a photographic image is not 
proportional to the length of exposure or the intensity of the 
incident light, but shows an initial lag (Fig. 17-1), one is not 
justified in comparing two densities and then saying that the 
intensities must have been in the same ratio. Instead, one may 
only say that if the density at one p6int is equal to that at another, 
then the intensities were also equal. The word ' density ' is here a 
technical term, being defined as 

, f intensity of incident light ) 

log \ - I . 

(intensity of transmitted light) ' 

This means that a scale ought to appear on each plate, and one 
way of obtaining this is to photograph a wedge of dull grey glass; 
the density will then be proportional to the distance from the 
edge of the wedge, and this may be measured by a micrometer 
fixed to the microscope. Thus one may say that the density of a 

* Dobson, Griffith and Harrison, Photographic photometry, 1926. 



CHAP. XVII] EXPERIMENTAL 91 

certain line is equal to that at a certain place on the wedge, and 
the latter may be measured on a scale which is a linear scale of 
intensity. 



'a 

CD 
P 



Log Intensity 
Fig. 17-1. Density-intensity graph of a photographic plate. 

2. The normal multiple! 

The Sommerfeld intensity rule has already been discussed, but 
in a form applicable only to multiplets in which AL = 1. 
Multiplets of the P -> P type, in which AL = 0, give their strongest 
lines when A J is zero, while the two groups arising from A J = 1 
are less intense than the chief lines but equal to one another. To 
include this type of transition the Sommerfeld rule may be 
restated:* 

The chief lines of any multiplet are due to those transitions in 
which AJ = AL; a weaker group, technically known as satellites 
of the first order, arise when A<7 = AL 1, while satellites of the 
second order occur when A<7 = AL 2. 

This rule is qualitative only; attempting to make it quantitative 
Sommerfeld in 1923 considered first those multiplets which arise 
by the combination of a single level with a multiplet level; the 
three SP lines in spectra of all multiplicities are of this type, and 
experiment f shows that the intensities due to the three transitions 



* Sommerfeld and Heisenberg, ZP, 1922, 11 131. 
t Dorgelo, ZP, 1924, 22 170. 



92 



INTENSITY RELATIONS 



[CHAP. 

vary as (2J + 1) for the three P terms; thus the intensities of the 
triplet lines 8 S 1 -> 8 P 2tlt0 of Mg are in the ratio of 5 :3 : 1, while 
those of the octet lines 8 S 3 j-> 8 P 4 ^ 8 | f 2| of Mn are in the ratio of 
10:8:6. 

From this result three important rules emerge. First, the in- 
tensity ratio is independent of the serial number n. Secondly, the 
intensity is determined as much by the level to which an electron 
is going as the level which it is leaving; in calcium, for example, 
the intensity ratios of 2 3 S->2 3 P and 3 3 P->2 3 S are identical, 
though one triplet is of the sharp and the other of the principal 
series. The third is a point of theory; the intensities are in the 



Term 


PO 


PI 


P 2 




DI 


4425-43 
25 


4435-67 
19 


4456-61 

1 


45 


D 2 





4434-95 
54 


4455-88 
18 


72 


r> 3 








4454-77 
100 


100 




25 


73 


119 


Intensity 
sum 



Fig. 17-2. Intensities in a diffuse triplet of calcium; the upper number is the 
wave-length, the lower the intensity measured by Burger and Dorgelo. 

ratios of the number of Zeeman components possessed by the 
level, and this fits in well with the practice of taking this number 
as the statistical weight of a level; a further significance will 
appear when the intensities of Zeeman multiple ts are considered. 

The next step was to examine the transitions between two 
multiplet levels. Working in this direction Burger and Dorgelo* 
first verified the validity of the above rules for the PD doublet of 
sodium where the D levels are not resolved, and then turned to 
the PD multiplet of calcium; in it they found that the sum of the 
intensities of the lines originating from one P level was to the sum 
of the intensities from another P level as the statistical weights 
of the levels. And the same held true for the three D levels. 

Fig. 17-2 gives their measurements, the upper figure in each 



Burger and Dorgelo, ZP, 1924, 23 258. 



XVII] THE NORMAL MULTIPLEX 93 

square being the wave-length and the lower the intensity adjusted 
to a scale in which 100 represents the brightest line. The sums of 
the intensities of the lines originating from the various P levels 
are given at the bottom, 25: 73: 119, and it will be observed that 
they are roughly in the ratio of 1: 3: 5. Similarly, the intensities, 
45, 72, 100, arising from the three D levels are roughly in the 
ratio 3:5:7. 

The summation rule used alone enables us to calculate the 
intensities resulting from the combination of two doublet levels 
(Fig. 17-3), but it will not suffice for more complicated multiplets. 



Term 


Pt^l* 




Si 


5 1 
9 


6 
9 




5 10 


SI 



Term 


D U 


D* 




fc 


14 


1 
20 


15 
20 




14 


21 


SI 



Fig. 17-3. Theoretical intensity ratios of diffuse and fundamental doublets. 

Thus, consider a PD triplet in which the intensities are those 
shown in Pig. 17-4. Burger and Dorgelo's summation rule shows 

T = " 3 - = "5 

3 == ~~ir~ == 7" 

But this gives only four equations to determine five ratios. To 
resolve the problem Russell,* among others, called in the corre- 





3 P 3 Pi 3 Pa 




3D l 


20 


15 1 


36 


3 AJ 





45 15 


60 


3 >3 





84 


84 




20 


60 100 





Fig. 17-4. Assumed intensities 
of a diffuse triplet. 



Fig. 17-5. Theoretical intensities 
of a diffuse triplet. 



spondence principle. His argument cannot be given here, but his 
result may be reviewed. 

* Russell, Nat. Acad. Sci. Proc. 1925, 11 314, 322; Sommerfeld and Honl, 
Preuss. Akad. Wiss. Berlin, 1925, 9 141; Honl, AP, 1926, 79 274; Kronig, ZP, 
1925, 31 885, 33 261; Dirac, PUS, 1926, 111 281. 



94 INTENSITY RELATIONS [CHAP. 

As the intensities of a multiplet are determined by the levels 
between which the electron jumps and not by the direction of the 
jump, it is not necessary to consider AL = 1 but only one of 
these; arbitrarily, then, we elect to consider only Z/-> (L 1) and 
L->L. For each of these transitions there are three values of A<7, 
so that six formulae may be expected, and these take their 
simplest form if J is defined as the larger of the two quantum 
numbers concerned. 

In the transition L-> (L 1) the correspondence principle gives 

for J->/-l /_ = j. 



fbr(J-l)W I + = L . 

In the transition L-+L the summation rule shows that the two 
groups of satellites arising from A J = + 1 must be identical, so 
that only two formulae are needed: 



.___.__. 

forJ->(J-l) S(2L+l) 

OT (J-1)-W ^- 



In these equations P ( J), Q (J) and R (J) are convenient abbre- 
viations defined as 



In theory these formulae should compare the intensities of* 
any two lines arising in a transition from one configuration to 
another, but they are valid only when the coupling is Russell- 
Saunders and there are no inter-system lines. As very few 
spectra satisfy this condition the formulae are normally applied 
only to the intensities of components of a single multiplet, and 
for this purpose the first factor, which is a function of S and L 
only, may be dropped. 



XVII] 



THE NORMAL MULTIPLEX 



95 



INTENSITY TABLES 



1 

1 2 


Doublets 


if 


xKnool 


11 2 


S 

21 31 


3J 2 4 

2J 31 tj 


1 40'0 20O 

u [20-0 10-0 


556 PD 
11-1 100 






64-3 7-2 
7-2 100 


70-0 DF 
5-0 100 




74-1 37 
3-7 100 


77-1 
2-9 


FG 2J 3 6 

1(10 3J 4} 5J 


5*l 


* 1 


50-0 
500 100 


$fi 


79-5 
2-3 


2-3 81-0 GH 31 
100 19 100 41 


'* I 


10-0 20-0 
100 


55-6 11-1 
11-1 100 


<V"<. 


> 


83-1 1-5 84 
1-5 100 1 


4 HI 4J 

3 100 51 


2 

2 3 


4 


1 2 


64-3 7-1 
100 


70-0 5O 
50 100 


85 


6 1-1 5} 

1 100 61 


1 2 3 
'PU 

5 


74-1 3-7 
100 


77-1 
2-9 


2-9 1 


1 20O 60-0 100 


i 


100 




26-7 PP 
26-7 200 33-3 
^\ 33.3 100 


23-8 PD 
17-9 53-6 
1-2 17 '9 100 



1 1 

2 2 


3 

3 


2 34 


79-5 


2-3 81-5 -9 
100 1-9 00 


3 45 831 -5 84 

*H oo i 


4 1-3 

3 100 


1 10O 800 
i 11 800 100 


36-2 121 DD" 
12-1 55-8 12-5 
^\12-5 100 


46-7 
8-8 
0-2 


69- 
8- 


DF 

100 


22 4 
33 4 




4 6 85 


6 1-1 86-5 10 
100 1O 100 


1 29-6 3-7 220 17'6 ^\ 


2} 100 19-0 100 






52-6 6-6 FF" 
6-6 69-6 6-7 
^\_6'7 100 


58- 
6- 76-7 
0- 5- 


FG 
100 


2 
33 5 
445 6 


5667 

6 

6 7 


i 11 11 37-5 120 0-5 
i 2i 1\ 630 12-0 
31 100 


45'9 8-7 ""*>v. 
8-7 64-2 8-9 
8'9 100 








62 4-1 GG 
4- 76'9 4-2 
^/^ 4-2 100 


65-8 GH 
3-4 81-2 
03 3-4 10f 


3 
4 4 

5 5 


i 11 21 21 
1J 3* 31 

<i 

1 U 2J Z 


53-3 6-5 
73-5 6- 
100 


580 5-2 ^ 

5-2 73-8 5'2 
5-2 100 


' */ 


68-4 2-8 11H 
2-8 81-3 29 
\v^ 2-9 100 


70-9 
2-4 
O2 


HI 4 

84-3 & 5 
2-4 100 6 5 


riplets 


31 


21 3J 3 
8} 4} 4 

5 

S 

11 21 


62'5 4-1 O5 
79-2 4-1 
100 


65-5 34 

3-4 794 
3-4 


\ 

34 

100 






72-8 
2-1 

X 


2-1 II" 5 
84-3 2-1 60 
2-1 100 J 7 

T 


21 

34 


3J 41 4J 
61 


68-6 2-8 
82-9 


O2 
2-8 
100 


70-7 2-4 \ 
2-4 82-9 2-4 
2-4 100 


31 41 

4 
31 4J 


1 61 
51 


72-9 2-1 01 
86-4 2-1 
100 


74-5 
1-8 


1-8 "\ 

85'5 1-8] 
1-8 100 1 


1J 33-3 66-7 100 1 1J 2J 


1 7-9 39-7 PP 20-8 20-8 PD 
1 1J 39-7 12-7 42-9 4-2 26-7 52-5 
21 42-9 100 2-5 22-5 100 


U 

4131 


51 61 51 

5 

41 51 6J 


4 

21 

41 * 6 

5J41 51 6J 


14'6 14-6 DD" 
J14-6 23-3 20-4 
* ( ^,20-4 50-4 16-6 
, , l.v^ .^1 ^\ 16-6 100 


28-0 
11-2 448 
8 14-6 < 
6 


8'6 
14 


DF 

100 


1 
312 


2 100 100 




34-9 8-7 
8-7 45O 
^-xll-7 f 


17 

6-5 
9-1 


9-1 

100 


42-9 
6-9 
3 


57-4 
9-1 76-4 
2 6-9 


FG 
100 


14-3 17-9 ^^ 
. 1 35-7 7-1 17-9 7-1 28-8^\ 
* -i 35-7 35-7 28-6 36-7 25O 
3 100 25O 100 






<$' 


47-2 
6-7 


6-7 
67-3 75 
7-6 74-8 


GO" 

6-8 
100 


52-4 

4-7 


GH 
65-2 

6-2 810 
-09 4-7 100 


1 16-7 160 1-7 
2 350 19-4 1-1 
* 3 62-2 15-6 
4 100 


26-1 
112 


11-2 ^\^ 

35-8 15-2 \^ 
15-2 59-9 12O 
12-0 100 


71-2 7-1 
7-1 100 




66-5 
4O 


40 HH 
65-1 5-3 
5'3 79-9 4O 
^\ 4O 100 


59-1 
3-4 70-5 
O5 4-5 84'1 

O4 3-4 


HI 

S 
100 


1 2 32 

4 *: 

5 


36-4 


8-7 -4 
51-9 11-4 
73-1 


8- 
100 


41-7 
7O 


7O 
51-9 
9-3 






61-4 2-9 
2-9 70-4 3-9 
\. 3-9 83'2 


ir 

2.9 8 

100 1 


1 


234 


48-1 


5-6 


16 


51-7 4-7 




Quartets 




79O 5-6 
100 


6-3 


77-6 4-8 
4-8 100 


2 


3 


4 54 

7 


56O 3-9 
68-1 


O7 
5-2 06 
82-7 3-9 
100 


58-7 
3-4 


3-4 \. 
68-0 4-3^-^ 
4-5 81-7 3-4 
3-4 100 


3 4 065 

41 < 

8 


61-8 


2-9 04 6 
72-6 3-9 03 
80-3 2-9 
100 


8 2-6 ^-^ 
fl 72-5 S-i^X 
3-4 84-5 2-6 
2-6 100 



Fig. 17' 6. Multiplet intensities. The intensity of each component is given as a 
percentage of the strongest line of the multiplet. The numbers outside the 
frames are L and J, the former in heavy type. The tables may be applied to 
(jj) coupling (p. 150), related multiplets (p. 104) and hyperfine structure (p. 183). 
(After White and Eliason, PR, 1933, 44 753.) 



96 








CASH 



98 








7-2 



100 INTENSITY RELATIONS [CHAP. 

The equations for the jump L->(L 1) may be illustrated by 
the three lines 3 D 1A3 -> 3 P 2 . In the 3 D term L is 2 and S is 1, so 
that in the jump 

from J = 3to J = 2 /_ = \ r (5.6- 1 .2) (4. 5- 2) = 168, 

from J = 2to J = 2 / =30, 

from J=l to J = 2 1+ = %- 

This leads to the intensity scheme of Pig. 17-5. Incidentally, too, 
this result satisfies the early qualitative rule of Sommerfeld, 
which stated simply that 

/_>/>/+. 

Fig. 17-6 gives a list of the intensities calculated by these 
formulae, each line being expressed as a percentage of the 



Terms 


Pi* 


'P.* 


P.* 


D, 


3079-6 
(20) 
18-3 








6 I>ii 


3073-1 

(28) 
25-8 


3081-3 
(12) 
13-1 





D* 


3062-1 

(18-7) 
18-7 


3070-3 
(36-6) 
34-4 


3082-1 

(4-8) 
Lapped 


6 Dsi 





3054-4 
(51-4) 
51-3 


3066-0 
(28-6) 
26-1 


6 4i 








3044-6 
(100) 
100 



Fig. 17-7. Intensities of the w 6 P->3d 6 ( 5 D) 4s 6 D multiplet of Mn i. The 
upper figure is the wave-length, the middle the theoretical intensity, and the 
lower the observed intensity. 

strongest line, this being a convenient practice because one per 
cent, is about the accuracy which can be attained with the photo- 
graphic technique developed in recent years. This technique 
leaves no doubt that these formulae are valid in very many 
spectra; as examples, Fig. 17-7 shows a PD sextet from Mm, 
and Fig. 17-8 a DF quartet from Tin. 

The formulae are very seldom applied to the comparison of 



XVII] 



THE NORMAL MULTIPLEX 



101 



different multiplets, but Wijk* has tried them out on the quartets 
and doublets of n, a light atom in which the inter-system lines 
are very weak. This work roughly confirms the theoretical 



\v 3d 3 

3d 2 .4p\ 


* 


- 


*, 


*., 


-., 


3161-19 

(70) 
72 





__ 








3154-18 

(28) 
28 


3161-76 
(112) 
112 


__ 





* 


(2-0) 


3152-24 
(37) 
35 


3162-56 
(171) 
168 





. 





(1-4) 

' 


3155-65 

(29) 
30 


3168-52 
(250) 
249 



Fig. 17-8. Intensities of the 3d 2 4p 4 D->3d 3 4 F multiplet of Tin. The theo- 
retical intensity is in brackets. 

quartet-doublet intensity ratio of 2 : 1 ; thus the intensities of the 
4 P -> 4 S and 2 P -> 2 S lines were found to be as 1-6 : 1, and two other 
empirical ratios were 2-6 and 2-1. 

3. The super-multiplet 

In the mercury spectrum the division into singlets and triplets 
has little experimental justification, and many inter-system lines 
are strong; moreover, the sum rule in its simple form is but poorly 
obeyed. Accordingly, Omstein and Burgerf suggested that when 
the coupling is no longer Russell-Saunders, the sum rule ought to 
be extended. For this there is a precedent in the laws of the 
Zeeman effect, which define certain sums for a single multiplet 
when the coupling is Russell-Saunders, but only for all terms of 
a configuration when the coupling is abnormal. 

In order to make the experimental work as significant as 
possible, Ornstein and Burger examined first a configuration of 



* Wijk, 2P, 1928, 47 622. 

t Ornstein and Burger, ZP, 1926, 40 403. 



102 INTENSITY RELATIONS [CHAP. 

two electrons, which gives rise to a triplet and a singlet term. 
Moreover, they were careful that one of the two combining triplet 
terms should be unresolved. A super-multiplet satisfying these 
requirements is found in some DF combinations of calcium and 
strontium; if the intensities of the singlet and triplet lines are 



Terms 


^2 


3 ^i 


3 D 2 


3 D 3 


IF 


s 











3 F 





*i 


3 


^3 



Fig. 17-9. Assumed intensities in a fundamental super-multiplet. 

written s and t l9 t 2 and t 3 respectively, as in Fig. 17-9, the sum 
rule applied to the vertical columns states that 

s t t t 

5 == 3 :== 5 == T 

Thus theory suggests that the intensity of the singlet should be 
equal to the mean intensity of the three triplet lines, whereas 
the intensities actually observed* and quoted in Fig. 17-10 





Ca 


Ca 


Sr 


Transition 


A 


Int. 


A 


Int. 


A 


Int. 


iD 2 _iF 


4878 


4-3 


4355 


4-7 


5156 


4-4 


3 D 8 - 3 F 
3 D 2 - 3 F 


4586 
4581 
4579 


7-0 
5-0 
2-5 


4099 
4095 
4093 


6-9 
5-0 

2-8 


4892 
4869 
4855 


6-8 
5-0 
3-4 


Mean triplet 
intensity 




4-8 




4-9 




5-1 



Fig. 17-10. Observed intensities in three fundamental super- multiplets. 

show that it is rather weaker. But the singlet is of considerably 
longer wave-length than the triplet, and it has been shown* 
that when the intervals are large the sum rule should be applied 
not to the intensity itself, but to the intensity divided by y 4 ; 
and, in fact, if the intensity 4-3 of the singlet line is multiplied 
by (4878/45S2) 4 the corrected intensity is 5-5, a figure which is as 
much larger than the mean intensity of the triplet as the first 
figure was too small. 

* Ornstein, Coelingh and Eymers, ZP, 1927, 44 653. 



XVII] 



THE STJPER-MTJLTIPLET 



103 



With this satisfactory result Ornstein and Burger* were ready 
to tackle a group of lines in the mercury spectrum. The lines 



Terms 



"Pi 



Fig. 17-11. Assumed intensities in a diffuse super- multiplet. 

which should appear are shown in Fig. 17*11; and the sum rule 
applied to this figure leads at once to the equations 

__ = ^ 4 + *l + *3 + *6 = V+ *2 + *5 ^ 

3 ~ 5 ~ 3 1 



575 3 

The eleven lines concerned in the relation differ so in wave- 
length that if all the intensities were measured close agreement 
with experiment could not be expected unless the *> 4 correction 
were applied, and at the time this work was done the i> 4 correction 
had not been tested out. But the intervals of the D terms are 
small, and as these equations require that 



t 21 

a check may be applied with measurements on only those four 
lines which arise from the combination of 3 P 2 with the D terms. 



Wave-length 


Combination 


Intensity 


3650 
3655 
3663 
3663 


I 1 


100 
10-8) 

[ 7.9/ 18 ' 7 



Fig. 17-12. Observed intensities in a diffuse super-multiplet of Hg I. 

The empirical results are shown in Fig. 17-12. The line t e is so 
weak that if measured alone its intensity would certainly be less 

* Ornstein and Burger, ZP, 1926, 40 403. 



104 INTENSITY RELATIONS [CHAP. 

than 1 per cent, of t , but it lies so close to i 4 that the two may be 
conveniently measured together after widening the slit of the 
spectroscope. The figures show that when the inter-system line 
is included the sum rule is satisfied, whereas if it is omitted 
(^3 + ^e) i s on ty * ^ per cent, of ^ instead of the 1 9 per cent, predicted. 
These experiments clearly show that in certain spectra the sum 
rule is valid only if the singlet and triplet lines are treated as 
parts of a single whole; if this is a general phenomenon, then the 
intensity of successive lines in singlet and triplet series should 
decrease according to the same law, so that the relative intensity 
may be independent of the serial number; and in fact Ornstein 
and Burger* have confirmed this prediction. 

4. The iron-frame elements 

In the analysis of the iron frame elements at the Bureau of 
Standards, Russell and his co-workers have relied more on in- 
tensities than on multiplet intervals or magnetic splitting factors. 
Indeed, if the general intensity laws were not obeyed these spectra 
would probably still await analysis. The strongest lines arise 
from transitions in which only a single electron orbit changes; and 
this is in agreement with the correspondence principle, which 
indicates that those terms between which strong combinations 
appear must be built up from the same state of the ion. In con- 
trast, transitions involving a change in the ion are much less 
probable, and the lines resulting are either absent or fainter even 
than the weak inter-system lines. Moreover, when only one 
electron jumps, the intensities of related multiplets can be 
obtained from the formulae designed to give the intensities of 
related lines; Russellf suggested a law of this kind, while Kronig 
used theory to show that if the coupling is Russell-Saunders the 
figures are identical and Fig. 17-6 can be used. For this purpose 
S is replaced by t L, L by I and J by L, where ^ is the orbital 
moment of the ionic term, I the orbital moment of the jumping 
electron and L their resultant. 

In the iron frame elements, though the relative intensities of 

* Ornstein and Burger, ZP, 1926, 40 403. 

t Russell and Meggers, Bur. of Standards, Sci. P. 1927, 22 332. 



XVII] 



THE IRON-FRAME ELEMENTS 



105 



the multiplets are admirably regular, the relative intensities 
within the multiplets are often abnormal. Russell's* visual 
estimates showed that in Ni I components of small J give fainter 
lines than they should, and later measurements amply confirm 
him. Not only are individual intensities irregular, but also the 
sums taken over all the terms of a multiplet with the same J. 



Statistical 
weight 


5 


7 


9 


11 


13 


Sum 


Quotient 


3 


(30) 
9-5 








___ 


Theory 
Expt. 


(29-7) 
9-5 


(9-9) 
3-2 


5 


(8) 
11 


(41) 
16 





__ 





(49-5) 

27 


(9-9) 
5-4 


7 


(0-5) 
^1 


(12) 
24-5 


(57) 
25 








(69-2) 
50-5 


(9-9) 

7-2 


9 





(0-6) 
~1 


(12) 
29 


(76) 
44 





(89-0) 
74 


(9-9) 

8-2 


11 


Theory 
Expt. 





(0-3) 
-1 


(8) 
41 


(100) 
100 


(108) 
142 


(9-9) 
12-9 


Sum 


(38-5) 
21-5 


(53-8) 
41-5 


(69-2) 
55 


(84-6) 

85 


(100) 
100 


__ 


__ 


Quotient 


(7-7) 
4-3 


(7-7) 

r>-9 


(7-7) 
6-1 


(7-7) 

7-7 


(7-7) 

7-7 







Fig. 17-13. Comparison of theoretical and experimental intensities in a F-*G 
quintet of Ni I; this quintet arises as c! 8 s ( 4 F) 5s 5 F->d 8 s ( 4 F) 4p 5 G. 

Fig. 17-13 shows this; for when the sum rule is valid, the intensity 
sum divided by the statistical weight yields a constant, but in 
Ni i and Co i the quotient varies from one J to another. 

In a general way spectroscopists have long realised that the 
Russell-Saunders coupling, which predominates on the left-hand 
side of the periodic table, gives way to less regular coupling as one 
passes to the right; so that no one was surprised when titanium 

* Russell, PR, 1929, 34 825. 



106 INTENSITY RELATIONS [CHAP. 

was shown to obey the intensity laws more closely than nickel. 
Nickel and cobalt indeed form the ultimate members of a series, 
which grows progressively less regular. In Ti n 62 per cent, of the 
lines obeyed the formulae to within 5 per cent., but in Ti i, where 
Harrison* measured twenty -six strong multiplets, the proportion 
was down to 58 per cent.; in chromium f and manganese J still 
more violations were observed, while in cobalt and nickel hardly 
a single multiplet is regular. 

Various efforts have been made to trace the cause of the 
irregularity. In Zri many intensities are abnormal because two 
terms of the same configuration and the same J have also nearly 
the same energy; these terms share their intensities, just as they 
share their magnetic splitting factors. In particular, the transition 
4d 2 . 5s . 5p 1 F 3 ^ 4d 3 . 5s 5 F is observed because d 2 . sp 1 F 3 lies near 
d 2 .sp 5 D 3 , their energies being 24,387 and 23,889 cm.- 1 respec- 
tively. || And as the multiplet separations become greater as one 
passes from left to right across the table, the multiplets overlap 
and perturb one another more . ^ But adequate as this explanation 
may be in its place, it is necessarily unable to show why lines 
involving small values of J are weak compared with those in 
which J is larger unless indeed many lines of lower multiplicity 
and therefore in general smaller J remain unidentified. Moreover, 
this explanation would suggest strong correlation with departures 
from the interval and Zeeman rules; but in fact Frerichs,** having 
examined selected multiplets from some elements of the iron 
frame, found that the correlation with the interval rule is poor, 
while Harrison in his detailed study of titanium found no corre- 
lation with either rule. Often those multiplets which split 
irregularly in the magnetic field and have irregular intervals 
obey the intensity laws well, while those which have regular 
values of g obey the intensity laws badly. And an attempt to 

* Harrison, JOSA, 1928, 17 389. 
t Allen and Hesthal, PR, 1935, 47 926. 
J Seward, PR, 1931, 37 344. 
Ornstein and Buoma, PR, 1930, 36 679. 
|| Kiess, C. C. and Kiess, H. K., BSJ, 1931, 6 621. 
f Harrison and Johnson, PR, 1931, 38 773. 
** Frerichs, AP, 1926, 81 842. 



XVII] THE IKON-FRAME ELEMENTS 107 

attribute the abnormal weakness of certain lines to the abstrac- 
tion of energy by inter-system lines was no more successful. 

5. Alkali doublets 

In general the intensity ratio in a series of multiplets is in- 
dependent of the serial number, but this is not true of the principal 
doublets of the alkalis nor of the similar doublets of Tli. 

The controversy* about the alkali doublets has lingered on for 
many years because of the great experimental difficulties, the 
most serious being self-absorption, which can be avoided only by 
working at low temperatures and low current densities; but the 
general features are now clear (Fig. 17-14). The diffuse and funda- 



Ele- 
ment 


Doublet 


Intensity ratio 


Transition 


Wave- 
length, A. 


Calcu- 
lated, 
Fermi 


Experimental 


Na 
Kb 
Cs 


2 2 P~>1 2 S 
2 2 P->1 *S 
3 2 P^ 2 S 
2 2 P-> 2 8 
3 2 P-> 2 S 
4 2 P^ 2 S 
3 2 P-> 2 S 
4 2 P-> 2 S 


5890-96 
7665-99 
4044-47 
7800-947 
4202-16 
3587-92 
4555-93 
3877-89 


2-0 
2-0 
2-16 

? 

2-60 
2-97 
4-3 
7-15 


Ro. 1 1-98 
Ra. 1-91 
Ra. 2-10 
Ra. 1-85 
H. 2-55, K.H. 2-71, Ro. 2 2-58 


H. 3-25, K.H. 3-32, Ro. 2 2-90 
F.W. 3-3, Ra. 3-85 
K.H. 8-50, Ro. 2 7-40, F.W. 4-6, H. 8-0 



Fig. 17-14. Intensity ratios of some principal doublets of the alkalis. 

Observers 

F.W. Fiichtbauer and Wolff, AP. 1929, 3 359. Extrapolated to allow for self- 
absorption. 

H. Hiibner, AP, 1933, 17 781. Photographic comparison of lines emitted by 
burner at 2800. 

K.H. Kohn and Hiibner, PZ, 1933, 34 278. Emission spectrum. 

Ra. Rasetti, N. dm. J924, 1 115. Anomalous dispersion. 

Ro. 1 Roschdostwenski, AP, 1912, 39 307. Anomalous dispersion. 

Ro. 2 Roschdostwenski, T. Opt. 1., Petrograd, 1921, 13 1. Anomalous dispersion. 

mental doublets give the normal ratios of 9:5:1 and 3:2 in caesium, f 
and presumably in all other spectra; in the principal series, on the 
other hand, the normal ratio of 2 : 1 is found only in sodium and 
potassium J; the deviation increases rapidly with atomic number 

* Joos, Hb. d. Expt. Phys. 1929, 22 313. 

t Filippov, ZP, 1927, 42 495. 

% Fiichtbauer and Wolff, AP, 1929, 3 359. 



108 INTENSITY RELATIONS [CHAP. 

and is quite unmistakable in caesium. In the latter Rasetti* and 
Roschdostwenski,f both of whom used the accurate method of 
anomalous dispersion, found ratios of 3-85 and 7-40 in the second 
and third principal doublets respectively; while SamburskyJ 
states that after rising to a maximum value of 25 : 1 in the fifth 
doublet, the intensity ratio decreases to 5 : 1 in the eighth. In 
the first doublet the ratio deviates very little from the normal 
value of 2 even in caesium . 

This much was known when Fermi applied the quantum 
mechanics to the problem, and showed that if certain terms, 
ordinarily neglected, are taken into account, deviations very 
similar to those observed should arise. Thus theory shows that the 
deviation will increase rapidly with atomic number, but should 
not affect the first doublet of the principal series; while the intro- 
duction of numerical values leads to intensity ratios of 4*3 and 
7-15 for the second and third doublets of caesium; for the first 
doublets theory gives a ratio somewhat less than 2, but the 
difference is too small to measure. The agreement here obtained 
with experiment is probably as close as can be expected. 

In Tl i, which like the alkalis has a single electron outside closed 
shells, similar deviations occur. In the m 2 P U ^ -> 2 2 S$. series, 
experiment shows that the intensity ratios when m = 4, 5, 6, 7 
are 4-4, 6-6, 6-Oand5-2.|| 

6. The Zeeman multiple! 

As with the normal so with the Zeeman multiplet, certain 
simple rules have been established, but these suffice to determine 
the intensity ratios only in the simpler transition; in the more 
complex, reliance must be placed on formulae deduced with the 
aid of the quantum mechanics. 

Three rules are usually cited, ^f but of these the first states only 
the well-known fact that the Zeeman multiplet is symmetrical 
about the undisplaced line. The second adds that the intensity 

* Rasetti, N. Cim. 1924, 1 115. 

f Koschdostwenski, T. Opt. /., Petrograd, 1921, 13 1. 
t Sambursky, ZP, 1928, 49 731. Fermi, ZP 9 1930, 59 680. 

|| Williams and Herlihy, PR, 1932, 39 802. 
If Ornstein and Burger, ZP, 1924, 28 135. 



XVII] 



THE ZEEMAN MULTIPLEX 



109 



sum of all lines originating in one Zeeman level is equal to the 
intensity sum of all lines originating in any other Zeeman level; 
and this holds true if the word 'ending' is substituted for 
'originating'. This law appears at first analogous to the Burger 
and Dorgelo sum rule, the statistical weight of each Zeeman level 
being unity; but further examination shows that the relation is 
closer than analogy, for a term splits to (2J+ 1) Zeeman com- 
ponents, so that the normal multiplet rule is a necessary conse- 
quence of the Zeeman rule. 



M 




1 


2 


_.._ 


1 


1 







1 




1 















-1 










_ 1 




-1 


-1 




-1 


2 





Total intensities 



a 
a* 



Fig. 17-15. Assumed intensities of the Zeeman components of a 3 S 1 -> 3 P 2 line. 

The third rule concerns the polarisation, and states that if the 
various components emitted in any direction are combined the 
resulting beam must be unpolarised. Thus in the normal Zeeman 
triplet observed transverse to the magnetic field, the sum of the 
intensities of the two cr components must be equal to the intensity 
of the TT component. These rules appear simple enough, but the 
simplicity is in part only apparent, for the intensities mentioned 
in the sum and polarisation rules are not the same; the sum rule 
applies to the total radiated intensity, while the polarisation rule 
applies to the intensity observed in a particular direction. Thus 
when a pattern is observed transverse to the field, those oscilla- 
tions which produce a components vibrate in a circle whose plane 
is perpendicular to the magnetic axis; one component of this 
vibration is along the line of sight and so invisible; thus only half 
the radiated intensity of a cr component is observed. On the other 
hand the oscillators which are producing TT components vibrate 



110 INTENSITY RELATIONS [CHAP. 

along the magnetic axis, so that the whole of the radiated inten- 
sity reaches an eye looking transverse to the field. 

As an example of the way in which these three rules are applied 
consider the ^ -> 3 P 2 transition.* Fig. 17-15 gives on the left the 
possible values of the magnetic quantum number M , and on the 
right the total intensity radiated in each transition, the TT and a 
components being separated for convenience. The consequences 
of the symmetry rule are embodied in the notation; the sum rule, 
applied to the components of the 3 P 2 term, states that 



while applied to the 3 S X term it shows that 
6 + 2a 2 = b l + a x + a 3 . 

In order to apply the polarisation rule, elect to observe the 
pattern transverse to the magnetic field; then the argument 



Ele- 
ment 


Line 


Intensity 





7T 


a 


^7T 


Zo 


Theoretical 


5 


15 


30 


30 


40 


30 


30 


15 


5 

3 
6 
3-5 
5 


100 


100 


Mg 
Ca 
Zn 
Cd 


5183 
6162 
4810 
5085 


Observed 
Observed 
Observed 
Observed 


5 
4 
5 
5 


16 
13 
15 
15 


30 
29 
29 
29 


32 
30 
32 
32 


39 
41 
41 
41 


32 
28 
31 
31 


30 

28 
29 

27 


14 
14 
15 
14 


103 
99 
104 
104 


98 
94 
97 
95 



Fig. 17-16. Observed intensities of the Zeeman components of a 3 S 1 -> 3 P 2 line 
in various spectra. 

given above shows that the total radiated intensity of the TT 
components must be equal to half the total radiated intensity of 
the & components; that is, 

6 + 2&! = % {2a x + 2a 2 + 2a 3 } 
= a 1 + a 2 + a 3 . 

The three simple rules thus determine the four unknown ratios, 
being satisfied by the values 



These predictions for the 3 S 1 -> 3 P 2 line have been amply con- 
firmed by Van Geel,f as Fig. 17-16 shows; moreover, similar 

* Ornstein and Burger, ZP, 1924, 29 241. 
t Van Gteel, Diss. Utrecht, 1928, 60. 



XVII] 



THE ZEEMAN MULTIPLEX 



111 



predictions for the two other lines of the triplet are equally 
satisfactory (Fig. 17-17). 



Lino 


Transition 


Intensity 


a 


7T 


<T 


STT 


2a 


6122 


S^Px 


Theoretical 
Observed 


15 
17 


15 
16 


30 
30 


30 

28 


15 
15 


15 
15 


60 

58 


60 
63 


6102 


Sr^'P. 


Theoretical 
Observed 


10 
9 


20 
20 


10 
10 


20 
20 


20 
19 



Fig. 17- 17. Intensities of the Zeeman components of two calcium lines. 

Though these three rules suffice when the J values of the two 
terms concerned are small, in more complex transitions resort 
must be had to the correspondence principle* or to the quantum 
mechanics.! Calculations based on these principles show that 
for the transitions </->(J 1), the intensities are given by 

a Jump M->(M-l) I_ = p(M)p(M-I), 

77 Jump M->M / = 

a Jump (M-l)^M I + = 
while for the transitions / -> J 

77 Jump M^>M I Q = 

a Jump M~>(M-l) I=p(M)q(M-l). 

or (M-l)->M 

In these equations the transitions considered make J and M 
the larger of the two quantum numbers concerned; while p, q and 
r are abbreviations, defined by 



The intensities given by these formulae are the total radiated 
intensities. The formulae for the transition from (/ 1) to J are 
not quoted, because the intensities are independent of the direc- 
tion in which the electrons jump, so that one may consider always 



Intensities calculated from these formulae are given in Fig. 
17-18; as the formulae do not contain L or S the Zeeman inten- 

* Honl, ZP, 1925, 31 340; AP, 1926, 79 288; Kronig, ZP, 1925, 31 885. 
t Heisenberg and Jordan, ZP, 1926, 37 263. 



112 



1 ' M> K/f 

7A? 

M" X l 



2 2 "' ?\ 



M" 



3 3 M' 01 

l\ /l 
(0) 6 (1) 5 (4) 3 (9) 
I/ \l/ \|/ \! 

jr o V 2 7 X 3 



A\ A\ A 



5 5 M' 1 

l\ /l\ 
(0) 15 (1) 14 (4) 12 (9) 9^(16) 5(25) 



M* 0123 



' * ?\ /i\ A A A A /? 



M . 



1 1 M' O v A 2 v 3 V 4 5. 

l\ /l\ /l\ /l\ /l\ /l 
(0) 28 (1) 27 (4) 25 (9) 22(16) 18(25) 13 (36) T. (49) 

I/ \l/ MX M/ M/ \'/ \l/ \l 

3/" X 1 2 3 4 7 N 5 N 6 7 

Fig. 17-18 a. Integral; AJ = 0. 

Table of Zeeman intensities. The table is divided into four sections according 
as J is integral or half integral, and according as AJ is or 1. 



J' J 

1 M' 





l\ 
(1) IN 



M" 




113 




M 



3 4 M' 




4 5 Jtf' 0, 




5 6 




6 7 




28 / \ 36 
(49) X (48) (45) 





Fig. 17-18 &. J integral; AJ = 1. 



114 



/t 

(1) 



-\ A /,' 

8 (1) 6 (9) 



2* 2| M' -4 i 14 24 

\ /l\ / l\ / I 
18 (1) 16 (9) 10 (25) 



3J Jr -J i IV 21 31 

\ /?\ /r\ /r\ /r 

32 (1) 30 (9) 24 (25) 14 (49) 



44 " '"' -'\ /f\ /',\ /N / 3 ,\ 



5J If' -i 1 It 24 /3i. 4i 54 

\ /l\ /l\/l\/l\/l\/l 

72 (1) 70 (9) 64 (25) 54(49)40 (81) 22(121) 

/ \l/ \ I / \ I / \ I / V I / \ I 
M" -i X i li 24 X 34 N 44 7 X 54 



64 it' -4 4 N IK ,a4 x 34. 44 54 64 
\ /l\ /l\ /l\/l\ / |\ / |\ /i 

98 (1) 96 (9) 90 (25) 80 (49) 66 (81) 48(121)26(169 

/V/V/V/V/V/Xi/V 

M" -4 \4 7 \^ X 24 X 34 *i 54 6J 

Fig. 17-18 c. J half- integral; AJ = 0. 



1 il 



M" 



115 



il 21 ir -j 



-1 



/l\ 

3 (6) 

x 1 



H 



(4) 

>i 



21 



21 31 M' -i 



A 



HO 



15 



21 



(6) 



41 



-.V 



K 

' UP 



iK 



\ 



21 



2 K 



28 



10 (20) Y (18) A ( 14 > 



V 



3 



I/ 



/:' 

(8) 



X 36 



31 



41 



41 51 M' -i 



x x x x X 

x /|21 / 28 /| 36 /| 45 /| 55 
15 (30) Y (28) X (24) Y( 18 ) X (10) 
X \ I 10 \ I 6 \ I 3 \ | /I \ | 

x X X 



51 61 



JP -1 



28 



15 



2 1\ 31 41 51 N 

/I /l \/\ <* / 78 
(36) Y(30) Y( 22 ) X( 12 ) \ 



10 



3 



1 



U 



2f 



31 7 



4^ 



5i 



6J 



61 71 






I 36 



28 (56) Y (54) 

I 21 \ I / ] 
I/ \V 



055 
50) X (44) 



X 2\ *\ / \ 

X I 78 / I 91 / I 105 
\/ ' \/ ' \ 

(36) Y ( 26 ) X ( 14 ) \ 
' \ I ' \ i i 

/3 V 1 \ 4 

; ol 61 



Fig. 17-18 d. J half -integral; AJ = 1. 



8-2 



116 INTENSITY RELATIONS [CHAP. 

sities are a function of J only, so that the components of the lines 
8 P 2 -> 3 S 1 and TJJ-^D! have the same intensity ratios, though 
they do not occupy the same positions. Like the simpler rules 
these formulae have been confirmed by the experiments of Van 
Geel, who has measured lines in the octet system of Mn i, and in 
the septet and quintet systems of Cri (Figs. 17-19-17-21); but 



24 24 



20 



12 



Theory 



19-4 



11*4 



Observed 



10 



15 



21 



3-4 



6-6 



16-8 



21 



Fig. 17-19. Intensities of the Zeeman components of the 4754 A. line of Mn i; 
this line arises as a 8 S 3i ->z 8 PV The pattern is (7) (3) (5) 9 11 13 15 17 19/7. 
On the left are the theoretical, and on the right the measured intensities, the 
brightest ?r and o components being adjusted to fit. After Van Geel, Diss. 
Utrecht, 1928, 65. 

work on the iron row shows that the agreement is not always as 
good as that shown in the lines chosen here as illustrations. 

Having obtained satisfactory intensity formulae for normal 
multiplet lines, two extensions suggest themselves; first, one may 
enquire whether the formulae are applicable to inter-system lines, 
and second, what intensities are to be expected in the partial 
Paschen-Back effect. To these questions also Van Geel has 
offered some answer.* 

As an inter-system line he chose ^-^Pg, 3663-3 A., of Hgi, 

* Van Geel, Diss. Utrecht, 1928 and ZP, 1928, 47 615. 



XVII] 



THE ZEEMAN MULTIPLET 



117 



80 



60 



80 



Theory 



10 



30 



60 



55 



Observed 



27 



62 



Fig. 17-20. Intensities of the Zeeman components of the 5205 A. line of Cr i; 
this line arises as z 5 P 1 ->a 5 S 2 ; the pattern is (0) (1) 3 4 5/2. After Van Geel, 
Diss. Utrecht, 1928, 68. 



18 19-3 



16 



10 



Theory 



15 



9-7 



Observed 



10 



(not measured) 



15 



15 



Fig. 17-21. Intensities of the Zeeman components of the 5208 A. line of Cr i; 
this line arises as z 5 P 3 -^a 5 S 2 ; the pattern is (0) (I) (2) 3 4 5 6 7/3. After Van 
Geel, Diss. Utrecht, 1928, 67. 



118 INTENSITY RELATIONS [CHAP. 

and obtained the intensity pattern shown in Fig. 17-22. This is 
certainly rather irregular, but then so is the pattern of the 
neighbouring triplet line, 3 D 1 ~> 3 P 2 , 3662-9 A. (Fig. 17-23), and 



80 



82 















7 


3 




2 


2 















2 


2 2 


3 




i 

3 


) 3 


2 


T 


2 

heor 



3 

y 


3 


2 



2 


3 
3 


! 3 


2 
5 

ot 


2 2 

serv 


1 
3 

ed 


16 
22 




Fig. 17-22. Intensities of the Zeeman components of the 3663-3 A. line of Hg i; 
this line arises as 3 x D 2 ->2 3 P 2 , and the pattern is (I) (2) I 2 3 4/2. After Van 
Geel, Diss. Utrecht, 1928, 77. 



72 



70 



72 



42 



27 



54 



I 1 



Theory 



30 



54 



Observed 



62 



Fig. 17-23. Intensities of the Zeeman components of the 3662-9 A. line of Hg i; 
this line arises as 3 3 Dj->2 3 P 2 ; the pattern is (0) (2) 1 3 ,5/2. After Van Geel, 
Diss. Utrecht, 1928, 77. 

as this sd configuration produces two diads instead of a singlet 
and a triplet, the coupling must be abnormal. 

For the intensities of the partial Paschen-Back effect appeal 
must be had to the quantum mechanics, which has been applied 
by Darwin* and others to predict both the intensity and displace- 
* Darwin, C. G., PRS, 1927, 115 1. 



XVII] 



THE ZEEMAN MTJLTIPLET 



119 



Theory 



24 



42 42 



3 P, 3 D 



i I LJ 7 

cr 3 



36 
104 



42 



7T 6 



(T 



42 



27 27 



54 54 



Experiment 



16 16 


1 


2 


1 


2 


1 


2 


7T 














<T 2 






1 1 
2 2 






1 
2 


6 


6 6 


6 



3829 A 



24 



42 



46 



3832 A 



36 
100 



2 I 
12 



16 
30 28 



3838A 



53 52 



Fig. 17-24. Intensities of the Zeeman components of a diffuse triplet of Mg i; 
the lines arise as 3 3 D->2 3 P l z . This is an example of the partial Paschen 
Back effect. After Van Geel/Diss. Utrecht, 1928, 84. 



120 INTENSITY RELATIONS [CHAP. 

ment of the magnetic components of any normal multiplet in any 
field. That this theory is valid few doubt, for it is of very general 
application and is known to give correct results in weak and 
strong fields. Further confirmation in intermediate fields is 
however still welcome, so that Van GeeFs measurements on a 
Mgi triplet, which exhibits the partial Paschen-Back effect, are 
worth quoting (Fig. 17-24). They confirm the theory admirably.* 

7. Rates ultimes 

A common method of analysing an unknown salt is to add a 
little to a carbon arc ;| if the powder happens to be a pure calcium 
salt, a great many calcium lines will appear, but as the proportion 



Arc spectra 


Spark spectra 


Element 


Wave- 
length 


Terms 


Element 


Wave- 
length 


Terms 


K 
Ca 

Sc 


7665 
4227 
4779 


"PH-^S* 

iP^S/ 
*F H ^D 21 


Ca 
Sc 
Ti 


3934 
3614 
3349 


2 Pir^ 2 Si 
3 F 4 ->*D 3 
4 G 5r > 4F 4i 


Ti 
V 




3635 
3185 
4254 


3 G 5 ->"F 4 

sics- 


V 

Cr 
Mn 


3093 
2836 
2576 


5 G 6 ->*F 6 

6 *V* 6 I>4i 

7 r 4 Vs3 


Mn 
Fe 
Co 

Ni 


4031 
3720 
3452 
3415 


:E:C:?? 

4 G 6i -> 4 F 4i 


Fo 
Co 

Ni 
Cu 


2382 
2389 
2416 


6 F 5i ->D 4i 

*G 6 -> 6 F 5 
4 G 5i ->*F 4i 



Fig. 17-25. Some raies ultimes. 

of calcium in the powder is diminished step by step, the weaker 
lines successively disappear until finally only one is left; this is 
known as the raie ultime, and is in fact the 4227 A. line, arising 
as ^-^SQ. This method of analysis was developed by de 
Gramont.J 

The raies ultimes are not necessarily the strongest lines in the 
spectrum as ordinarily produced, nor are they in general the lines 

* See also Back's measurements on a diffuse doublet of copper, Vol. i, 117. 

f Twyman and Smith, Wavelength tables of spectrum analysis, 1931. Ryde 
and Jenkins, Sensitive arc lines of 50 elements, 1930. Both book and pamphlet 
are published by Adam Hilger. 

t De Gramont, Comptes Rendus, 1920, 171 1106. 



XVII] RAIES ULTIMES 121 

which require the least energy to excite them, the resonance lines. 
Instead they are determined by four conditions, of which two are 
energy conditions.* The first states that the lower term is always 
the ground term, and the second that the higher term is of the 
same system. As inter-system lines are in general weaker than 
lines arising within a system, this condition is surprising only as 
excluding lines, such as the 2536 A. ^-^So line of Hgi, which 
are exceptionally strong for other reasons. Subject to these two 
conditions, and in part also to the fourth, the energy required to 
excite the line must be as small as possible. The fourth condition 
states that when the energies are nearly equal, the raie ultime 
will usually arise from a transition in which &L is 1 in prefer- 
ence to one in which it is + 1 ; but in aluminium and its homo- 
logues the 2 D term lies so much higher than the 2 S that the raie 
ultime is 2 S$ -> 2 P$ , the fourth condition notwithstanding. 

BIBLIOGRAPHY 

Frerichs in the Handbuch der Physik, 1929, 21, deals with theory and its 
empirical justification. Van Geel, Intensiteitsverhoudingen van Magnetisch 
Gesplitste, Spectraallijnen, 1928, contains a thorough study of Zeeman in- 
tensities; this is a dissertation presented to the University of Utrecht. 

For experimental methods: 

Dobson, Griffith and Harrison, Photographic photometry, 1926; 
Ornstein, Moll and Burger, Objektive Spektralphotometrie, 1932. 

* Laporte and Meggers, JOS A, 1925, 11 459. Meggers and Scribner, how- 
ever, have proposed a new rule : 'A raie ultime originates in a simple interchange 
of a single electron between an s and a p state, usually preferring configurations 
in which only one electron occurs in these states.' The raie ultime of Hf IT is 
5d 2 . 6p 4 G 5 j . . . 5d 2 . 6s 4 F 4t , though 4 F is not the ground term. BSJ, 1934, 13 
657; 1935, 14 629. 



CHAPTER XVIII 
THE SUM RULES AND (jj) COUPLING 

1. Deviations from the Russell-Saunders coupling 

The low terms of the light elements are easily divided into multi- 
plets, and the multiplets into configurations. In general the com- 
ponents of a multiplet differ in energy by an amount which is 
small compared with the height which separates one multiplet 
from another; and similarly the interval separating two terms 
of a configuration is usually small compared with the height 
which separates one configuration from another. Each level is 
characterised by a certain value of J, and each multiplet by 
values of L and S. J and L are determined primarily by selection 
rules and S by the number of components in a multiplet; but in 
the allotment of quantum numbers the interval ratios, magnetic 
splitting factors and intensities all have to be considered. More- 
over, J is the vector sum of L and S. All these regularities are 
regarded as arising in the Russell-Saunders coupling of the 
electrons, and conversely any irregularity is attributed to some 
distortion of the coupling. 

Deviations from these rules occur frequently in elements of 
high atomic weight, and in the high terms of a spectrum; they are 
rather more common on the right-hand side of the periodic table 
than on the left. But the various rules are not equally sensitive; 
the interval ratios are often abnormal when the g factors and 
intensities are normal; while the g factors are rather more easily 
disturbed than the intensities. This must not be taken to mean 
that terms in which the interval ratio is normal and the inten- 
sities abnormal do not sometimes occur; but in the analysis of an 
irregular spectrum like Ni i intensities usually give the surest clue 
to the names of the terms. There are spectra, however, such as 
argon, in which none of these clues are worth much, for the terms 
are no longer divided into multiplets but only into configurations; 
values of L and 8 cannot then be assigned. Finally, there exist 



CH. XVIII] DERIVATIONS FROM RUSSELL-SAUNDERS 123 

a few spectra in which different configurations lie at the same 
height and so perturb one another. 

Yet however abnormal a spectrum, the J values of each con- 
figuration remain unchanged, and there is strong evidence that if 
the displacements, g factors and intensities are summed for terms 
having the same values of J, then the result is the same in all 
spectra. The question remains over how many terms the sum is 
to be taken, and in this the energy seems to be crucial; in simple 
spectra in which each multiplet is well separated from other 
multiplets, the rule is valid for each multiplet separately; when 
the multiplets are intermingled, but the configurations distinct, 
then the sum must be taken over all terms of the configuration; 
this is the form in which the sum rules are usually met. But when 
two configurations overlap, then the sum must extend over both. 

2. Invariance of the g sum 

In the Zeernan and Paschen-Back effects the sum of the 
magnetic energies of all terms, which have the same M and 
which arise from a single multiplet, is proportional to the field; 
or if the increments of energy are measured in terms of the normal 
increment cho m , then their sum is independent of the field, and 
I l Mg= S (M L + 2M S ). 

J L.S 

This sum rule makes possible the calculation of the weak field 
splitting factor without the aid of the quantum mechanics; 
applying, as it does, however, only to a single multiplet, it is 
valid only when the coupling is Russell-Saunders. 

The rule may be generalised, however, for an electron con- 
figuration by summing over all terms of a configuration. For if 
the sum is independent of the field intensity, it should not change 
in a field so strong that each electron vector precesses inde- 
pendently about the magnetic axis; the coupling is then 

{(^HKlaHJ...^^^)...} 
and the sum rule reads 



M is of course S (m t -i-m s ). As an example, consider a pd con- 
figuration giving rise to the six terms 3 PDF, X PDF (Fig. 18-1). 



124 SUM RULES AND (jj) COUPLING [CHAP. 

Among these there are four with components in which M is 3, 
and in these S (m t + 2m s ) is 14. In a weak field these components 
appear as parts of the 3 F 4 , 3 P 3 , 3 D 3 and ^3 terms, whose magnetic 
splitting factors are , jf , and 1 respectively, so that Sgr is 4| 
and %Mg is 14 as theory requires. 



*! , 




m m 


S(ro,+ro,) 


2(m, + 2w,) 


SrojW, 














1 2 


1 2 
1 


1 t 


4332 
3221 


5331 
4220 


H i -i -H 
100-1 





-1 




2110 
100-1 


3 1 1-1 

200-2 


i i -i -1 
01-10 




-2 




-1 -1 -2 


1 -1 -1 -3 


-i It -It i 




2 
1 


t t 


3221 
2110 


4220 
3 1 1-1 


1-1 1-1 









100-1 


2 0-2 


0000 




-1 




0-1-1-2 


1 -1 -1 -3 


illi 

222? 




-2 




-1 _2 -2 -3 


-2 -2 -4 


-1 1-1 1 




-1 2 

1 


t i 


2110 
1 0-1 


311-1 
200-2 


i -it H -i 

0-110 









-1 -1 -2 
-1 -2 -2 -3 


1 -1 -1 -3 

-2 -2 -4 


-i -i i i 

-1001 




-2 




-2 -3 -3 -4 


-1 -3 -3 -5 


-it -i i H 



Fig. 18' 1. Magnetic quantum numbers of a pd configuration in a field so strong 
that the electronic vectors precess independently. 

Thus far the sum has been assumed independent only of the 
field, but if it remains unchanged in a field so strong that all 
electronic vectors are uncoupled, it must surely be independent 
of the coupling. And a logical consequence of this hypothesis is 
that the sum of the splitting factors is independent of the coupling 
when summed over all those terms of a configuration which have 
the same value of J. For let the sum of the (/values of terms having 
J a be Z# a , and when M = b let %Mg = v b ; then if the highest 
value of J is J f , when M = J', 



or 



and as the right-hand side is independent of the coupling, so also 
is Sgr,,. When M = (/'-!), 



Again, the right-hand side is independent of the coupling, and so 



XVIII] INVARIANCE OF THE g SUM 125 

therefore must ^(J'_D be. Clearly this argument can be extended 
to all values of J. 

The constancy of the g sum was first deduced by Pauli* and 
Lande| from theory, but in the last decade experiment has amply 
confirmed it. In the spark spectrum of chromium J the 4 P^ and 



Term 


g factor 


Lande 


Empirical 


F t 
"D* 
4 D* 
4 P* 


-0-667 
3-333 

2-667 


-0-671 
2-841 

3-145 


Sum 2g 


5-333 


5-315 



Fig. 18-2. g factors of those terms of the 3d 4 ( 5 D) 4p configuration of Cr n, 
which have J = J . An example of the sum rule. 



Term 


g values 


g sums 




Lande 


Empirical 


Lande 


Empirical 


*PI* 


1-60 


1-60 


1-60 


1-60 


Sit 


1-73 
1-33 


1-63 
1-43 


I 3-06 


3-06 


S! 


2-67 
0-67 


2-53 
0-81 


1 3-34 


3-34 



Fig. 18-3. g factors of the p 4 ( 3 P) 5s terms of A n, showing that the sum rule is 
obeyed. 

6 I> terms of the 3d 4 ( 5 D) 4p configuration show very irregular g 
values, but the sum for the four terms which have a J value of 
| agrees closely with that predicted by Lande (Fig. 18-2). 
Other examples of the sum rule are to be found in the spark 
spectra of neon, argon|| and krypton,TJ in Lai, Lan** and 
Agn.tt Fig. 18-3, which cites the p 4 ( 3 P) 5s configuration of An, 

* Pauli, ZP, 1923, 16 155. 

t Lande, ZP, 1923, 19 112. 

t Kromer, ZP, 1928, 52 542. Cm. 

Bakker and de Bruin, ZP f 1931, 69 19. Ne n. 

|| Bakker, K. Akad. Amsterdam, Proc. 1928, 31 1041. An. 

If Bakker and de Bruin, ZP, 1931, 69 36. Km. 
** Russell and Meggers, B8J, 1932, 9 665. Lai, Laii. 
ft Shenstone and Blair, PM , 1929, 8 765. Ag n. 



126 SUM RULES AND (jj) COUPLING [CHAP. 

brings out also one important corollary of the sum rule; 4 P 2i is the 
only term arising from this configuration which has a J value of 
2, and so its g value must be that predicted by Lartde whatever 
the coupling. 

Configurations in which the g sum is abnormal are rare, but not 
unknown; usually the one which deviates is known to overlap 
another in the energy scale. In K n* the g sum of terms having a 
J value of 1 in the configuration 3p 5 ( 2 P) 4s is 2-57 0-02 instead 
of 1-50; this configuration overlaps 3p 5 .3d, but not all the 3d 
levels are yet known, so that the combined g sum cannot be 
calculated. In Rbii a similar deviation occurs, where two 
configurations overlap. f 

That the g sum rule is broken when two configurations overlap 
is of interest, because the quantum mechanics shows that the sum 
of the magnetic energies of all states having the same projection 
of angular momentum on the axis of the magnetic field is in- 
dependent of the coupling between the vectors. As the sum has 
to be taken over all states of the atom, the theory in this form does 
not give much information; if, however, only states which have 
nearly the same energy influence one another, J all empirical 
results are seen to hang together. The rule is valid for a single 
multiplet in spectra whose coupling is Russell-Saunders, since a 
single multiplet is there isolated; it is valid for a configuration 
when a configuration is isolated; and when two configurations 
overlap it is still probably true if the sum is extended over both, 
though this point has not yet been tested. 

3. Invariance of the T sum 

In the Paschen-Back effect evidence is found that the sum of 
the displacements of those components of a multiplet, which 
have the same M , remains constant when the strength of the 
magnetic field varies. That the similar law for the g sum remains 
valid for any coupling provided the sum is extended to all terms 
of a configuration, suggests a similar extrapolation for the F sum. 

Compared with the g sum, the F sum is unsatisfactory; whereas 

* Whitford, PR, 1932, 39 898. 

t Laporte, Miller and Sawyer, PR, 1931, 38 843. 

% Goudsmit, PR 9 1931, 37 664. 



XVIII] 



INVARIANCE OF THE F SUM 



127 



theory can dictate absolute g values, it can dictate displacements 
only relative to an undetermined centroid, and only as a multiple 
of an undetermined constant A. Accordingly, the F sum rule is 
not susceptible of direct verification as the g sum rule is; and 
indeed had there not been some regularities which cried aloud for 
explanation, it seems hardly probable that Goudsmit could have 
pushed ahead on so flimsy a scaffolding. 



Parent spectrum 


Derived spectrum 


Spectrum 


Interval 


Spectrum. 


Interval 




p.A 2 P 




( 2 P) ns A 3 P 


On 


64 


Ci 


3s 60 4s 45 5s 54 


Sin 


287 


Si i 


4s 275 5s 283 


Pm 


560 


PII 


4s 527 5s 547 


Siv 


950 


S in 


4s 450 5s 924 


Civ 


1495 


01 iv 


4s 1446 


Gen 


1768 


Ge i 


5s 1661 6s 1740 7s 1765 


Snu 


4253 


Sin 


6s 3988 7s 4201 




p 3 .A 2 D 




( 2 D)/is.A 3 D 


On 


30 


Oi 


3s 20 




p 3 .A 2 P 




( 2 P)s.A 3 P 




5 




3s 17 




p 5 .A-P 




( 2 P)ws.A 3 P 


Ne n 


782 


Nei 


3s 777 4s 780 5s 778 6s 781 


Nam 


1371 


Nan 


3s 1357 


An 


1431 


Ai 


4s 1410 5s 1397 6s 1414 7s 1433 


Km 


2164 


KII 


4s 2642 


Km 


5371 


Kri 


5s 5220 


Xeii 


10117 


Xei 


6s 9129 




cP.A 2 D 




( 2 D)ws.A 3 l> 


Nin 


1507 


Nil 


4s 1508 5s 1506 6s 1506 


Pdn 


3539 


Pdi 


5s 3530 6s 3532 7s 3539 


Ptn 





Pti 


6s 10132 



Fig. 18-4. Comparison of doublet intervals with those of the triplets derived 
from them, when an s electron is added. 

The regularities mentioned connect the arc and spark spectra of 
an element. Thus in a number of spectra the triplet resulting from 
the addition of an s electron to a doublet ground term has the 
same extreme interval as the doublet. The 3 P 2 interval from the 
s 2 .p( 2 P)ns configuration of Sii is equal to the 2 P interval of 
Sin, and this is true also of isoelectronic spectra. Again, the 
( 2 P) ns 3 P 2)0 interval of the inert gas spectra is independent of the 



128 SUM RULES AND (jj) COUPLING [CHAP. 

chief quantum number n and equal to the 2 P interval of the ionic 
ground term; and the same is true of the very similar d 9 ( 2 D) m 
configuration in nickel and palladium (Fig. 18-4). Standing in 
contrast to these three groups of spectra in which the arc and 
spark intervals are identical stand the alkaline earth triplets 
whose extreme intervals obey the doublet laws, just as their 
spark doublets do. 

To account for these regularities, assume that the F sum rule, 
like the g sum rule, is valid in a field so strong that the electronic 
spin and orbital vectors precess independently round the field 
axis, provided the sum be then taken over all those terms of a 
configuration which have the same value of M . Then construct a 
table of all the values which i M L and ^M^ can assume in the 2 P 
term of an ion, and of m l and m s for the s electron. Then if a 
sufficiently strong field be postulated, 



and y^am^, 

where A and a are the interval quotients of the ground term of the 
ion and the electron respectively; A is thus determined by the 
ionic term, and a presumably by the Lande doublet formula; 
however, when Fig. 18-5 is made out from these equations, it 
shows that a vanishes provided that m l is always zero, as it is 
when the electron moves in an s orbit. 



t M L m l t M s m 3 


MA y/ 


M L Ms 


M 


r/A 


104* 


i 


1 1 


2 


1 











1 





-1 


~~ 2 


_ j 





-i 


i o 4 -4 


i o 


1 


1 


i 

















-i 


-i 


-1 


-1 


-1 


10-4 i 


-i o 


1 


1 


i 

2 

















-i 


i 


-1 


-1 


i 


i o -4 -i 


-i o 


1 -I 





-i 











-1 





i 


i 


-1 


-2 


i 



Fig. 18-5. Electronic and atomic displacements in a system consisting of an ion 
in a 2 P state and an s electron. 



xvni] 



INVAKIANCE OF THE T SUM 



129 



The r sums are to be taken over terms having the same value 
of M , so that this table must be re-arranged in the form of 
Fig. 18-6. 



\ 






\Jf 


-2 -1 


i 


2 


M a \ 








I 


-k 





t 





-t o 


* 







4 


-i 




-1 


J o -j 






zr/A 


I - 1 





J 



Fig. 18-6. Atomic displacements of the system of Fig. 18*5 in a strong field. 

But the F sum is independent of the coupling, so that these 
sums must be those found empirically in a weak field. If F 2 , T l9 
IY and F are the displacements of the 3 P 2 , 3 P 1 , 1 P 1 and 3 P terms 
respectively, then arranging these by their M values we obtain 
Fig. 18-7. 



v _ . 


-2 -1 1 


2 


2 
1 
1 



IV ' i\> r\' 

ID 



Fig. 18'7. Atomic displacements of the system of Fig. 185 in a weak field. 
Accordingly P _ j^ 



i+-. 
r =- A] 



These equations show that in the atom 

3p 3p _ p P _ 3 A 
*2~~ *Q~ * 2~ L 0"" 2^9 

whatever the coupling; and moreover that this is equal to the 
2 P interval of the ion. 

When the addition of an s electron to a 2 D term is considered, a 
similar argument shows that 



A being now the interval quotient of the ionic 2 D term. While 



130 SUM RULES AND (]]) COUPLING [CHAP. 

when the method is applied to the alkaline earth triplets, in which 
a p or d electron is added to a 2 S ground term, it shows that the 
extreme triplet interval should depend only on the electronic 
quotient a and not at all on the ionic quotient A. Thus the 
invariance of the displacement sum satisfactorily explains the 
intervals observed in three different columns of the periodic table. 

But if these were the points chiefly needing explanation, they 
do not limit the usefulness of the theory; with its aid Slater* 
has explained why the alkali doublets fit a formula developed for 
X-ray spin doublets, while Goudsmitj has related together the 
interval quotients of the numerous terms which may arise from a 
single configuration. 

As an example of an X-ray spin doublet, consider the Lu Lm 
doublet which arises from a p 5 group of electrons. The orbital 
and spin vectors of this group, restricted as they are by the 
exclusion principle, appear in Pig. 18-8. 



m l 


til. 


^L MS 


y/a 


J/. 


r/a 


110 0-1 


i -i i -i i 


1 i 


i -i o o -\ 


li 


1 

2 




-i 


~i 










110-1-1 


i -i i i -i 


o \ 


i -i o -i i 


* 







~ $ 


-I 










100-1 -1 


i i -i i -i 


-1 i 


1 00-| i 


- A 


* 




-1 


i 

~ 2 


~2 


-H 





Fig. 18-8. Electronic and atomic displacements of a p 5 configuration. 

These permitted combinations are rearranged according to 
their M values in Fig. 18-9, and the sum of the displacements is 
obtained. But the only two permitted values of J are | and l, so 



V 

*s\ 


-H 


-i i 


1* 


-i 


-i 


i o 
o i 


-i 


^1 stla 


-i 


i 1 


-i 



Fig. 18-9. Atomic displacements of a p 5 configuration in a strong field arranged 
by the corresponding values of M and M s . 

* Slater, PR, 1926, 28 291. 
t Goudsmit, PB, 1929, 31 946. 



XVIII] INVARIANCE OF THE F SUM 131 

that if the displacements in zero field are F^ and F u , the dis- 
placements in a weak field must be those shown in Fig. 18*10. 









li 



-i 






Fig. 18-10. Atomic displacements of a p 5 configuration in a weak field. 

Comparison of these two tables shows that, if the F sum is 
independent of the coupling, then 



= a, 



so that 

showing that the interval is equal to that of an alkali P doublet. 
To extend this method to other groups of equivalent electrons 
Goudsmit had to postulate Russell-Saunders coupling of the 
atomic vectors. Thus the d 2 configuration gives rise to the terms 
3 F, 3 P, 1 G, X D and 1 S, or six unknowns, since F is zero in all singlet 
terms. Calculations based on an assumed strong field however 
give only five equations, one for each value of M from to 4; so 
that the F values are indeterminate. Should we assume however 
that the 3 F and 3 P terms obey the Lande interval rule, then the 



V 

M 8 \ 

I 


-4 -3 -2 -1 





1234 


-li -1 


-i 
-i 


i 1 li 
i 





li 

1 lr 

i o -i 

- i -1 -li 


2 
1 


_ 2 


li 1 i 
i -i 

-li 


-1 


i o 
HI i o 


If 


-1 -li 


Sr/a 


li 1 -i -1 


-2 


-1 -i 1 li 



Fig. 1 8' 1 1 . Atomic displacements of a d 2 configuration in a strong field, arranged 
by the values of M and M s . 



132 SUM RULES AND (jj) COUPLING [CHAP. 

displacements of their components may be stated in terms of only 
two unknowns A F and A p . This is shown in Figs. 18-11, 18-12. 



\ Jf 

L.J\ 


-4 -3 -2 -1 





1 2 


3 


4 


|: 


3/4 F 3/4 F 3/4 F 3^4 F 
-;lF -Ay -Ay 
-4Ay -4Ay 


-Ay 
-4 Ay 


3/1 F 3^4 F 
-/IF -Ay 
- 4 A F - 4^4 F 


3.4 F 
- Ay 


3,4 F 


p" 


AP -AP 


AP 
-Ap. 
-2Ap 


Ap Ap 
-Ap 






i 


0000 



















Fig. 18-12. Atomic displacements of a d 2 configuration in a weak field, arranged 
by the values of M and Lj . 

The F sum rule shows that 
when M = 4 3A F = l|a, 

= 3 2A F = a, 

= 2 -2A 



= -2A V -2A P = -2a. 

And these equations are satisfied if 

A _ A i n 
JP ./i F g-ti'. 

Proceeding in this way Goudsmit* was able to calculate the 
interval quotient A of different components of many super- 
multiplets in terms of the interval quotients a of p or d electrons; 
the results are summarised in Fig. 18-13. 

This theory has been strikingly successful in predicting experi- 
mental facts. In the d 7 configuration of Ru n all the terms should 
be inverted except the 2 F term, and so in fact experiment shows 
that they are. f While in the d 3 configuration of Ti nj the relative 
separations are in very fair agreement with theory; Fig. 18-14 
shows this, the separation of the 2 H term having been fitted to the 
experimental value. 

* Goudsmit, PR, 1928, 31 948. 
. t Meggers and Shenstone, PR, 1930, 35 868 a. 
% Russell, Ast. PJ. 1927, 66 283. 
Pauling and Goudsmit, Structure of line spectra, 1930, 163. 



XVIII] 



INVARIANCE OF THE T SUM 



133 



Con- 
figuration 


Multiplet 


Interval 
quotient 


Extreme 
interval 


Con- 
figuration 


P 


2 P 


a 


li 


-P 6 


P 2 


3 P 


ia 


ija 


-P 4 




2 D 








-P 3 




2 P 










d 


2 D 


a 


2ia 


-d 9 


d 2 


3^ 


Ja 


3Ja 


-d 8 




3 P 


ia 


l|a 




d 3 


4F 


la 


3ia 


-d 7 




2 H 


la 


ifa 






2 G 




lo a 






2 F 


-fa 


- /2 a 






2 D 




r '(l 






2 P 


fa 


a 




d 4 


6 D 


i a 


\a 


-d 6 




3 H 


To a 


i o a 






3 G 










3 D 


~~ iV a 


~s 




d 5 


All 








-d 5 



Fig. 18-13. Atomic interval quotients of terms arising from shells of p and d 
electrons in terms of the electronic interval quotients. 



\ J 


\ i 11 21 31 41 51 


Term\ 












6 4 F 


Observed 


75-8 


103-4 


128-4 







Calculated 


U-l 


103-6 


133-2 





a*P 


32-0 


122-3 













44-4 


74-1 











a 2 H 





. 








97-8 












(97-8) 


a 2 G 











120-5 













120-0 




6 2 F 








-59-9 














-51-8 






6 2 D 





1294 











a r> 





a 


. 


. 









2 = 74-1 











2 P 


125-0 
















88-9 











This state has not been identified. 



Fig. 18-14. Term intervals in the d 3 configuration of Ti n; to obtain the cal- 
culated values the 2 H term has been fitted to the experimental value. 



134 SUM RULES AND (jj) COUPLING [CHAP. 

Nevertheless, in spite of its successes the theory has its diffi- 
culties; of these one example will suffice. In the p 5 .ns terms of 
neon, theory shows that F , (T l + F/) and F 2 are independent of 
the coupling and therefore of the chief quantum number. Now F 
has always been interpreted as the displacement of a term from 
the centroid of the multiplet, so that for the 1 P term ly should be 
zero; indeed F has been assumed zero for all singlet terms in some 
of the above calculations. But if this assumption is made (F x - F ) 



Term 


^ 3 Fo 3 Pi 3 P 2 








w-Sg ms 3 ms 4 ms 6 






\ Inter- 




r -r 


r ' _{- p _ 2r 


\val 




2 


110 


\ 


r ' r r r r r 

1 1 L 1 0~ 1 l A 1 ~ l 2 






m \ 








1 


38040-7 39110-8 39470-2 39887-6 








1070-1 359-4 417-4 


776-8 


710-7 


2 


(14506-5) (14651-9) (15141-5) (15432-2) 








(145-4) (489-6) (290-7) 


(780-3) 


(-344-2) 


3 


7272-9 7323-1 8016-7 8101-3 








50-2 693-6 84-6 


778-2 


-6 


4 


4201-8 4223-5 4962-1 5004-8 








21-7 738-6 42-7 


781-3 


-716-9 


5 


2605-4 2616-6 3372-4 3396-7 








11-2 755-8 24-3 


780-1 


- 744-6 


6 


1667-7 1675-1 2440-0 2456-1 








7-4 764-8 16-2 


781-0 


- 757-4 


7 


1072-4 1077-3 1848-5 1858-1 








4-9 771-2 9-6 


780-8 


- 766-3 



Figures in brackets have been intrapolated from the series formula. 
Fig. 18-15. Energies and intervals of the s terms of neon; the term values are 
measured down from the series limit. 

should be independent of n just as F 2 - F is; a prediction which 
experiment does not support. Moreover, the most obvious way 
of dodging the difficulty is blocked; for if one suggests plausibly 
enough that when the coupling is no longer Russell-Saunders one 
may not rightly speak of a singlet term, still though iy need not be 
zero, yet (I^ + IY) must be constant. And if this be admitted, 
theory predicts that 

(r 1 +r 1 ')-2r =(r 1 -r )+(r 1 '-r ) 

should be constant, a prediction quite at variance with experiment 
(Fig. 18-15). 



XVIII] THE INTENSITY SUM 135 

4. The intensity sum 

That the intensity sum is proportional to the statistical weight 
(2J + 1) is a thesis, which has been developed by successive stages 
from the SP combination, in which it is true of a single line, 
through the general multiplet, PD, to the super-multiplet or con- 
figuration in which the sum must be taken over all lines which 
originate in terms having the same value of J* 

This development is so closely analogous to the development 
of the g and F sums, that one expects similar deviations to occur 
when configurations overlap. And in fact abnormal intensities in 
Bai have been ascribed to this cause. "j* 

5. General coupling of two electrons 

The coupling of electron vectors postulated by Russell and 
Saunders explains that division of levels into multiplets which is 
characteristic of light atoms. It explains, for example, why in 
the s 2 p . s configuration of C I the four levels are divided into a 
triplet below and a singlet above; it even explains the 2 : 1 interval 
ratio; but when in Pb i these four levels divide into two diads, the 
Russell-Saunders coupling fails. What then is to be put in its 
place ? 

In the model the interaction of ion and electron is represented 
as the coupling of four vectors. This means that there are six 
interactions, but these belong to only four different types, since 
(l^i) and (I 2 s 2 ) are identical and so are (l^) and (! 2 Si); of these 
four types, (s 1 s 2 ), (l^g), (l^) and (l^), the quantum mechanics 
states that the fourth may be neglected, unless the atom is ex- 
tremely light, but the other three are all important. In spectra 
which conform to the Russell-Saunders type, the spin coupling 
(s 1 s 2 ) determines the separation of terms of different multi- 
plicity, the orbital coupling (Ijlg) that of terms of different name, 
and the orbit-spin coupling (l^) the multiplet intervals. As the 
separation of the terms is a measure of the coupling, and in 
Russell-Saunders spectra terms of different multiplicity are 

* Harrison and Johnson, PR, 1931, 38 758, give the full theory and compare 
it with experiment. 

t Langstroth, PRS, 1933, 142 286. 



136 SUM RULES AND (jj) COUPLING [CHAP. 

widely separated, the (s 1 s 2 ) coupling must be strong. The (1^) 
coupling is weaker than the (s^) but stronger than the (liS 1 ), 
for terms with different names but the same multiplicity are less 
widely separated than terms of different multiplicity but more 
widely than different components of the same multiplet.* 

If the evidence of the quantum mechanics is to be accepted, and 
the (^Sg) coupling ignored, there are still three alternatives to the 
coupling postulated by Russell and Saunders. If the latter is 
written 

(A) {( 
the other three are 

(B) {( 

(C) {[(I 1 s 1 )s 2 ]l 2 } = {[j 1 s 2 ]l 2 } = {j'l 2 } = j, 

(D) {[(l lSl ) 1 2 ] sj = {[ j^] s 2 } = { j"s 2 } = J. 

These three all show an ion, whose orbital and spin vectors are not 
at once unlinked when a second electron is added, but differ in the 
influence the ion has on the coupling of the series electron. Thus 
in (B) the coupling (I 2 s 2 ) is preserved and the atomic resultant J 
appears as the sum of two electronic vectors J 1 j 2 . In (C) the ion 
shows a special attraction for the spin vector s 2 of the second 
electron, and so breaks the (I 2 s 2 ) coupling; while in (D) the ion 
attracts particularly the 1 2 vector. 

All three coupling types have been considered by those who 
have tried to interpret abnormal spectra; in particular, the 
magnetic g factors have been calculated and compared with 
experiment in more than one spectrum ;f but the result of this 
work has so far been to show that types (C) and (D) have no 
advantage over the simpler (jj) coupling of type (B). Incident- 
ally, too, the three are identical when the electron added 
occupies an s orbit. 

The further discussion of abnormal spectra will therefore be 
simplified by treating the ( jj) coupling as though it were the only 
alternative to that postulated by Russell and Saunders. 

* Hund, Linienspektren, 1927, 91 f. 

f For g factors of all four coupling types, see p. 145. 



(jj) COUPLING 



137 



XVHI] 

6. (jj) coupling 

In the change from weak to strong magnetic field, while the 
energies change, the number of states and their magnetic quantum 
numbers, M, do not; similarly, in the change from (LS) to ( jj) 
coupling, while the relative energies change, the J values do not. 
Accordingly, in the complex spectrum of a heavy metal, such as 
platinum, values of J can be assigned to the empirical terms, but 
the Russell-Saunders notation, depending as it does on L and $, 
is of little use. 





1 


Names if 


*1 I* 


Jl J2 


j 


coupling is R.S. 





4 i 





'So 






i 


3 Sj 


1 


4 4 





sp 






1 


3P IP 




4 14 


1 


1 ' 






2 


-*- 2 


1 1 


4 4 









4 14 


1 
1 


IS 3 p 

1 




li 4 


2 
1 


ip 3g 3J> 3J^) 






2 


in 3 ? :> 3 r> 




u- 14 





^2 x 2 L/ 2 




i 








2 








3 


3 ^3 



Fig. 18-16. Terms arising from the jj coupling of two unlike electrons in s.s, sp 
and p . p states ; the J values are the same as those of the corresponding Russell- 
Saunders terms. 

To illustrate the invariance of /, consider the terms arising 
from the (jj) coupling of two electrons. The values of j permitted 
a single electron are (Z |), and the terms arising from the com- 
bination of two electrons can be deduced by combining the two 
j vectors. When the electrons are not equivalent, J is simply the 
vectorial sum of j l and J 2 , and there are no restrictions; thus two 
electrons having j values of 1| and 2| produce four states having 
J values of 1, 2, 3, 4. Other examples are given in Fig. 18-16. On 
the other hand, when the two electrons are equivalent, the Pauli 
exclusion principle does not allow two electrons with the same 



138 SUM RULES AND (jj) COUPLING [CHAP. 

values of n, I, j and m; but when this condition is introduced, as it 
is in the derivation of Figs. 18 17, 18-18, the resulting J values are 
still identical to those developed by the (LS) coupling. The J 



1, 1. 


Jl J2 


-H m, 


M 


J 


Names with 
R.S. coupling 


1 1 


4 4 
4 14 
14 H 


4 -4 
H 4 

~ 2 
-14 

4 -4 
-14 
-4 -H 




2 
1 


-1 
-2 



1 2 

2 


^ r* 



Fig. 18*17. Terms arising from the jj coupling of two equivalent p electrons. 













Names with 


*1 *2 Z 8 


Jl J2 J3 


m l m 2 w 8 


3f 


J 


R.S. coupling 


1 1 1 


4 4 H 


4 -4 14 


14 










4 


4 


H 








-4 


-4 










-14 


-14 








4 14 H 


4 14 4 


24 










_~i| 


4 










4 -4 


4 


9 1 


2P 






- li 


-4 


^2 


* 






-4 -H 
















14 


2P . 2 DiA 4 S 1 i 






-4 14 4 


14 












4 










- l| 


-4 


4 


2 l-^2i 






4 -4 


-4 










-14 


-H 










_ 1 _ J 1 


-24 








14 H 14 


U 4 -4 


H 












L 










-4 -it 


2 

-4 


14 








4 -4 -H 


-14 







Fig. 18-18. Terms arising from the jj coupling of three equivalent p electrons. 

values to be expected from more complex configurations are 
shown in Fig. 18-19. 

Turning from the states themselves to their energies, consider 
first the addition of an s electron to an ion in the 2 P state; this 
actually occurs in columns IV and VIII, and much is known of the 



XVIII] (]j) COUPLING 139 

resulting terms. The two ionic levels are denned by j l , which here 
assumes the values 1 J and J. The addition of the second electron 
splits each of the levels in two, for j 2 can orient itself parallel or 
anti-parallel to ] lt J 2 is here identical with s 2 , since 1 2 is zero. 
Thus the atomic level scheme consists of two ' diads ' ; and the 



Con- 
figura- 
tion 


Number of elec- 
trons in which j is 

4 14 2J 





Number of levels in 
1 2 3 


which J is 
4 5 


6 


P 2 


2 
1 1 
2 


1 
1 


1 


1 
1 








d 2 


2 
1 


1 
2 


1 
1 


1 


1 
1 
1 


1 


1 
1 




d 4 


4 
3 
2 
1 


1 
2 
3 
4 


1 

2 
1 
1 


1 
1 
2 


1 
4 
2 

1 


1 
2 
3 


1 
3 1 
2 1 
1 


1 
1 


Con- 
figura- 
tion 


j 
4 14 


24 


4 


1* 


2J 


J 
3* 


44 54 


64 


P 3 


2 1 
1 2 
3 


1 


1 

1 

1 


1 








d 3 


3 
2 

1 


1 
2 
3 


i 
1 


1 
1 
2 

1 


2 
2 

1 


1 
2 


1 
1 1 
1 




d 5 


4 
3 
2 
1 


1 
2 
3 
4 
5 


i 

2 
1 


2 
3 
2 


1 
2 
4 
2 
1 


2 
3 
2 


1 1 
3 1 
1 1 


1 



Fig. 18- 19. Terms arising from various numbers of equivalent p and d electrons. 

distance between the diads, being due to the coupling (l^), must 
be greater than the interval of either diad, for the latter is due to 
(j 1 j 2 ). Further, the relative positions of the two terms can be 
foretold, for the energy is due primarily to the interaction of l t 
and s x and secondarily to the interaction of s l and s 2 . Hund's 
rule states that the energy of interaction of s x and s 2 is small 



140 SUM RULES AND (jj) COUPLING [CHAP. 

when the angle between them is small, so that in the lower level 
of each diad Sj and s 2 will be parallel. The levels constructed on 
this principle are shown in Figs. 18-20 and 18-22, the former 

Ionic levels Vector coupling Atomic levels J 

-L* * J = h-s 2 1, 



S 2 



S 2 -* 

i-* J=ii-s 2 i,-i 



Fig. 18-20. Energy levels resulting when an s electron is added to an ion in an 
erect doublet state; jj coupling is assumed. 

C Si Sn Pb 

'F>< - - - - 'P, 



628 1252 



HOO 1037 3715 12900 



195 



77 273 , 3 P. 

20-0 327 } P 

Fig. 18-21 . Intervals of low s 2 p . s terms in four elements of column IV ; the scale 
is adjusted so as to make the 1 P 1 3 P interval the same in all elements. Note the 
change from LS coupling in C I to jj in Pb I. 

representing an erect and the latter an inverted parent term; the 
first agrees well with the empirical s 2 p . ns terms of tin and lead 
(Fig. 18-21), and the second with the p 5 ( 2 P) ns terms of the inert 
gases (Fig. 18-23). 



XVIII] (jj) COUPLING 

Ionic levels Vector coupling Atomic levels 



141 



Fig. 18-22. Energy levels resulting when an s electron is added to an ion in an 
inverted doublet state; jj coupling is assumed. 



Serial 
number 



Separation from s 5 
500 1000 1500cm" 




Term 
value 



- 5000 
cm" 1 



- 10,000 



- 39,000 



Pig. 18'23. Intervals of the s terms of neon; in each configuration the s 5 or 3 P 2 
term lies lowest and the s 2 or 1 P 1 term highest. Note the change from LS 
coupling in the lowest term to jj coupling in the high terms. 



142 SUM RULES AND (jj) COUPLING [CHAP. 

But one may ask, why does the addition of an s electron to a 2 P 
ground term produce two diads in columns IV and VIII, when the 
addition of a p electron to a 2 S ground term produces triplets and 
singlets in column II. The couplings which have to be con- 
trasted are 

[s l (I 2 s 2 )} = (s x ] 2 } in the alkaline earths, 

and {(Ii s i) s 2} = {h s 2) in column IV. 

In both the coupling of the electronic vector j with the isolated 
spin vector will decrease rapidly in strength with increase of the 
chief quantum number, the coupling energy being roughly pro- 
portional to n*~ 3 . But the interaction of the orbital vector with its 
own spin vector differs in the two columns; in the alkaline earths 
the orbital vector concerned is the orbital vector of the series 
electron, so that the coupling (I 2 s 2 ) will decrease in strength with 
increase of the chief quantum number just as the {js} coupling 
does; in column IV, on the other hand, the orbital vector con- 
cerned is the orbital vector of the ion, and the coupling of this 
with its own spin vector remains unchanged throughout the 
series, being determined by the doublet interval of the ion.* 

In the addition of an s electron to a 2 P term, the energy sequence 
of J values happens to be identical with that produced by (LS) 
coupling, but the two will not always agree. In the 5s 2 . 5p 4 ( 3 P) 6s 
configuration of Ii| the five levels can be named 4 P 2 fcii,*> 
2 P 1 j ^, for the J values occur in that order from below upwards; 
but the intervals are 1459, 4803, 924 and 4530 cm.- 1 , and so are 
actually more consistent with a (jj) coupling; for they divide the 
terms into a lower diad, which we interpret as ( 3 P 2 .6s) 2i >lt , a 
middle diad ( 8 Pi.6s)^ fl j and an upper monad ( 8 P .6s)j; the 
critical will not fail to observe, however, that if the (jj) coupling 
was rigid, the J values of the middle diad would be interchanged. 

But in fact even in those spectra in which the terms arising 
from different ionic states are most widely separated, spectra 
such as Rni, Csn, Xei and Xen, the individual terms of a con- 
figuration are arranged in no consistent order. In Rni the four 

* Pauling and Goudsmit, Structure of line, spectra, 1930, 104. 
t Evans, S. F., PRS, 1931, 133 417. 



XVIII] .(jj) COUPLING 143 

terms ( 2 Pi$.pu) might lie consistently below the two terms 
( 2 Pi*-P*)> but in fact the six empirical terms cannot be separated 
into two groups. 

7. Calculation of g for any coupling 

Less important than the sum rule at the moment because data 
is scanty, but destined perhaps to be equally useful, is the 
calculation of g for any coupling. Following Lande, Goudsmit 
and Uhlenbeck* have shown that if any vector Z is the resultant 
of two other vectors X and Y, so that the permissible values of Z 
are determined by 
then \X+Y\>Z>\X-Y\, 

g(Z}= 



Y(Y-1)-X(X+1) 

"~ 9( '' 



With this assumption consider the four coupling types of an 
earlier section. 

(A) {(l 1 l 2 )(s 1 s a )} 

J is the sum of the L and S, so 



2J(J'+1) 
Now L is the sum of the vectors l x and 1 2 , so 



= l,ifg(l) = l for all values of I. 

And similarly g (S) = 2, if g (s) = 2 for all values of *. Substituting 
these values in the expression for g (J) gives at once the usual 
Lande formula 



~ 2J(J+1) 

* Goudsmit and Uhlenbeck, ZP, 1926, 35 618. 



144 SUM RULES AND (jj) (COUPLING [CHAP. 

This analysis brings out, perhaps more clearly than any other, 
the cause of the whole anomalous Zeeman effect, which is nothing 
else than the double magnetism of the electron. 

If there are more than two electrons active one may assume 
that the binding of s x and s 2 is tighter than that of their resultant 
s i, 2 with s 3 ; then one may first work out g (s lf 2 ) and then combine 
s i, 2 w ^ ft s 3 . But for the Russell-Saunders coupling g (L) is always 
1 and g(S) always 2. 

(B) {(Iis 1 )(l 2 s 2 )} = (j 1 i 2 } = j. 

J is compounded of j x and ) 2 , so 



J(J+ 1)+.? 2 

~ 



~ 2J(J+l) i ' 

The g (j^) of this expression appears in Lande's table simply as 
the g factor of some doublet term, for ] 1 is the sum of Ij and s 1? 
only one electron being active. 

Very similar to this (jj) coupling for two electrons is the binding 
of the series electron near the limit of a term sequence; indeed the 
equation is unaltered, save that the ground term of the ion is not 
necessarily a doublet. 

(C) In the coupling 



J is the resultant of j' and 1 2 , so 

j(j+i)+j'(/+i)-/ 

g { J) _ _.._. _ 



In this equation g (1 2 ) = 1, and j' is the resultantof j x and s 2 , so that 



Here g (fa) may be taken from Lande's doublet table, while g (a 
is 2, as always for a single electron. 



XVIII] CALCULATION OF g FOB ANY COUPLING 145 

(D) The coupling {[(liS 1 )! 2 ]s 2 } is so similar to (C) that it need 
not be worked out in detail. 

The values to be predicted by each of these four coupling types 
have been worked out for certain spectra whose Zeeman splitting 
is irregular, but no close agreement with experiment has ever 
been found. Coupling types (B), (C) and (D) often give better 



J 


Coupling scheme 


</ values 


J 




A B C D 

Jl J2 k f S 2 


^ * %Fal 




3i 

2i 


4 D 3i 2 1J 2i 1 3 J 
*P H 2 IJ 2 1 2 J 
4 D 21 1 14 14 1 2 * 
*D 2i 2 4 14 1 3 | 


1-43 1-43 1-43 1-43 1-43 

1-60 1-44 1-53 1-53 1-60 
1-37 1-40 1-40 1-40 1-33 
1-20 1-33 1-24 1-24 1-24 


34 
24 


1* 

i 


*P H 2 14 14 1 1 4 
4 IV 14 14 1 2 1 

4 Su 2 4 24 l i 4 

'D^ 1 4 i 1 2 i 

*P H 1 14 4114 

4 P* i 4 i* i o 4 
*D* ^ i 1 i i 
a P* i 14 i l i i 

2 S|. 2 14 14 1 1 4 


204-17 4-17 4-17 4-17 4-17 

1-73 1-47 1-49 1-50 1-73 
1-20 1-33 1-29 1-30 1-20 
2-00 1-67 1-84 1-83 2-00 
0-80 1-22 1-11 1-10 0-90 
1-33 1-38 1-33 1-33 1-23 

207-06 7-06 7-06 7-06 7-06 

2-67 1-78 2-11 2-00 2-67 
0-00 0-67 0-67 0-67 0-00 
0-67 1-22 0-89 1-00 0-99 
2-00 1-67 1-67 1-67 1-68 

20 6^33 JET33 5^3 5-33 ^34 


1* 

i 



Fig. 18-24. g factors of the p 4 ( 3 P) 4p terms of A n compared with values cal- 
culated for four different couplings. The sum rule is valid although the g factors 
are abnormal. (Bakker, K. A/cad. Amsterdam, 1928, 31 1041.) 

agreement for certain terms, but none of them has been found to 
give close agreement even for one configuration in one element. 
A good example of results obtained is afforded by the ( 3 P) 4p 
configuration of An (Fig. 18-24). 

As there is evidence that departures from the interval rule and 
Lande's g formula are both signs of a break from the Russell- 
Saunders coupling, a study of the variation of g in a series or in a 
sequence of homologous spectra has been a long felt want. 
Recently Pogany* has supplied the need by studying the change 
in g in the p 5 . ( 2 P) ns terms of the inert gases. This configuration 
produces two terms having a J value of 1, and in neon both in- 
* Pog&ny, ZP, 1935, 93 376. 



146 SUM RULES AND (jj) COUPLING [CHAP. 

tensity laws and magnetic splitting factors show that the lower 
is 3 P X and the higher 1 P 1 .* Of these 3 P X approaches the lower 
limit of the ion, and must therefore flow to the (jj) coupling term 
of ( 2 Pj . s), with a g value of 7/6, while the higher term approaches 
the higher limit and must flow to ( 2 P^ .s) x with a g value of 4/3. 
Thus as the coupling changes the magnetic splitting factor of 



1-5 



1-4 



1-3 



1-2 



1-0 



Xe Kr 



A 




Fig. 18-25. g factors of the s terms of the inert gases, showing the transition 
from LS to jj coupling. (After Pogany, ZP, 1935, 93 376.) 

the 3 P X term flows from 1-5 to 1-17, while the g factor of the 1 P 
term flows from 1-0 to 1-33; this shows that the g values cross and 
that for some particular coupling the two g values must be equal. 
Experiment has not yet revealed the steps in this transition in the 
series of neon, but the low terms of all inert gases are readily 
accessible and Pogany has shown five steps in the analogous 
transition from the (LS) coupling characteristic of light to the 
(jj) characteristic of heavy atoms; in neon the g values approach 
the ideal values of 1-5 and 1-0, being 1-47 and 1-03, whereas in 
krypton they are equal, and in xenon become 1-20 and 1-30 
(Fig. 18-25). A similar transition can be detected in the p terms 
(Fig. 18-26). 

* See p. 42. 



XVIII] CALCULATION OF g FOB ANY COUPLING 



147 



(LS) 
coupling 


Neon 
( 2 P) 3p 


Argon 
( 2 P) 4p 


Krypton 
( 8 P) 5p 6p 


Xenon 
( 2 P) 6p 


(JJ) 

Coupling 


Term g 


Term r/ 


Term g 


Term g g 


Term g 


Ji J* 3 


3 P 

% o 


Pi 
Pa 


Pi 

P5 


Pi 
p 5 


Pi 
Ps 


i i o 
H 1} o 


3 P X 1-5 
*l\ 1-0 
3 D! 0-5 
'Sj 2-0 


p 2 1-340 
p 5 0-999 
p 7 0-099 
Pio 1'984 


p, 1-379 
P4 0-819 
p 7 0-840 
Pio 1-962 


p 3 1-425 1-384 
p 4 0-619 0-635 
p 7 1-028 1-046 
p 10 1-891 1-820 


Pa 

P4 

p 7 1-02 

Pio 


t H i-s 

i i 0-67 
li H 1-33 

H i 1-6 


3 P 2 1-5 
3 D 2 1-17 
^a 1-0 


p 4 1-301 
p 6 1-229 
p 8 1-137 


p 3 1-248 
p e 1-302 
p a 1-121 


p, 1-163 
Pe 1-400 1-406 
p 8 1-116 1-110 


p 3 1-183 
Pe 1-402 
P 9 M13 


i H i-i? 

It H 1'33 
It 1-17 


3 D 3 1-33 


p 9 1-329 


p 9 1-333 


p 9 1-333 1-333 


P8 


H It 1-33 



Fig. 18-26. g factors of the p terms of the inert gases, showing the transition 
from LS to jj coupling. These terms arise as p 5 ( 2 P) np. 

Sources. Ne: Back, AP, 1925, 76 330, which is in good agreement with Murakawa 
and Iwama, Inst. Phys. and Ghem. Tokyo, 1930, 13 289. A: Pogany, ZP, 1935, 93 
364, which agrees well with Terrien and Dijkstra, J. de Phys. 1934, 5 443. Kr and Xe : 
Pogany, ZP, 1935, 93 376. 

8. Electronic displacements 

In an earlier chapter, while trying to explain why terms are 
inverted if they arise from a shell more than half full, resort was 
had to the theory that the atomic displacement F may be re- 
garded as the sum of electronic displacements y l and y%\ and it was 
shown that provided the coupling is Russell-Saunders, the relation 
between the two is 

F = y l + y 2 = cos (LS ) S^ Zj cos (l x L) s l (Sj_ S) 

= LS cos (LS) S0! l } cos (1 L L) ^ cos (s l S). 

JU o 

...... (13-2) 

The quantity summed in this expression is commonly abbre- 
viated as the interval quotient A, so that 



(18-1) 



If this equation is applied to the addition of an electron to an 
ion, the expression for the interval quotient A will in general 
contain two interval quotients a x and a 2 , and no method is known 



148 SUM RULES AND (jj) COUPLING [CHAP. 

separating these. But under certain conditions the expression 
simplifies; thus if either the ion or the electron is in an s state, or if 
the ion is in a singlet state, one of the interval quotients vanishes; 
while if the two electrons are equivalent a^ and a 2 are equal. The 
method cannot be extended to the combination of three electrons, 
unless two are assumed so tightly linked that they are quite 
undisturbed by the third electron. 

Thus consider the addition of an electron (I 2 s 2 ) to an ionic S 
term defined by (l^); then since l : is zero, a^ vanishes from the 
expression for A, and there is left simply 



! cos(s 2 S) (18-2) 

j to 

In this equation 



/, -/-- 2L(L+l)~~ 

= 1, when Z x = and L = 1 2 , 
so that the expression for A simplifies to 

A = a 2 2S~(S+1)~ ~~" ( * 8 ' 3 ^ 

Now when an electron is added to a term with spin vector s l , two 
terms will be produced with spin moments (^ + J) and (^ |); if 
these have interval quotients A + and A_, 



And similarly it may be shown that 

A = -^ 2 - 

- (^,+iy 

Applied to the alkaline earth spectra the expression for A + 
leads directly to the results already obtained by the sum rule; but 
applied to the d 5 ( 6 S)wp configuration of Cri and Moi, the 
formulae lead to results which are new; thus the 7 P term should be 
erect and the 5 P term inverted, while both should have the same 
interval quotient. In Cri the two terms obey the interval rule 
well, and the 5 P term is inverted, but the interval quotients 



ELECTRONIC DISPLACEMENTS 



149 



XVIII] 

instead of being equal bear a ratio of 9 : 1 (Fig. 18-27). In Mo I the 
terms do not obey the interval rule and both are erect ; while if the 
theory is applied to the p 3 ( 4 S) up configuration of column VI the 
results are even more unsatisfactory. 

Agreement, however, is only to be expected if the p 3 and d 5 
groups are so firmly bound in an S state that the addition of the 





Cri 


Mo i 


Terms 








AV 


A 


Av 


A 


3d 5 (S) 4p 
for Cr i 


? p 2 
7 p 3 

?p 


81-4 
112-5 


27-1 
28-1 


257 
449 


86 
112 


and 


i 4 










4d 5 ( 6 S) 5p 
for Mo i 


6 Pi 
5 P 2 
B Pa 


-5-7 

-8-8 


-2-9 
-2-9 


121 

87 


61 
29 



Fig. 18-27. Intervals of the d 5 ( 6 S) p configuration in Cr I and Mo i. 

p electron does not disturb them, and if the coupling of the 
ion and electron is Russell-Saunders. That experiment does not 
here support theory shows only that these assumptions are 
invalid, for a very valuable application of the same theory has 
been made to the displaced terms of beryllium, magnesium and 
isoelectronic spectra. The 3s.3p 3 P and 3p 23 P of the mag- 
nesium-like spectra have many of them identical intervals as 
Fig. 18-28 shows. Now according to the above theory the 
intervals should be determined by 



where 



I s 

^^^ cos (l z L) ~ cos (s x S) 

J O 

7 

+ a 2 -fc 
LJ 



). ...(18-4) 



For the 3s . 3p configuration the first term of this equation is zero, 
and there remains simply A |a 2 . For the 3p 2 configuration, on 
the other hand, the two terms of this equation are equal, and since 
L = S = l l = l 2 =l and s 1 = s 2 = |, there results again A = \a^ . Thus 
the interval quotients are equal, and since both are 3 P terms their 
displacements and intervals are also equal. 



150 SUM RULES AND (jj) COUPLING [CHAP. 

Bechert* has advanced even further than this and has been 
able to apply a theory of Goudsmit'sf to account for the dis- 
crepancies from the 2 : 1 interval ratio, but the theory involves 
the use of the quantum mechanics and is beyond the scope of 
this book. 





3a.3p 3 P 


3p a 3 P 


A3P 
1 1, 2 


A3P 

a r o. i 


A'P'^/A'P ,,! 


A 8 P 1(2 


A 3 P . ! 


A'P 1>2 /A3P 0>1 


Mgi 
Alii 
Sim 
Piv 

Sv 
Clvi 


40-6 
122-6 
261-3 
469-1 
767-1 
1183-7 


20-1 
64-1 
130-7 
227-1 
360-4 
521-3 


2-02 
1-91 

2-00 
2-07 
2-13 
2-27 


40-6 
122-6 
261-3 
469-1 
767-1 
1183-7 


20-5 
59-7 
130-1 
234-7 
412-4 
668-0 


1-98 
2-05 
2-01 
2-00 
1-86 
1-77 



Fig. 18-28. sp 3 P and p 2 3 P intervals in spectra isoelectronic with Mg I. 

9. Abnormal Intensities 

Kronig has shown that the intensity tables given in the 
previous chapter may be applied to configurations in which the 
coupling is (j j), if 8 is replaced by j l and L byj 2 , where j l is taken 
to be the quantum number which does not change in the transi- 
tion.:]: 

Abnormal intensities due to (j j) coupling must be distinguished 
from those due to the overlapping of multiplets and configura- 
tions; to obtain clear evidence of the validity of this formula, one 
would wish to measure the intensities of lines arising in a con- 
figuration well separated from all others and exhibiting the 
intervals characteristic of (jj) coupling. 

10. Perturbed terms 

There is one factor producing abnormal series, interval ratios, 
g factors and intensities, which has only recently received the 
attention it deserves. It is known as perturbation, and is best 
introduced by a study of a perturbed series. 

Of perturbed series, the diffuse series of calcium affords a clear 

* Bechert, ZP, 1931, 69 735. 
t Goudsmit, PR, 1930, 35 1325. 

J White and Eliason, PR, 1933, 44 753. Bartlett, PR, 1929, 34 1247, 
derived formulae for (jj ) coupling. 



XVIII] PERTURBED TERMS 151 

example. The first four members of the 3 D term sequence contract 
in the usual way, but the next three expand anomalously; the 
expansion reaches a maximum at the seventh term, the succeed- 
ing triplets contracting again as they approach the series limit. 
This may be shown in two ways, by plotting the displacement of 



-20 



Displacement 
-10 10 cm? 1 20 




Fig. 18-29. The 4s nd 3 D term series of calcium showing perturbation. The 
abscissae are the displacements from the centroid, which is shown dotted. 

each term from the centroid against the energy (Fig. 18-29) and 
by plotting the effective quantum number against the energy 
(Fig. 18-30). 

Similar abnormalities have been noticed in the 3 F series of 
Al n* and the 2 P series of Cu I, f and their cause has been elucidated 
by Russell and Shenstone. J They show that these anomalous 
series only occur when a term of another series intrudes; thus 
between the sixth and seventh terms of the 4s nd 3 D sequence of 

* Sawyer and Paschen, AP, 1927, 84 1. 
f Shenstone, PR, 1929, 34 1623. 

t Russell and Shenstone, PR, 1932, 39 415. White, Introduction to atomic 
spectra, 1934, gives a clear and full account of this work. 



152 SUM RULES AND (jj) COUPLING [CHAP. 

calcium there lies the 3d 5s 3 D term, a term be it noted with the 
same values of L, S and J, but with an interval much greater 
than that to be expected at this height in the 4s nd series (Fig. 
18-32). When this intruding term is excluded from the sequence, 
all succeeding values of the quantum defect are reduced by one, 
and the graph of the defect against the energy comes to resemble 
an anomalous dispersion curve (Fig .18-31). Moreover, if a formula 

Quantum defect 



0-5 



1-0 



2-0 



E/ch 



2000 



4000 



6000 
cm? 1 



8000 




Fig. 18-30. The quantum defect (n n*) for the 3 D term sequence of Ca I with 
the intruding term included. 

is developed on anomalous dispersion lines,* very good agreement 
with experiment can be obtained. 

Clearly all spectroscopic terms do not perturb one another; 
analysis alone does not reveal what conditions are essential, but 
the quantum mechanics provides an answer to this important 
question. If two levels have the same characteristic quantum 
numbers and lie close together, the eigenfunction of each level 
contains some components of the eigenfunction of the other, so 
that both levels belong in part to both configurations. Stated in 
other words this means that when two states perturb one another, 
* Langer, PR, 1930, 35 649 a. 



XVIII] 



PERTURBED TERMS 



153 



there is a certain probability that the atom will jump back and 
forth between the two without energy being radiated. The assign- 
ment of a given level to a definite electron coupling is therefore 
indefinite; it becomes more definite the further the levels are 
apart. More precisely two levels perturb one another when both 
have the same J and both are odd or both even; the two terms 



Quantum defect 

w n* 

0-5 1-0 



1-5 



E/ch 



2000 



4000 



6000 
cm7 



8000 




Fig. 18-31. The quantum defect (n n*) for the 3 D term sequence of Ca I with 
the intruding term removed. Note how similar this graph is to that character- 
istic of anomalous dispersion. 

need not belong to the same configuration, or be derived from the 
same state of the ion, but experiment shows that the perturbation 
is greater when the two terms have the same values of L and S if 
the coupling is (LS) or the same values of j l and j 2 if the coupling 

is (jj). 

Since the assignment of electron coupling is indefinite, each 
perturbed level is likely to have some of the properties of the 
other, and in fact much evidence has accumulated to show that 
the perturbing levels share their interval factors, their magnetic 
splitting factors and their intensities. 



154 SUM RULES AND (jj) COUPLING [CHAP. 

The quantum mechanics shows that in terms of energy per- 
turbation manifests itself essentially as a repulsion, but it is not 
difficult to show that repulsion leads logically to a sharing of 
intervals. Consider for example a narrow triplet lying close below 
a wide one; if one of these is odd and the other even, they will not 
perturb one another, and if the coupling is (LS) they will appear 
as shown on the left of Fig. 18-33. If however both terms are 



Observed 
term value 
cm." 1 


Configura- 
tion 


n 


n* 


71-71* 


Calculated 
term value 
cm."" 1 


T (obs.)- 
T (calc.) 


28969-1 


4s 3d 


3 


1-946 


1-054 


26465 


2504 


11556-4 


4s 4d 


4 


3-081 


0-919 


11556 





6561-4 


4s 5d 


5 


4-090 


0-910 


6562 


- 1 


4255-5 


4s 6d 


6 


5-078 


0-922 


4252 


+ 3 


3002-4 


4s 7d 


7 


6-045 


0-955 


3002 





2268-3 


4s 8d 


8 


6-955 


1-045 


2287 


-19 


1848-9 
1551-3 


3s 5d 
4s 9d 


9 


7-702 
8-410 


1 

0-590 


^orcign term 
1551 





1273-1 


4slOd 


10 


9-284 


0-716 


1276 


- 3 


1045-6 


4s lid 


11 


10-244 


0-756 


1048 


- 2 


869-8 


4sl2d 


12 


11-232 


0-768 


873 


- 3 


734-0 


4s 13d 


13 


12-227 


0-773 


737 


- 3 


628-0 


4s 14d 


14 


13-219 


0-781 


630 


_ 9 



Fig. 18-32. Series calculations of the anomalous 4s nd 3 D X series of calcium. 
The calculated term values are obtained from a formula designed on the lines 
of those used to explain anomalous dispersion. (After Russell and Shenstone, 
PR, 1932, 39 415.) 

even, the levels with the same J will repel one another, and as the 
repulsion is greater the nearer the levels are to one another, the 
3 P terms which are nearest undergo the greatest displacement; 
thus the narrow triplet is widened and the wide triplet is narrowed ; 
this is shown on the right side of the figure. Moreover, if the 
Harrow term lies above the wide, the same sharing of the intervals 
results. 

Of the sharing of magnetic splitting factors much evidence has 
accumulated. Thus is Zn the 3 P 2 and X D 2 terms of the 4d 2 .5s 2 
configuration should have g values of 1-5 and 1-0, whereas in fact 
both have the same g value, 1-25; these terms are separated by 
915cm.- 1 * Further examples from Zn are shown in Pig. 18-34, 



* Kiess, C. C. and Kiess, H. K. f BSJ, 1931, 6 660. 



XVIII] PERTURBED TERMS 155 

while the phenomenon has been observed in Til, GUI, Mil* 
and La n. In all these spectra the two perturbing terms belong 
to the same configuration, but the deviating g sums of Kn, 
Rbn and Pnni make it probable that this is not an essential 
condition. In Pbinf the g value of the 6s.6p 3 P 2 term, which 



3 p o 



3 P, 



3 p o 

it 



Unperturbed Perturbed 

One term odd Both terms 

and one even odd 

Fig. 18-33. Changes produced by perturbation in wide and narrow triplets 
when these lie close to one another. 

should be 1-50 whatever the coupling, is in fact 1-35. This can be 
most reasonably explained if the term is perturbed, but what 
unidentified configuration is likely to lie near enough is not clear. 
Short of complete sharing, the g factors may be more or less 
distorted. A method of calculating the precise change in g caused 
by neighbouring states was first developed by Houston J for the 

* Shenstone, PR, 1927, 30 264. 

t Green and Loring, PR, 1932, 41 389a. 

j Houston, PR 9 1929, 33 297. 



156 SUM RULES AND (jj) COUPLING [CHAP. 

ps configuration; Goudsmit* later extended the method to the ds, 
and Laporte and Inglisf to the p 5 . s and d 9 . s configurations. The 
only empirical constant which these formulae contain is one 
easily determined from the energies of the terms. 

Though perturbed terms share their magnetic splitting factors, 
one must not too readily assume the converse, that when two 
terms share their splitting factors they are perturbing one 
another. The 3 P 1 and 1 P 1 terms of the 4p 5 ( 2 P) 5s configuration 



Configuration 


Term 


E/hc 


g theory 


g observed 


4d 2 .5s 2 


3 p a 


4,186 


1-500 






1D 2 


5,101 


1-000 


1-25 


4d 3 .6s 


3 F 4 


12,342 


1-250 






3 G 4 


12,761 


1-050 


1-15 


4d 2 .5a 


*G 4 


26,931 


1-000 




5p 


3 F 4 


26,938 


1-250 


1-13 


4d 3 .5p 


5p 2 


34,761 


1-833 






1 D 2 


34,850 


1-000 


1-42 


4d 3 .5p 


IF S 


36,760 


1-000 






3 G 3 


36,942 


0-750 


0-87 



Fig. 18-34. Sharing of magnetic splitting factors in Zr i. 

of Kri both have g factors of 1-25, but they are separated by 
4930 cm." 1 , and in fact their g factors have been explained as due 
to a particular coupling intermediate between (LS) and (jj) 
(Fig. 18-25). 

The sharing of intensities is also well established. In Zn 
singlet terms have been found combining with quintets, but only 
when the singlet has a quintet neighbour or the quintet a singlet 
and the two perturbing terms have the same J.% Moreover, in 
barium Langstroth has identified the terms which perturb the 
first three multiplets of the diffuse and fundamental series, and 
has shown that the experimental intensity sums are those re- 
quired for (LS) coupling. In this comparison an uncalculable 
parameter appears connecting the intensities of two multiplets 

* Goudsmit, PR, 1930, 35 1325. 

t Laporte and Ingiis, PR, 1930, 35 1337. Pogany, ZP, 1933, 86 729, con- 
firms the predicted values in Kr i. 
J Details on p. 106. 
Langstroth, PRS, 1933, 142 286. 



XVIII] PERTURBED TERMS 157 

arising in different configurations; but this may be determined 
experimentally provided some lines occur in each multiple! 
which are only slightly perturbed. A study of perturbed terms 
leads naturally to the identification of lines previously regarded 
as anomalous, for a weak multiplet may have one or more of its 
lines intensified by perturbation until they become strong enough 
to stand out in the spectrum. Several fragments of multiplets, 
whose other components are so weak that they escape observa- 
tion, have in fact been found. 

In barium no attempt was made to calculate the precise in- 
tensities of individual lines, for this is only possible when the 
parent configurations of all perturbing terms are known, and as 
yet the analysis of Ban is insufficiently advanced. Indeed in- 
dividual perturbed intensities seem to have been calculated and 
compared with experiment only once, by Kast* working on Sri. 
He found satisfactory agreement, but the perturbation in the 
two terms considered was not as large as one could wish con- 
sidering the magnitude of the experimental error. 

BIBLIOGRAPHY 

Pauling and Goudsmit, The structure, of line spectra, 1930. 
* Kast, ZP, 1932, 79 731. 



CHAPTER XIX 

SERIES LIMIT 
1 . J values 

Evidence has already been adduced to show that in the spectra of 
N, A H and Ne where the limit is a multiplet, some series converge 
to one component and some to another. To recall the point at 
issue consider the displaced terms of calcium; five terms of the 



2 D limit 



Of CciH 


-^ - - w 

/I x- 




/i / x 


12,000 




cm" 1 


i 


/ 




/ c 


9' 6.1 




1 


1 




( 


, 


8,000 


o c 

1 


> P 5d 




1 


/ 




1 


/ 




1 


I 


4,000 


1 

1 


1 
1 
i 




1 


\ 
\ 




~ ; 


\ 




/ 


\ 


2 S limit n 
of Call U 


?' ' 


\ 
\ 

> o 3d 



Fig. 19*1. Splitting of the 3d.nd 3 P terms of Ca i showing that all three do not 
tend to the same limit. 

d.7ip 3 P series are known and the separations are plotted in 
Fig. 19-1, showing quite clearly that 3 P 2 converges to an upper 
limit, while 3 P 1 and 3 P converge to a lower; these limits are 
naturally interpreted as the 2 D 2i and 2 D xi terms of Can. 

All these terms have been named because they approximate to 
the Russell-Saunders ideal; but there are other terms such as the 



CHAP. XIX] J VALUES 159 

( 2 P) p and ( 2 P) d terms of neon which cannot be named though 
their series have been worked out, and the limits they approach. 
Naturally then the question arises : cannot theory predict which 
terms will approach each limit? This was the problem which 
Hund set himself, and his solution will be considered in due 
course, but in that J is more easily determined than the orbital 
and spin vectors, it must take precedence. 

Empirically the J values of unknown terms are always more 
easily determined than the multiplet structure. And theoretically 
the J values retain their significance even when the coupling is 
most irregular and L and S have no meaning. In particular, if 
both the series limit and the orbital vector of the series electron 



V- 

Limit \ 


] 


L 




2 


2 ^s | Pi 


P2 


P5 


P4 


i 


2 1 > 

1 i? Ps 


P7 


PlO 


P6 


k 



Fig. 19*2. Paschen's p series in neon and the limits to which they tend. 

are known, then the J values of the terms approaching that limit 
are readily determined. 

Ask, for example, which of the p terms of neon approach the 
lower 2 P^ limit of Ne n. When the chief quantum number of the 
series electron is sufficiently large the coupling is roughly (jj) and 
the problem is simply to find what J values can result from a term 
having j l = 1 J and a p electron having^ = | or 1. When^ 2 = the 
permitted values of J are 1 and 2; while when J 2 =H> J w ^ 
assume the values 0, 1, 2 or 3. Thus the J values of the terms 
approaching the lower limit should be 0, 1, 1, 2, 2, 3; while those 
approaching the upper 2 P^ limit will have J values of 0, 1, 1, 2; 
and this is in fact the division actually observed. 

And these facts may be simply summarised in a cell diagram, 
constructed to show the limits from top to bottom and the J 
values from left to right. 

This diagram shows that the structure of certain terms is 
determined uniquely, thus the empirical p l term is the only term 



160 SERIES LIMIT [CHAP. 

arising by the addition of a p electron to a 2 P$ limit and having 
/ = 0; and it is thus the only term whose structure can be ex- 
pressed symbolically as ( 2 P^ . p) . But unfortunately no method 
is known of distinguishing two terms which have the same limit 
and the same value of J, though theory shows clearly that the 
one arises when the p electron has J 2 =2 an d the other when 
j 2 = 1|. p 6 and p 8 must both be written ( 2 Pi^.p) 2 > for they can- 
not be distinguished as ( 2 Pi.p$) 2 and ( 2 Pi*-Pu)2- 

The same method when applied to the ( 2 P) d terms of neon or 



\ 
















V- 







I 


4 


I 




3 I 4 


Limit \ 
















^i 






B i' 


S l" 


s/'" 


a/" 




'^U 


d fl 


d 2 


d 6 


d/' 


d 3 


d/ 


d 4 d/ 



Fig. 19-3. Limits of the ( 2 P)wd terms of neon and argon. 



v 

Limit \ 

2 ^14 



Fig. 19-4. Limits of the ( 2 P)ns terms of silicon. 

argon gives Fig. 19-3, while applied to the 3p.ns configuration of 
silicon it gives Fig. 19-4. 

The J values of all known series fit in with these requirements, 
and the agreement is equally satisfactory whether the low terms 
are roughly Russell-Saunders as they are in nitrogen and the s 
terms of neon, or whether a large gap separates the terms tending 
to the upper and lower limits as in the p and d terms of argon. 

2. Hand's theories 

The real problem, however, is not to account for the empirical 
terms by assuming a (jj) coupling, but to name them with the 
Russell-Saunders symbols. 

Towards the solution of this problem Hund has made two 



xix] HUND'S THEORIES 161 

pronouncements. In the first* he fixed the limit towards which a 
term series must converge, and fixed it given only the ion, the 
series electron and the symbol of the term; but though this theory 
is successful enough when both terms and limit are erect it fails 
badly when the limit is inverted as it is in neon.| Thus the 
( 2 P)/&s configuration yields two terms having J= 1, 3 P X and ^j 
Hund's early theory states that of these 3 P X will always approach 
the 2 P^ limit, and 1 P 1 the 2 P 2i limit; but though this prediction is 
correct in silicon it is incorrect in neon. 

Hund's revised prediction J is less precise and therefore less 
useful; it has usually been taken to mean that terms arising from 



Term 


71=5 


Av 


3 ^ 3 
3 JD 2 
3 >i 

^2 


19533-2 

18802-5 
18398-6 
16122-5 


730-7 
403-9 
2276-1 



n 6 


Av 


Limit 


108313-0 
107817-0 
107309-3 
107631-5 


496-0 
507-7 
-322-2 


195,195 
194,824 
194,268 
195,978 



Fig. 19-5. Values of the limits to which the four terms of the 4d . na configuration 
of Zr in tend. 

the same configuration and having the same J do not cross as they 
approach the limit; and in this form the theory is certainly in 
closer agreement with experiment. Thus in silicon the 3 P 1 term 
lies below the 1 P 1 term and accordingly 3 P X will approach the 
lower limit, namely 2 P^ of Si n; in neon 3 P 1 , being s 4 in Paschen's 
notation, again lies below x P t or s 2 , so that again 3 P 1 approaches 
the lower limit, but this time the limit is inverted and the lower 
component is 2 P^ . 

There are many similar successes to the credit of the revised 
theory, but it is not without its own problems. Consider the 
4d.?is configuration of Zrin for example ; the levels of this con- 
figuration are shown in Fig. 19-5, measured upwards from the 
3 F 2 ground term. Each of these pairs of terms is treated as part of 
a Rydberg sequence, and the limits calculated. 

These seem to show that 1 D 2 , though below 3 D 2 in the low 

* Hund, Linienspektren, 1927, 184 f. 

t Shenstone, N, 1928, 121 619; 122 727. 

{ Hund, ZP, 1929, 52 601. 

Kiess, C. C. and Lang, BSJ ', 1930, 5 321. 



162 SERIES LIMIT [CHAP. 

terms, yet tends to a higher limit, for the separation of the limits 
of 1 D 2 and 3 D 2 works out as 1 154 cm." 1 , which compares well with 
the interval of the 2 D term of Zr iv, which is 1250 cm." 1 That the 
1 D 2 sequence should converge to the upper limit is in accord with 
Hund's early theory, but contrary to the usual interpretation of 
his later pronouncement. 

A letter, however, written by Hund to Mack* shows that his 
statement has been interpreted too rigidly, for he specifically 
limited his prediction to terms which showed no symmetry 
property, and the letter states that any experimental evidence of 
crossing is to be taken as evidence of a symmetry property of the 
system. Accordingly the crossing of levels having the same J can 
never be in disagreement with Hund's conjecture, and the latter 
is in fact only a convention for naming levels where experiment 
does not distinguish between them. Mack pointed this out. 

But even in this very limited form one may question whether 
the convention is useful, for if the Russell -Saunders notation is 
not to have any of its usual implications, it is surely better 
abandoned, and one which has no implications at all adopted in 
its place. And in fact Russell has advised that terms whose con- 
figuration and coupling are still undetermined shall be specified 
simply by numbers. 

Present theory thus appears unable to make any general 
pronouncements, but it is not therefore valueless; experiment 
shows that in a large number of spectra, terms having the same J 
do not cross, and accordingly the consequences of this hypothesis 
are worthy of study, if only as an ideal with which the empirical 
may be compared. This ideal is the more useful in that if all terms 
obeyed Hund's energy rules only two types of convergence would 
be found, one when the limit is erect, the other when the limit is 
inverted. The erect type of convergence is identical with that 
dictated by Hund's first theory. 

Take as an example the convergence of the terms of a ( 3 P) nd 

configuration when the limit is first erect and then inverted 

(Figs. 19-6, 19-7). When the limit is inverted all components of a 

multiplet tend to approach the same limit, but when the limit is 

* Mack, PR, 1929, 34 34. 



xix] HUND'S THEORIES 163 

erect they tend to approach different limits; and in this the 
( 3 P) d terms are only one example of a general trend. 

A word should be added on the filling up of these figures; the 
number of cells in each row and their J values have been con- 



\ 
















V 


i 


\ 1 


* 




k 


3 


i 4* 


Limit \ 
















3 P 2 


2 P 


4Jt> l 1 2P li 


2 D 


a D 


2 *\t 


2 F 3 i 


4J) 4Ji 


















'Pi 




'* \ ^li 


4 H 


4P 2i 


4 I>H 


4 F 3i 




'P. 






4 *ii 


4 *u 









Fig. 19-6. Convergence of ( 3 P)wd terms when the limit is erect ; the low terms are 
assumed to obey Hand's energy rules and terms with the same / do not cross as 
they tend to the limit. 



\' 

Limit \ 



1* 



2i 



3^ 



Fig. 19*7. Convergence of ( 3 P)nd terms when the limit is inverted, the assump- 
tions being the same as in the previous figure. 

sidered earlier; the terms arising from ( 3 P)d are 4 F, 4 D, 4 P, 2 F, 2 D, 
2 P in that order from below upwards; accordingly, starting with 
4 F, insert each of the four components in the lowest cell which 
its / value permits; having finished 4 F continue to 4 D and so 
through 4 P arid 2 (FDP) until all seventeen cells are full. 

A number of these convergence types are given in Fig. 19-8. 



BIBLIOGRAPHY 

Chapter xix of White's Introduction to atomic spectra may be usefully read, 
though its subject "Series Perturbations" is parallel to rather than a develop- 
ment of series limits. 











O 














o 












gn 














e 






& 
















CO 




O 


&< 




cc 


ft 






P 


O 






% 


CO 


P 


? 






* 


CO 




* 


& 


fl CO 
| 


& 


p 




E? 


^ 


| 




PH 

CO 


fr 




fr 


&< 





P., 


^ 


(M 


PH 

CO 


& 







p 


p 




P 


p 







p 




ft 


ft 






PH 


p 




& 


p 

CO 




fi^ 


p 




SP 


? 






PH 






* 


* 






PH 




PH 


PH 






PH 

CO 






<? 


* 






PH 

CO 




2P 


OH 










O 












O 










































P 




CO 






CO 




gn 

gn 






p 

CO 






PH 


CO 


1 




p 
p 




PH 


P 

co 


s 




ft 


p 




P 


p 


1 


ft 


PH 

CO 




P 


P 






cp 


p 




* 


p 




8P 


p 

eo 




^ 


P 






OH 


PH 






PH 

CO 




* 


* 




PH 








y 


PH 






PH 

CO 




VQ 


PH 




PH 

CO 












O 


























CO 












CO 










fr 






P 








a- 






P 






* 






P 




fl 




PH 






P 








PH 







p 


o 


PH 






ft 




2 

1 


,-~s 




PH 






p 


OJ 

<> 


S- 






ft 




02 






/ I 



p p 



p p 











10 


O 
PM 




















? 


"* 


PH 






* 


O 


9 




^ 






PH 






9 


PM 




ft 








O 


PH 




H- 






PH 






p 


O 


CO 


E? 


PH 




CO 


& 


ft 


9 


fl 




PH 


9 


CO 


PH 


9 


PH 




PH 


ft 






? 


ft 


S 5 


. 




PM 


PH 




PH 


9 


9 


"M 


ft 


* 


PH 


fN 


ft 


* 


PH 




ft 


PH 


ft 


<M 


ft 


PM 


PH 




ft 


ft 


* 




ft 


PM 


PH 




PM 


P^ 


PH 




ft 


PH 


PH 


1 "~ l 


& 


PM 




'"' 


^ 


OQ 


ft 


" 




ft 


ft 


11 


PM 


op 


ft 




& 


ft 






8P 


PM 


ft 






PH 


ft 




ff 


%* 


ft 




& 










fr 










& 






PM 












































HIM 
















HN 


















9 




















PH 


CO 


ft 








E? 


^ 










ft 






PH 


ft 




PM 






Hoi 


PH 


9 




fl PHKM 






ft 


rH-N 




9 


PH 




ft 


ft 






ft 


9 


PH 


o 




ft 


PM 

rf 




ft 




9 




ft 


PM 






PM 


PM 


PH 


PH 




CO 


ft 




ft 


n 


&H 


HN 


IM 


** 




H*J 






" 


H^i 








HlOl 








~ 


< 


CO 

TH 


9 






ft 


ft 




& 


ft 


PM 




&- 


&< 






8> 


s- 


9 






PM 


ft 




SP 


PM 


ft 




e^ 


9 








&< 










PM 






PH 






^ 
" 














































CO 


9 














CO 
Hot 






ft 
ft 




PH 
PM 






<M 




ft 
ft 




"o ,, 






* 

g, 






ft 
ft 




-JIM 




PM 

PM 

IM 


V 








ft 
ft 


CQ 
HIM 


PM 


PH 




HC4 


9 
p 








ft ft ft 



CHAPTER XX 
HYPERFINE STRUCTURE 

1 . Empirical 

When the interferometers of Michelson , Fabry-Perot and Lummer- 
Gehrcke are applied to spectral lines, which appear single in a 
prism spectroscope, many are found to exhibit acomplex structure 
with component intervals of 0-1 to 1-0 cm." 1 This much has 
been known since these high resolving instruments were first 
invented, the structure being commonly referred to as hyperfme. 

The small intervals alone might suggest that the hyperfine 
levels can hardly be attributed to the same electron spin which 
produces the normal multiplet; and this suspicion gains support 
from the difficulty in fitting them into Hund's term scheme. 
Caesium, for example, must surely have a doublet structure, yet 
if a spectroscope of high resolving power is applied to certain lines, 
which should be simple, they appear as doublets with an interval 
of about 0-3 cm." 1 Time and again Hund's scheme has predicted 
how many terms an element should possess, and when the 
analysis has been completed, these and only these have been 
found. Yet when an element exhibits hyperfine structure, the 
extra levels cannot be fitted in. 

Clearly then some new explanation must be sought. In 1924 
Pauli* drew attention to the nucleus as a possible influence; but 
it was not until the following year that Schiller f brought forward 
the first experimental evidence in his work on the hyperfine 
structure of the 5485 A. line of Lin. This line arises from the 
2p 3 P ! >2 -> 2s 3 S X transition, and should therefore be similar to 
the 7065 A. line of Hei, for the latter arises from 3s 3 S->2p 3 P; 
but whereas the helium line is a triplet, Schiller showed that the 
5485 A. line of lithium has at least 14 components. 

As both the helium atom and lithium ion have two orbital 
electrons, they differ only in their nuclei; and so to the nuclei 

* Pauli, Nw, 1924, 12 741. 

t Schiiler, AP, 1925, 76 292; ZP, 1927, 42 487. 



CHAP. XX] EMPIRICAL 167 

must be attributed the hyperfine structure. Further, lithium has 
only two isotopes, Li 6 and Li 7 , so that even if these did pro- 
duce separate triplets they would account for only 6 out of the 14 
components; the nuclear property responsible must therefore be 
something other than a simple mass effect. 

2. Influence of nuclear mass 

In both hydrogen and ionised helium, the series are governed 
by the relation 



but the Rydberg Constant, R, has a slightly different value in the 
two spectra, 109,678 in hydrogen and 109,722 in helium. This 
small difference Bohr explained as due to the different mass of 
the two nuclei; for if the mass is infinite 



But when the mass of the nucleus is finite, the electron and nucleus 
both revolve about the common centre of gravity; to correct for 
this one substitutes for the mass of the electron, m e , the quantity 

M 

-Tt~Jr 

M + m e 



e 



This theory clearly shows that the spectral lines of the heavy 
isotope of hydrogen will be displaced, each line of the Balmer 
series having a weak component on its short wave-length side ; 
moreover, as the mass of the isotope is 2, the intervals of 
the first four lines, H a to H 8 , should be 4-16, 5-61, 6-29 and 
6-65 cm.^ 1 * Photographs show that in fact a weak satellite does 
occur in this position, and that the satellite is stronger when the 
concentration of H 2 is increased. 

When there is more than one electron, the theory is much more 
complicated, but Hughes and Eckartj have provided a solution 
for systems of two and three electrons. The separations of the 

* Urey, Brickwedde and Murphy, PE, 1932, 40 1. 
f Hughes and Eckart, PR, 1930, 36 694. 



168 HYPERFINE STRUCTURE [CHAP. 

lithium isotopes, Li 6 and Li 7 , is in reasonable agreement with 
theory.* The measured intervals are : 

Li ii 2p 3 P->2s 3 S 5485 A. 1-06 cm." 1 
Lii 2p 2 P->2s 2 S 6708A. 0-345cm.- 1 
3p 2 P-^2s 2 S 3233 A. 0-56 cm.- 1 

For atoms with more than three electrons, no theory has been 
evolved, and in fact a displacement due to mass alone seems to 
have been demonstrated only in neon. Each arc line of this 
element is accompanied by a faint companion of shorter wave- 
length. If the single electron theory was not invalid, it would 

CX 

suggest that the intervals should be given by = 247 . 10~ 8 , while 

experiment shows that this ratio assumes the values 437 . 10~ 8 
in the lines 2p m ->ls 2 , and 368. 10~ 8 in the lines 2p m ->ls 345 . 
Thus the qualitative agreement is satisfactory, f 

3. The extended vector model 

The first theory put forward to explain hyperfine structure^ 
assigned to the nucleus an angular momentum I, and made 
this combine with the electronic moment J to form a resultant 
atomic moment commonly written F. Then F must be quantised 

as well as I, and 

J + 1 = F. 

Previous experience with the similar linking of L and S to form 
J suggests that possibly F will change only by 1 or 0, and that 
the transition from F = to F = will be forbidden; further, one 
may hope that the multiplet intervals will satisfy the Lande 
interval rule. This hypothesis was at first only a guess, but evi- 
dence drawn both from experiment and from the calculations of 
the wave mechanics shows that the guess is fortunate. 

Evidence will be adduced first in support of the interval and 
selection rules; thus certain lines of the bismuth spectrum were 

* Hughes, PR, 1931, 38 857. Cf. Granath, PR, 1932, 42 44. 
f Hansen, N, 1927, 119 237; Nagaoka and Mishima, Imp. Acad. Tokyo, 
Proc. 1929, 5 200, 1930, 6 143; Thomas and Evans, E. J., PM, 1930, 10 128. 
t Pauli, Nw, 1924, 12 721. 



PLATE VII. HYPERFINE STRUCTURE 

1. Potassium resonance lines, 7699 and 7665 A., 2 P-- 2 S. Light from a 
potassium lamp was examined with a Fabry -Perot etalon, after passing 
through a beam of potassium travelling at right angles to the line of sight ; 
the absorption pattern possesses a fine doublet structure, the Dopplor 
width in absorption being much less than in emission. 

2. Rubidium resonance lines, 7800 and 7948 A., 2 P-^- 2 S. Photographed 
with a reflection echelon, each line consists of four components; the weak 
outer components are due to Rb 87 , and the strong inner components to 
Rb 86 . As the hfs is the same for both lines, it arises in the common level 2 S. 

3. Caesium line, 4555 A., 2 P r j-> 2 S. The hfs revealed by a Lummer- 
Gehrcke plate consists of doublets, arising in the 2 S level ; the intensity 
ratio of 1-27 : 1 shows that I = 3. The fringes of 4593 A., 2 P$ -* 2 S, appear 
very faint. 

4. Gallium resonance line, 4033 A., 2 S -> 2 P$ . A reflecting echelon grating 
reveals three lines with intensity ratio of 4-9 : 6-1 : 5. The 2 S and 2 P terms 
have nearly the same interval so that two of the four components over- 
lap; the theoretical patterns are the same for 1 = J and 1= 1, but the 
intensity ratios are 1:2:1, and 5:6:5 respectively, thus I = 1. 

5. Indium line, 4101 A., 2 S-> 2 P}. The photograph on the left is taken 
with a reflecting echelon grating, while on the right this has been crossed 
with a Fabry -Perot etalon. Since the four streaks A, B, G, D lie on a 
diagonal, the pattern consists of these and not of D', A, B, C as the left- 
hand figure might suggest. The intensity ratio of 2-72:1-82; 1-00:2-74 
shows that I = 4 J. 

6. Thallium line, 5351 A., 2 S -> *Pi&. The left-hand photograph was taken 
with a reflecting 6chelon, in the right hand this has been crossed with a 
Fabry -Perot etalon. The line consists of two close doublets, for the com- 
ponents &' and B' can only be 6 and B appearing in the next order, since 
on the right the etalon fringes appear at the same height. The small 
interval is due to isotope displacement, a and 6 being due to T1 203 and 
A and B to T1 20 5 >" the larger interval is due to the hfs of the 2 S term. 

7. Thallium line, 3776 A., 2 S-> 2 P. The six components are arranged in 
three close doublets, but the pair B and 6 in the n th order overlap the 
pair C and c in the (n+ l) th order, for when the Echelon is crossed with 
a Fabry -Perot etalon, the fringes in these lines are double. 

All photographs were lent by Dr D. A. Jackson. 



Hate VII 



7699A.\ ,7665A. 



Potassium 



4503 A.v /455BA. 

<lr - -;r,-- f,. I--J-.A- - 



A. 



Ruhidium 



5 (a) 



S ? ^ 



Caesium 



m 

Gallium 
6(0) 6(W 



Thallium, 



V"M 



Indium 



Thallium 

A. 



fn 1 * 11 ) order 



n^) 



XX] 



THE EXTENDED VECTOR MODEL 



169 



early analysed* and the 4722 A. line, arising from the p a .sl t -> 
p 3 . 2 D u transition may be quoted as an example. The observed 
pattern is shown in Fig. 20*1 and analysis of this shows that the 
lower term, 2 D U , has intervals of 0-152, 0-198, and 0-255; these 
best satisfy the interval rule if F is assigned the values 3 to 6; and 
the vector model allows just these values if / is 4|; moreover, the 
model predicts always (2J+ 1) or (2/+ 1) components, according 
as / or J is the larger, and in fact the lj , 8 H and 2 D 2 ^ terms do 



Term. 



Intensities 



^l ^1 

H. 



Intervals 









IQ- 3 cm" 1 


4 






830 


3 














4 










1 52 =4 x^ft 


5 






198= 5 x 4 o 


6 


255 = 6 X42 



Fig. 20-1. Level diagram showing tho structure of the 4722 A. line of Bi I; the 
intervals given are empirical, the intensities theortical. (After Goudsmit and 
Back, ZP, 1927, 43 321.) 

split into 2, 4 and 6 levels respectively. Of these terms the two 
last obey the interval rule even better than the 2 D^ term cited 
above (Fig. 20-2). 

The analysis of bismuth by the interval rule has been followed 
up by work on Mn, Pr, La and Cs. That bismuth was the first 
element successfully analysed was not due only to chance, but to 
the existence of only one isotope. For where several isotopes 
occur, each may have a different nuclear spin, and each spin then 
produces its own hyperfine pattern. 

* Goudsmit and Back, ZP, 1927, 43 321. Zeeman, Back and Goudsmit, 
ZP, 1930. 66 1. 



170 HYPERFINE STRUCTURE [CHAP. 

Thus cadmium possesses six isotopes and these manifest 
themselves in the structure of the triplet 4678, 4800, 5086 A., 
which arises from the transition 2 3 S 1 ^2 3 P 1>2 .* T ne three 
hyperfine patterns have only one interval in common, namely 
0-396 cm." 1 , and the 2 3 S t term must split therefore to two and 
only two components; but as the number of components is always 
(2J+ 1) or (2/-h 1), / must be |; and since this value must hold 
for all three P levels the term scheme and line pattern should be 
those shown in Fig. 20-3. All the lines required by this scheme are 
in fact observed and have their theoretical intensities, but in 



Term 


F 


2 3 


4 


5 


6 7 


6pMD u 


Interval 
A 


-0-152 
- 0-038 


-0-198 
- 0-040 


-0-255 
- 0-042 





6p3.*D n 


Interval 
A 


0-256 0-312 

0-085 0-078 


0-385 
0-077 


0-491 
0-082 


0-563 

0-080 


6p 2 .7s.8 u 


Interval 
A 


0-379 
0-095 


0-473 
0-095 


0-563 
0-094 


. 



Fig. 20-2. Examples of the interval rule in bismuth. 

addition each gross line has a strong component shown by the 
dotted line A at the foot. This strong component has been 
attributed to isotopes of cadmium having no nuclear moment and 
hence no hyperfine structure. Of the six isotopes of cadmium 
which Aston has identified therefore some have a nuclear moment 
of \ and some of zero ; and the intensity of A relative to the other 
components makes it necessary to allocate the value \ to the odd 
isotopes 111 and 113, while all the even isotopes 110, 112, 114 
and 116 have 7 = 0. 

Cadmium is peculiar in that the hyperfine levels are inverted, 
the levels with the largest values of F lying lowest; this arrange- 
ment is rather rare among hyperfine structures thus far analysed, 
though the 2 D^ level of bismuth examined above happens also 
to be inverted. 

The results thus far cited may be taken to prove that the hyper- 
fine intervals satisfy the interval rule and that the selection rule 
is AJF= 1 or 0; but no evidence has been adduced to show 

* Schiiler and Briick, ZP, 1929, 56 291; 58 735. 



XX] THE EXTENDED VECTOR MODEL 171 

whether the transition from F = to F = is specifically forbidden. 
Consider therefore the 3776 A. line of Tli, a line which arises from 
the jump 2 2 Sj -> 2 2 P^; examined for hyperfine structure this line 



2'S, 



F 

i _ 



260 




2 149 

^ 



J_L 



Calculated 





Observed 



5086 A 



Fig. 20-3. Level diagram showing the structure of three cadmium lines. 

reveals an unsymmetrical triplet (Fig. 20-4).* As the initial and 
final terms have the same value of J, this structure can be ex- 
plained only if / is , and if the jump from ^ = to J^ = is 
specifically forbidden; any other value of / would give rise to 



* Schiiler and Briick, ZP, 1929, 55 575. Schiiler and Keyston, ZP, 1931, 
70 1. 



172 HYPERFINE STRUCTURE [CHAP. 

four components, and should two of these coincide then the 
triplet would be symmetrical. 

That the same selection and interval rules are valid for both 



F 
1 



707cm 1 



- 


CN 


- 



Fig. 20-4. Level diagram of the 3776A., 



, line of thallium. 



Gross structure 


Hyperfine structure 


Resultant of spin moments 
Resultant of orbital moments 
Vector sum of S and L 


S 
L 
J 


I 
J 
F 


Nuclear spin 
Electronic moment 
Vector sum of I and J 


Magnetic moment of spin 
Magnetic moment of orbital 
vector 


</(S).S 
<7(L)-L. 


<J (I)- 1 
g(J).J 


Magnetic moment of nucleus 
Magnetic moment of electronic 
vector 


Projection on magnetic axis: 
of S 
of L 
of J 


M S 
M L 
M, 


MI 
M, 
M P 


Projection on magnetic axis: 
of I 
of J 
of F 



.Fig. 20-5. Comparison of vectors used to explain gross and hyperfine structures. 

gross and hyperfine structures suggests a far-reaching analogy, 
which is summarised and extended in Fig. 20-5, so as to suggest 
rules for the Zeeman and Paschen-Back splitting. The angular 
momenta are given in units A/2?r and the magnetic moments in 
Bohr magnetons ^ 



XX] THE EXTENDED VECTOR MODEL 173 

That the interval rule is valid shows that if the interaction 
energy of I and J is E, then 

E/ch = AIJcos(IJ) 

= $A.{F(F+1)-J(J+1) -/(/+!)} ....... (20-1) 

The separation of the two levels F and (F 1) is then 



so that successive intervals in a multiplet term are proportional 
to the greater of the adjacent quantum numbers. 

Hyperfine multiplets usually obey the interval rule so well that 
exceptions attract an attention, which similarly deviating gross 
multiplets never obtain. These irregularities are to-day recognised 
as arising from at least two distinct causes, perturbation and 
absence of spherical symmetry in the electric field of the nucleus. 
As perturbation, however, produces also abnormal isotope 
displacements, and isotope displacements have not yet been 
considered, these irregularities are better postponed to a later 
section. 

4. Zeeman and Paschen-Back effects 

In work on the splitting of lines in the magnetic field, theory 
has long travelled ahead of experiment, so consider what splitting 
the vector model predicts.* 

In a weak field J and I combine to form F, and the projection 
of F on the magnetic axis H is quantised. According to the theory 
of the Zeeman effect, the increment of energy will be A, where 

. ...... (20-2) 



o m is here an abbreviation for the Lorentz unit 

f>Pf 

- = 4-698. lO- 



H being measured in gauss; while M F is restricted by the 
condition 



This energy equation gives the displacement of a level from the 
position it occupies when the magnetic field is zero; to obtain the 



Goudsmit and Backer, ZP, 1930, 66 13. 



174 HYPERFINE STRUCTURE [CHAP. 

displacement from the centroid a second term must be added so 
that the energy becomes 



...... (20-3) 

A is here the hyperfine interval quotient. 

In an earlier chapter g (J) was derived on the assumption that 
if two vectors X and Y combine to form a third vector Z, then 



this expression being itself derived from the wave mechanics. 
Now F = J + 1, so that 



...... (20-4) 

The magnitude of the hyperfine splitting itself and the theory of 
its cause both suggest that g (I) will be very small, about 1/2000 
say, so that in all fields which can be applied to the atom g (I) will 
be negligible, and g(F) may be written as 



} -. 

...... (20-5) 

This completes the description of the weak field. In a strong 
field J and I are no longer linked together, but precess indepen- 
dently round the magnetic axis, so that their projections on the 
magnetic axis have to be quantised separately. As in the theory 
of the Paschen-Back effect, so here 

Elch-AMjMj + MjgWon, ...... (20-6) 

where g (I) has been treated as negligibly small. 

This simple theory should give good agreement in fields so 
weak that o m ^ A y and in fields so strong that o m > A\ but in 
intermediate fields resort must be had to the quantum mechanics. 
Moreover, in all fields the quantum mechanics should give more 
accurate numerical values. 

A complex theory such as this is most satisfactorily tested, if 
applied, first to a transition producing a simple pattern, and 
afterwards to patterns of growing complexity. Accordingly, 



XX] ZEEMAN AND PASCHEN-BACK EFFECTS 175 

Green and Wulff first examined the 3092 A. line of Tin, which 
arises from Gs.Ts^Q-^Os.Gp 1 ?^* and then turned to more 
complex lines in thallium and bismuth. | They worked with the 
first and second spark spectra, because hyperfine intervals are 
there larger than in the arc ; and they examined each line in three 



No field Weak field 
5kg. 

F Mp 


Strong field 
Mj MI 40 kg. 
, i 


1 2 








2 -96cm 1 


,.T 




, 


Z 






, 


i "~~ 






h n ' 










~ Vi 






2 
















i 1 


1 2 

, 1 










~Z 














I I 



Fig. 20-6. Level diagram showing the splitting of the 3092 A., 1 S -> 1 P 1 , line of 
Tl n in weak and strong magnetic fields. The displacements shown are calcu- 
lated from the vector model. 

fields. In these heavy elements, the Doppler effect does not pro- 
duce so wide a line as when the atom is light; moreover, thallium 
and bismuth provide a convenient contrast, for their nuclear 
moments are ^ and 4| respectively, so that in a strong field the 
thallium lines split to two components while the bismuth split 
to ten. 

Consider then the 3092 A. line of Tl n; of the two terms, 1 S and 

* Green and Wulff, ZP, 1931, 71 593. 

f Green and Wulff, PR, 1931, 38 2176, 2186. 



176 HYPERFINE STRUCTURE [CHAP. 

1 P 1 (Pig. 20-6), from which it arises, the first does not split but the 
second has a hyperfine interval of 0-96 cm." 1 , so that the 
interval quotient A is 0-64 cm." 1 ; while in the weakest field 
used, namely 14,700 gauss, the Lorentz unit o m is 0-69 cm." 1 In 
this field then o rn is not 'much smaller' than Ay and the splitting 
is likely to be characteristic of an intermediate rather than of a 
weak field; but in fact the simple Zeeman theory does give good 
qualitative agreement. For the F= 1| and ^ components of the 
1 P 1 term g(F) works out at f and * respectively, so that the 
patterns predicted are (1)1 3/3 and (2) 2/3, while the dis- 



Field strength 


14,700 g 


43,350 g 


M P 


Vector 
model 


Quantum 
mechanics 


Vector 
model 


Quantum 
mechanics 


1* 


0-37 


0-37 


1-51 


1-51 


* 


1-10 
- 0-09 


1-06 
-0-05 


2-15 
0-32 


2-17 
- 0-025 


-k 


0-18 
-0-55 


0-11 

-048 


-0-32 
-1-51 


0-005 
-1-50 


-1* 


- 1-01 


-1-01 


.-2-15 


-2-15 



Fig. 20-7. Displacements of the 1 P 1 term of Tl u in weak and strong magnetic 
fields. 

placements calculated by equation (20-3) work out as 0-37, 
-0-09, -0-55 and - 1-01 for F= 1|, and 1-10 and 0-18 for F = %. 
Pig. 20-7 shows how these calculations compare with the more 
accurate predictions of the quantum mechanics. 

In contrast a field of 43,350 gauss produces a Lorentz unit of 
2-02 cm." 1 , so that splitting characteristic of a strong field is to be 
expected. In fact theory shows that the 3092 A. line splits to six 
components, whose displacements are (0-32), 0-32, 1-51, 2-15. 
The pattern thus consists of three pairs of lines, one at the cen- 
troid of the hyperfine doublet and the other two arranged sym- 
metrically on either side; and in general terms this is what 
experiment reveals, though the numerical agreement is not 
close. 

Better numerical agreement is, however, obtained if the more 
precise theory of the wave mechanics is substituted for the 



XX] ZEEMAN AND PASCHEN-B ACK EFFECTS 177 

vector model (Fig. 20-8, 9); the energies of the six 1 P 1 terms are 
then 



.(20-7) 



Jf,= -l* E v =\A-go m . 

E v is here to be measured in wave-numbers, and g is an abbre- 

viation for g (J) not g (F) ; moreover, g must be assigned the value 



M 
V 





I 



J. II . II 

Fig. 20-8. Fig. 20-9. 

Fig. 20-8. Splitting of the 3092 A., ^-^SQ , line of Tl n in a field of 14,700 gauss. 
The upper curve is the microphotometer trace taken from a photograph ; below 
is the theoretical pattern. (After Green and Wulff, ZP, 1931, 71 597.) 

Fig. 20-9. Splitting of the 3092 A. line of Tl n in a field of 43,350 gauss. (After 
Green and Wulff, ZP, 1931, 71 599.) 



178 



HYPERFINE STRUCTURE 



[CHAP. 

1-025 instead of 1 since the coupling is not pure (LS), but shows 
some signs of the (jj) type so that the g factor of the 1 P 1 term is 
influenced by other terms which lie near; the numerical value of 
the correction is obtained by the method of Houston.* 




20 40 Kg 

Field strength 

Fig. 20-10. Displacements of the hyperfine components of the 2 Sj and 2 P^ levels 
of Tl I in various fields. The displacements are calculated by equations (20-8) of 
the quantum mechanics. 

Thus theory interprets this simple pattern with great success; 
nor is it less successful with the more complex patterns of Tli. 
Back and Wulffj photographed the 3776 A., ^-^P^, line in 
fields of 17,050, 29,700 and 43,350 gauss. In these fields the 
Lorentz unit assumes the values 0-80, 1-40 and 2-08 cm." 1 , while 

* Houston, PR, 1929, 33 297. 

t Back and Wulff, ZP, 1930, 66 31. 



XX] ZEEMAN AND PASCHEN-BACK EFFECTS 179 

the hyperfine intervals of the 2 S$ and 2 P^ terms are 0-40 and 0-71 
respectively, so that all three fields are technically * strong'. The 
magnetic field and nuclear moment would thus separately split 
each term in two; the Zeeman components being determined by 
Mj = J, and the hyperfine components by M j = J. According 
to the wave mechanics the displacements of these four levels 
from the centroid are given by the equations: 



1 

-i 



-4 

i 



= 

o = 

-i --I -1 =A\-\go m ...(20-8) 

and shown graphically in Fig. 20-10. As previously g is here an 
abbreviation for g(J). 



No field 



Weak field 



Strong field 



5 Kg. Mj M, 40 Kg. 


-L J, 


F M F 










i 




Q 




1 





40cm 1 




- 1 [ 




~1 


- . n 









































* 


II 

ii 




















n 




















n 


















4- 5- 


n 




1 














Z 2 


n i 
1 1 




0- 


71cm" 1 




l_- 


t- 

_i_ 


' 1] ~" " " 
1 ' I 






o- 


it ! 





7T 

cr 



Fig. 20-11. Level diagram to show the structure of the 3776 A., ^-^Pj, line of 
Tl i in weak and strong magnetic fields. The diagram assumes that the laws of 
the vector model are valid. 



180 



HYPERFINE STRUCTUKE 



[CHAP. 

When the four levels of each gross term combine, they would 
give rise to six TT and eight a components in a weak field, but in a 
strong field two TT and four a components fade, for in a strong field 
transitions in which Mj changes its value are no longer allowed 
(Fig. 20-11). The empirical displacements are compared with this 
theory in Fig. 20-12, the centroid of the empirical pattern being 
adjusted so that the line of lowest frequency has the value 
dictated by theory. The empirical intensities are estimated, not 





Parallel components 


Perpendicular components 


Field 






in 
gauss 


Position (cm." 1 ) 


Intensity 


Position (cm." 1 ) 


Intensity 




Calc. 


Obs. 


Calc. 


Obs. 


Calc. 


Obs. 


Calc. 


Obs. 


17,050 


1-344 


1-39 


3-1 


3 


1-521 


1-62 


8-0 


9 




0-456 ) 
0-455 j 


0-50 


6-9) 
10-0 j 


10 


0-810 
0-633 


0-93 
0-76 


9-85 
2-0 


9 
1 




- 0-302 


-0-24 


6-9 


8 


0-278 


0-34 


0-15 


0-5 




-0-609 


-0-57 


10 


10 


- 0-075 


-0-05 


2-0 


3 




-1-190 


-1-19 


3-1 


3 


- 0-863 





0-15 















-0-963 


-0-94 


8-0 


6 












-1-368 


-1-368 


9-85 


10 


43,350 


2-89 


2-91 


0-8 


6 


3-08 


3-11 


9-4 


10 




1-36 


1-50 


9-2 


7 


2-45 


2-46 


10-0 


10 




1-28 


1-17 


10 


9 


1-55 


1-59 


0-6 


1 






-1-06 




2 












-1-20 


(1-19) 


9-2 




1-09 





0-02 









-1-32 




7 


-1-00 


-0-97 


0-6 


1 




-1-44 


(1-43) 


10 




-1-65 





0-02 









-1-55 




10 












-2-74 


-2-74 


0-8 


6 


-2-52 


- 2-52 


9-4 


10 












-3-00 


-3-00 


10-0 


10 



Fig. 20-12. Splitting of the 3776 A. line of TJ I compared with the predictions of 
the quantum mechanics in two magnetic fields. 

measured. To prove that the vector model gives a reasonable 
approximation to these results is left to the reader. 

In bismuth the theory is of course unchanged, but one line may 
be cited to show how the nuclear moment was first determined by 
the use of a magnetic field.* The 4722 A. line arises from the 
l^-^D^ transition, so that in the absence of hyperfine structure 
it should split to two TT and four a components. When the line was 
examined in a field of 43,340 gauss, these components were found, 



* Back and Goudsmit, ZP, 1928, 47 174. Zeeman, Back and Goudsmit, ZP, 
1930, 66 1. 



xx] 



ZEEMAN AND PASCHEN-BACK EFFECTS 



181 



but all were exceptionally wide, and four were clearly resolved 
into ten components (Fig. 20-13). Now the energy of a magnetic 
level is 



E/ch^AM.Mj 

where the second term determines the gross Zeeman level and the 
first term its hyperfine structure; as M T can assume (27 +1) 



No field 



71 



-4 



-3 



-2 



H =43,340^ 
4 cm". 1 



Fig. 20-13. Empirical structure of the 4722 A., l^-^D ^ , line of Bi I in a strong 
magnetic field. (After Back and Goudsmit, ZP, 1928, 47 179.) 

values, each gross term will have (21 -f 1) components (Fig. 20' 14). 
Moreover, as M x is not allowed to change in a transition the gross 
Zeeman lines will also split to (2/+ 1) components, the interval 
being A'Mj'-A'M/ (Pig. 20-15). Thus, if in fact the lines split to 
ten components the nuclear moment must be 4|. And it is of some 
interest to note that the value of the interval was also confirmed; 
the hyperfine interval quotients of the 2 D^ and 1^ terms are 
known to be 0-0403 and 0-166 cm." 1 respectively, so that the 
interval of the TT components should be 

A'MJ -A"Mj" = - 0-0403 ( - |) - 0- 166 ( - ) 
= 0-1031 cm." 1 , 

and of the outer cr components 

A'Mj-A"M/ = -0-0403 x|- 0-166 (- 1) 
= 0-0628 cm.- 1 

Now the width of the TT components was measured as 0-880 cm." 1 , 
so that the interval between successive components must be 
0-880/9 or 0-0977 cm." 1 The width of the outer a components is 
0-520 cm." 1 , and the interval accordingly 0-0577 cm." 1 Both are 
in satisfactory agreement with theory. 

In Figs. 20-16-17 evidence is presented for two still more com- 
plex lines, 2298 A., 2 3 S 1 ->2 3 P 2 of Tin and 5719 A., zp^P^ of 



No magnetic field 



Strong magnetic field 
(22,0009) 

No With No With 

hyperfine structure hyperfine structure hyperfine structure hyperfine structure 



Term 



cm. 



i- 



M 



-44 



+4J 



2 



1- 



-2- 



-ti* 



Fig. 20-14. Structure of the lj and 2 D^ levels, which produce the 4722 A. line 
of Bi i. The laws of the vector model are assumed, and the field strength has 
been reduced to half that actually used to keep the figure within reasonable 
limits; the g factors are abnormal being 1-225 and 2-088 in the two terms. 



CHAP. XX] ZEEMAN AND PASCHEN-B ACK EFFECTS 183 

Bi ii ;* in each figure the photometer curve appears above and the 
theoretical pattern below, and in both the agreement is all that 
can be desired. 



Term Mj 



MI 
41- 



21- 
II- 

J- 

__ 1 ~ 

" 2 1" 
-41 




cm 
4 
3 
2 
1 


1 
-2 
3 
4 



cm. 



Fig. 20-15. Level diagram to show the hyperfine structure of one gross a com- 
ponent of the 4722 A. line of Bi i. 

5. Intensities 

No absolute measurements of intensity seem to have been 
made, but the photometric curves obtained by Zeeman, Back and 
Goudsmit in 1930 showed that the intensity formulae deduced 
from the wave mechanics are qualitatively correct; while more 
recently these rules have been so widely applied to the analysis of 
the complex structures described in the next section and the 
results have been so satisfactory, that few serious deviations can 

exist. 

* Green and Wulff, PR, 1931, 38 2182, 2186. 



GO 

CO 



O5 

a ^ 



" 



3 

d 



- If 



-I 



a 




a I 



INTENSITIES 



185 



CHAP. XX] 

In order that the hyperfine components of a line may be 
observed with their theoretical intensities, however, the exciting 
source must fulfil certain conditions. Thus the temperature of the 
source must be as low as possible so as to reduce the Doppler 
broadening of the lines; the source is therefore worked in liquid 
air or liquid hydrogen. And secondly, the vapour pressure of the 




V- 



11 

J- II 

Fig. 20-17a. Splitting of the 5719 A. line of Bi n in a magnetic field of 14,700 
gauss ; again the photometer curve is above and theory below. The line arises as 
6p.7p 3 P ->6p.7s *P!. (After Green and Wulff, PR, 1931, 38 2186.) 

element in the source must be kept low, for high pressure leads 
to self-absorption; besides hyperfine intensities seem in some way 
disturbed by inter-atomic fields, though why they should be is 
not yet clear.* 

The intensity formulae, deduced from the wave mechanics by 
Hill,f correspond to the multiplet intensity formulae with the 
transformation (Fig. 20-5) already used in the interval rule. 

* Schiiler and Keyston, ZP 9 1931, 71 413. 
t Hill, Nat. Acad. Sci., Proc. 1929, 15 779. 





fig, of the A. line of Bi n in a field of 

A' ; : 
\ 




1 II 

Fig. 20-17c. Splitting of the 5719 A. line of Bi n in a field of 43,350 gauss. 



CHAP. XX] INTENSITIES 187 

In the jump </-> ( J 1) and 

F->(F-1) I_= l ~ 

JF 



while in the jump J -> J, and 

' 



where P(F) = (F + J)(F + J+1)- 1(1+1), 



)- 1(1+1). 

In all these formulae the transitions are so chosen that J and F 
are the larger of the two quantum numbers involved. Moreover, 
a term containing only J and / has been dropped since in fact 
the formulae are applied to the components of a single gross 
line. 

The Zeeman intensity formulae may be transformed in the 
same way and compared with the visual estimates of Back and 
Wulff.* 

6. Isotope displacement 

The vector model, based on the hypothesis of nuclear spin, 
solves many of the problems of hyperfine structure, but there is 
clear evidence that when several isotopes exist, the vector model 
does not suffice. 

Consider, for example, the Tli line, 5351 A. ,f which arises as 
7s 2 S t ->6p a P u ; work on the 3776 A. line of Tl has already been 
adduced to show that the nuclear moment of Tl is ^, so that the 
5351 A. line might be expected to split to three components with 
an intensity ratio of 5 : 2 : 1 as shown in Fig. 20-18; but in fact the 

* Back and Wulff, ZP, 1930, 66 31. 
f Schiller and Keyston, ZP, 1931, 70 1. 



188 HYPERFINB STRUCTURE [CHAP. 

line splits to four components, and these have intensities roughly 
in the ratio of 6-9 : 3 : 2-3 : 1, that is two pairs with an intensity 
ratio of 3 : 1 ; now the three lines of theory can be reduced to two 
with an intensity ratio of 3 : 1 if the two components of the 2 P X ^ 
term are not resolved. Accordingly, the empirical facts can be 
explained if there are two isotopes of Tl with an abundance ratio 
of 2-3 : 1, and if the term schemes of these two isotopes are dis- 
placed slightly relative to one another; in short that is if the term 

Term. F 



CM 


-I 


- 



Fig. 20-18. Structure of a normal 2 Sj-> 2 P^ line. 

scheme of Fig. 20-19 is postulated. In this diagram the energy of 
the 2 S^ term is supposed the same in both isotopes, though in fact 
only the displacements of the one term relative to the other can 
be measured; experiment then shows that the 2 P X ^ term is dis- 
placed through 55 X. in one of the isotopes 203 and 205. The 
existence of the isotopes 203 and 205 in the abundance ratio of 
1:2-3 has been confirmed by the analysis of many Tl n lines, while 
more recently Aston* has found a ratio of 1 : 2-40. 

Isotopes have been observed displaced in the lines of many 
elements, but of all mercury is the most complex, for it consists of 

* Aston, PRS, 1932, 134 571. 



XX] ISOTOPE DISPLACEMENT 189 

six isotopes;* of these the four of even atomic weight have zero 
moment, but the two odd isotopes have different nuclear mo- 
ments, namely | and 1|, and to make confusion worse con- 
founded the terms of one are inverted. 

To illustrate the methods by which such a complicated line 



Term 



7s. 



F Isotope 205 



403 



Isotope 203 



395 





h 


r 
I 
1 


r 
i 
i 


! 
i 
i 


i 

i 


i 
i 

i 


i 



-1CIIL- 



Fig. 20-19. Structure of the 5351 A., 2 Si- 
Keyston, ZP 9 1931, 70 3.) 



a Prf, line of Tl I. (After Schtiler and 



structure can be analysed, consider two mercury arc lines, 2536 
and 4078 A.,| which arise as 2 ^-> I % and 2 l S Q -> 2 3 P i; these 
lines are in fact particularly simple, for in one term J is zero. 

In the analyses described heretofore, three criteria have been 
used : first, the picking of a common hyperfine interval from lines 
with a common gross structure level; second, the interval rule; 
and third the intensity rules. Of these the first two suffice for the 

* Recent work has revealed more than six isotopes, but in work on hyperfine 
structure only those present in a proportion of more than 1 per cent, need 
usually be considered. 

t Schiiler and Keyston, ZP, 1931, 72 423. 



190 



HYPERFINE STRUCTURE 



[CHAP. 

analysis, when the structure is simple, but the last is the most 
valuable when the structure is complex. That the method has 
been so successful is perhaps the best evidence of the wide validity 
of the intensity formulae. 

To obtain the theoretical intensities of the components of a line, 
the intensity ratios of the components due to a single isotope must 
first be calculated, and these must then be weighted with the 



199 



201 











F 






7 ' Q 




i 






~ /S. OQ 


r T 


1 2 








i 










i 
i 

i 




/ 


1 1 


9 ( 


i b 










i 










i 










i 










I 


















2t 


i-}-" 1 


- { 










, } 


72 


7 


6p. 3 P, 46 


i 
5 


2 






4- 


i 


9 1 






185 




Z 2 



Intensity 



2-3 
a 



11-0 4-6 
A b 



69-9 



Displacement -449 -269-192 



6-8 
r 



273 



5-5 
B 



464 



Fig. 20-20. Structure of the 4078 A., 2 1 S ->2 3 P 1? line of Hg i. The displace- 
ments are given in 10~ 3 cm." 1 (After Schiiler and Keyston, ZP, 1931, 72 

428.) 

isotope abundance. Thus the even isotopes produce only one 
component each, but the isotopes 199 and 201, having nuclear 
moments of | and 1 J, produce two and three components respec- 
tively. These are shown as A, B and a, b, c in Figs. 20-20-21, and 
the theoretical intensity ratios are calculated as 2 : 1 and 1:2:3. 
But the mass spectrograph has shown that mercury contains 
16-44 per cent, of isotope 199, so that the absolute intensity of the 
A component should be of 16-44 or 10-96; and similarly since 
isotope 201 occurs to the extent of 13-68 per cent., the line b 



XX] 



ISOTOPE DISPLACEMENT 



191 



should be of absolute intensity | of 13-68 or 4-56. The intensities 
calculated in this way are summarised in Fig. 20-22. 



I* 



199 



727 



6s 



20] 

260 

] 

465 
~1 1-~1 



F 





Intensity 


204 A 
> - *^~ 
19-2 


a 202 

^29-3 


200 
23-8 


LJ2 S 

14-4 


B c 

I3-2L 




1 1 









Displacement 



-333 -178 



132,161 



394 



Fig. 20-21. Structure of the 2536 A., 2 'P^l %, line of Hg i. The displace- 
ments are again in 10~ 3 cm. - 1 (After Schiiler and Keyston, ZP, 1931, 72 434.) 



Isotope 


Abundance 
ratio 


Component 


Relative 
intensity 


Absolute 
intensity 


199 


16-44 


A 


2 


10-96 






B 


1 


5-48 


201 


13-68 


a 


1 


2-28 






b 


2 


4-56 






c 


3 


6-84 


198 
200 


9-89 
23-77 


No hyperfine structure 


9-89 
23-77 


202 


29-27 




29-27 


204 


6-85 




6-85 




99-90 




99-90 



Fig. 20-22. Intensities in a 



or 1 8 -> 8 P 1 line of Hg i. 



With these predictions in mind, the analysis of the structures 
shown in Figs. 20-20 and 21 presents no great difficulty, provided 
one understands that components separated by less than 
0-030 cm." 1 are not resolved. 

This somewhat complicated analysis of the 2536 A. line has 



192 HYPERFINE STRUCTURE [CHAP. 

been beautifully confirmed by Mrozowski,* who has shown that 
when separately excited the various isotopes behave like a mix- 
ture of independent gases. If light from a mercury arc is sent 
through mercury vapour in a magnetic field, various hyperfine 
components can be filtered out. By varying the field strength 
Mrozowski in this way isolated three groups of lines, (a) the 
394. 10~ 3 cm." 1 component, (6) the +161 and 333 components, 
(c) the 0-0 and 178 components. No matter which of these 
groups is used to excite cold mercury vapour, the resonance 
radiation contains only that group; when only the +161 and 

333 components are incident, only these two components 
are emitted. Thus each hyperfine line is itself a resonance line and 
there is no fluorescence. 

Fluorescence appears, however, when a little helium is added 
to the tube,f for the increased pressure means inelastic collisions 
for the mercury atoms. If the cold vapour mixed with helium is 
excited by the +394 line, the three lines +394, +161 and 

333 are emitted, for the +394 line excites both the 199 
and 201 isotopes and these after losing a little energy in colliding 
with a helium atom can return to the ground state while emitting 
the +161 or 333 line. The details are easily followed in Fig. 
20-21. On the other hand, irradiate the vapour with the 0-0 and 

178 lines, and only these lines are emitted, for these lines 
excite only the 200 and 202 isotopes, and as these have only one 
upper level they must radiate what they absorbed. 

The analysis of a single line (Fig. 20-23) does not determine the 
absolute isotope displacements of either term; it determines only 
the displacements of the isotopes in one term relative to their 
displacements in the other; and what is true of the analysis of a 
single line is true of the analysis of any number of lines, so that 
apparently the absolute displacements can never be determined. 
Many lines, however, which arise between high levels of the 
mercury atom show no hyperfine structure at all, so that all the 
terms concerned must have identical isotope displacements, and 

* Mrozowski, Sci. Bull. Acad. Pol. 1930, 464; 1931, 489. The lines with 
displacements of 132 and 161. 10~ 3 cm." 1 in Fig. 2021 were not resolved in 
these experiments; they are referred to on this page as the 161 line. 

t Mrozowski, ZP, 1932, 78 826. 



XX] ISOTOPE DISPLACEMENT 193 

this is extremely improbable unless the displacements of all are 
zero. In support of this thesis, theory and experiment show that 
isotope displacements must and do decrease, as the chief quantum 
number increases (Figs. 20-24-26). 

The hyperfine levels thus obtained may be simplified by sub- 
stituting for the odd components a single level at the centroid of 
the isotope, and when this is done an interesting regularity 



Red 



202 



Violet 



6072 A. 

4'P,-2 3 S I 



200 






198 






204 


121 




120 


118 | 


24 


128 




199 201 



200 



202 



198 



6716 A. 

4 1 P,-2 I S 



115 



118 



122 



204 



15 



128 



202 



201 



200 



2536 A 

IjM 


204 
| 155 


178.10~ 3 cm:' 


198 

161 | 


So 


209 


S 



201 



199 



Fig. 20-23. Centroids of the isotopes in three lines of Hg I. (After Schiiler and 
Keyston, ZP, 1931, 72 423.) 

emerges; the interval separating each even isotope from its 
neighbour is roughly constant and equal to the interval separating 
the odd isotopes; but the odd isotopes are not spaced mid-way 
between the even isotopes; this is clearly shown in Pig. 20-23 and 
is true not only in Hg i, but also in Pb i and Pb n. As the isotopes 
are not displaced in the upper levels of many lines, this property 
may well be demonstrated in a single line. 

The relative energies of the isotopes also need to be related to 
their masses, for there has never been any doubt that the sequence 

CASH 13 



194 



HYPERFINE STRUCTURE 



[CHAP. 

of the isotopes is the sequence of their masses, nor that in the 
arc and spark spectra of mercury the isotope of lowest atomic 



6sms Gs-mp fis-md 6s-ms 




Fig. 20-24. Isotope .displacements in Hg I. The wide splitting of the Sp. 1 ?! 
term is anomalous. (After KalJmann and Schiller, EEN 9 1931, 11 165.) 

weight lies lowest. In the light of recent theory this order seems 
to be general, but several spectra have been a little difficult to 
bring into line; thus the displacements in thallium seemed to be 
in different directions in the arc and spark spectra, but Breit* has 
* Breit, PR, 1932, 42 348. 



XX] ISOTOPE DISPLACEMENT 195 

since shown that this was due to a misinterpretation of certain 
lines of Tin and that in fact the isotopes of thallium are arranged 
like the isotopes of mercury, the smallest at the bottom. The 



6s-ms 



6s-mp 



5d 9 -6s 2 




Fig. 20-25. Isotope displacements in Hg n. (After Kallmann and Sckiiler, 
EEN, 1932, 11 167.) 

theoretical explanation is interesting; isotope displacements are 
due to the increase in the volume of the nucleus resulting on the 
addition of a neutron;* this causes the same charge to occupy a 
larger volume and so reduces the electrostatic energy of the 
system; as the electrostatic energy of a condenser is negative, 



* Schuler and Schmidt, ZP, 1935, 94 463. 



13-2 



196 HYPEBFINE STRUCTURE [CHAP. 

this means that the terms of the larger isotope lie higher than the 
smaller. 

Turning to the quantitative side, the displacement of one 
isotope relative to another seems to be the same for all terms of a 

6s 2 -ms 6s 2 - mp 




Fig. 20-26. Isotope displacements in Tl I. (After Kallmann and Schiller, EEN, 
1932, 11 167.) 

configuration; Fig. 20-27 shows this regularity in the 6s 2 . 6p 2 con- 
figuration of Pbi. Attempts actually to calculate the displace- 
ment have not yet met with complete success, because large 
corrections have to be made for the screening of one configuration 
by another, and these cannot be accurately estimated. Of partial 
solutions the most important is that produced by Breit,* who has 
* Breit, PR, 1932, 42 348. 



XX] ISOTOPE DISPLACEMENT 197 

related the displacement to the nuclear radius, the latter being 
assumed proportional to the cube root of the mass, but there is 
little doubt that other influences contribute.* 



it; in ap sp sp 

00 1^2 *2 *! r O 

204 204 

65 ,84 ? ? ? 

206 206 

72 88 90 85 83 

208 208 



Fig. 20-27. Isotope displacements in the 6s 2 . 6p 2 configuration of Pb I. 

7. Deviations from the interval rules 

In general hyperfine multiplets obey the interval rule better 
than gross multiplets, but this very regularity makes exceptions 
the more striking. When two gross levels lie near one another and 
satisfy certain conditions they perturb one another; one may 
expect the same phenomenon among hyperfine levels, and in fact 
Schiiler and Jonesf have shown that when in Hgi the 6d x D 2 
and 6d 3 D 1 levels lie at a distance apart comparable with their 
hyperfine intervals, the interval rule is no longer valid and the 
isotope displacements are anomalous. In the Hg 201 isotope the 
hyperfine intervals of the 6d x D 2 term are 181, 301 and 313. 10~ 3 
cm." 1 , numbers which are in the ratio of 3-0 : 5-0 : 5-2 instead of 
in the normal ratio of 3 : 5 : 7. Moreover, in these terms the even 
isotopes are all coincident, showing that there is no isotope dis- 
placement, but the centroids of the odd isotopes instead of 
coinciding with the even isotopes lie farther apart. This suggests 
at once that the reason why both intervals and isotope displace- 
ments are abnormal, is that the two terms perturb one another, 
for the characteristic sign of perturbation is repulsion. Among 
gross multiplets two components can perturb one another only 
if they have the same /, and so among hyperfine multiplets we 
may expect components to perturb one another only if they have 
the same F\ if this is true the even isotopes will not be displaced, 
for in them / is zero, and the two levels will have different values 

* Breit, PR, 1933, 44 418a; Bartlett and Gibbons, PR, 1933, 44 538; 
Grace and More, PR, 1934, 45 169. 

t Schiiler and Jones, ZP, 1932, 77 801. 



Hg' w 


(H) Hg 2 


"(I-li) 


Unperturbed terms 
(Calc.) 


Perturbed terms 
(Observed) 


Unperturbed terms 
(Calc.) 


F 


F 






i 


i * F 
Even J 7! 
isotopes f L l 

385 1 


t/l ' 




4 


W 




325 












C-G- r C.G. 




1 




Cc 






T^ P ~r 

p . k 




3( 


33 


^6d 3 D, 




















r 


li 
'2 




1 


i \\ 


^6 , 












1 


15 


|_ 






' L 








U 


1 










: 1 












^ 2 


"fi^ij 


* 






c 


> 




















1 


i 






r"^ 


^42 2 f 
167 








181 










( 2\ 


2~2 j 






_, 2 


.T l2 ~ 


















2 


'9 












3( 


)l 
















F 




2 1 ) 






C/-> 






jj 


o _ 




J78 * 




/i lir\ 


U. 






C.G. C.G. 


2 


... 




1 


T. 


2 





















>o 
















313 


3 ( 


1 










U- 


3! } 








2 108 












1^ ^ 




) 





Fig. 20-28. Two perturbed terms of mercury. In the middle between the two 
uprights is the observed term system, while to left and right the terms are 
shown in the positions they would occupy if they were not perturbed. The 
argument by which the various displacements are obtained is fully given by 
Schiller and Jones, ZP, 1932, 77 806. 



CHAP. XX] DEVIATIONS FROM INTERVAL RULE 199 

of F, namely 1 and 2. This makes the investigation much simpler 
than the analogous investigation of two gross multiplets, for the 
even isotopes provide a fixed scale of reference. 

A bird's eye view of the changes produced by perturbation is 
provided by Fig. 20-28; in the 199 isotope system, the levels in 
which F is 1| perturb one another, while the levels in which F is | 
above and 2| below remain undisturbed. As the two levels in 
which F is H repel one another, the 1 D 2 term has an enlarged and 
the 3 D 1 a reduced interval. In the isotope 201 on the other hand 
three components wander, for there are levels with F values of 
|, 1| and 2|- in both gross terms; only the F = 3J level of the 1 D 2 
term remains undisturbed. The repulsion of the levels with F =\, 
1J and 2| leads to a great reduction of the 2|~3| interval, and a 
consequent departure from Laiide's interval rule. 

When the interval rule is not obeyed the interaction between 
the nucleus and the electron shells is no longer proportional to the 
scalar product of the two vectors, and the vector model fails;* 
the quantum mechanics shows, however, that two states lying 
close to one another perturb one another and gives a satisfactory 
account of the displacements. t 

As perturbation is a phenomenon well known when two gross 
multiplets lie close to one another, physicists have naturally 
tried to use it to explain all deviations from the interval rule. But 
whereas two gross levels may perturb one another when 2000 cm .- 1 
apart, two hyperfine levels must lie within a few units of one 
another, and so it is much less probable that an unknown level 
lies close enough to produce the observed distortion. And in fact 
Schiller and Schmidt have shown that some multiplets in Eu 151 , 
Eu 153 ,J Lu 175 and Hg 201 || do not satisfy the interval rule, and 
that perturbation is an inadequate explanation. Instead of the 
displacements of the levels from the centroid being proportional 
simply to cos(IJ), a second term proportional to cos 2 (IJ) 

* Casimir, ZP, 1932, 77 811. 
f Goudsmit and Bacher, ZP, 1933, 43 894. 
t Schiiler and Schmidt, ZP, 1935, 94 457. 
Schiiler and Schmidt, ZP, 1935, 95 265. 
|| Schiiler and Schmidt, ZP, 1935, 98 239. 



200 HYPERPINE STRUCTURE [CHAP. 

appears; this second term has a coefficient small compared with 
that of the normal cos (IJ) term, but though the deviations are 
small, they are greater than the experimental error. Whether 
this second term affects the extreme interval is doubtful, its 
obvious result is to make the levels crowd towards the levels of 
large or small F, the one when the term is positive the other when 
it is negative. 

The appearance of a cos 2 term means that the interaction of 
the nucleus and electrons cannot be wholly explained as due to the 
action of a magnetic nuclear dipole on the electrons; the form 
the deviation takes suggests that the new force is electrostatic in 
origin, and is due to a lack of spherical symmetry in the electric 
field of the nucleus.* 

8. The spin of the nucleus 

The spin of an atomic nucleus may be obtained from the hyper- 
fine structure of a line, from the deflection of an atomic ray in a 
magnetic field and from the alternating intensities of band 
spectra. All three methods have been applied to sodium, and all 
give the same nuclear spin; and more generally where two methods 
have been used the results are consistent. Besides these three 
methods there are others which are permissible in theory, but 
which do not seem to have been used as yet; these are the specific 
heat at low temperatures f and scattering. J 

An atomic ray can be used only if the resolution is increased by 
including a magnetic velocity selector ; this consists of an in- 
homogeneous magnetic field, which spreads the beam out into a 
velocity spectrum. A movable slit selects a part of the beam 
homogeneous in velocity to about 10 per cent., and this then 
passes through a weak inhomogeneous field of the Stern-Gerlach 
type; thereafter a third magnetic field is used to focus the beam 
on the detector wire. This technique has only recently been per- 
fected, but already in Rabi's hands it has disclosed the spin of 

* The equations for the interaction of such a core with the nucleus have 
been given by Casimir, Physica, 1935, 2 719. 
t Dennison, PRS, 1927, 115 483. 
t Sexl, Nw, 1934, 22 205. 
Rabi and Cohen, PR, 1933, 43 582a. 



XX] THE SPIN OF THE NUCLEUS 201 

potassium and in Stern's the magnetic moments of the proton 
and deuton,* important quantities which could not have been 
easily measured by other methods. When applied to sodium the 

J3i 




50 
Position 



60 70 

of Detector Wire 



80 



Fig. 20-29. An atomic ray of sodium split into four components in passing 
through a magnetic field. The high resolution is obtained by using an inhomo- 
geneous magnetic field and a slit to select a beam homogeneous in velocity to 10 
per cent. The figure shows the points obtained in one particular run. The peak 
marked A is due to atoms other than those selected. (After Rabi and Cohen, 
PR, 1933, 43 582.) 

beam splits into four components as shown in Fig. 20-29; the 
spin of sodium is therefore l|.f 

In the application of band spectra J to this purpose, the rela- 
tive intensities of the alternating bands of symmetrical molecules 

* References to particular elements appear in the bibliography of h.f.s. 
t Breit and Rabi, PR, 1931, 38 2082a; Rabi and Cohen, PR, 1933, 43 582a; 
Rabi, Kellogg and Zacharias, PR, 1934, 46 157; Dickinson, PR, 1934, 46 598. 
J Jevons, Band spectra of diatomic molecules, 1932, 140. 



202 HYPERFINE STRUCTURE [CHAP. XX 

are measured; C1 35 C1 35 is a symmetrical molecule, C1 35 C1 37 is not; 
there are no alternating intensities in the bands of unsymmetrical 
molecules. The rotational levels of a symmetrical molecule 
divide into two systems, known as symmetrical or (s) and anti- 
symmetrical or (a) ; a level of one system never combines with a 
level of the other; (s) combines only with (s) and (a) only with (a). 
An (s) line defined by J lies between two (a) lines defined by 
( J 1 ) and ( J + 1 ) , but its intensity is not a mean of its neighbours ; 
the symmetrical lines are strong and the anti-symmetrical lines 
are weak. Theory ascribes this alternating intensity to the nuclear 
spin of the atoms, and shows that if the intensities are as I 8 to I a , 



or in tabular form : 

/= J 1 1J 2 2 3 
I s /I a = ao 3 2 1-67 1-5 1-4 1-33 ... 

When / is zero, the alternate lines are missing, so that the 
appearance of the anti-symmetrical lines is quite definite proof 
that / is not zero, but as intensities are not easily measured 
accurately, this method is not well adapted to measuring large 
nuclear moments; any estimate greater than H is certainly 
dubious. The method has been applied to show that the nuclei 
He 4 , C 12 , O 16 , S 32 and Se 80 have no nuclear spin, and to estimate 
the nuclear spin often other elements; in the table of values these 
are indicated by a B. 

An examination of the spins obtained by hy perfine structure and 
band spectra (Figs. 20-30-32) shows that they divide nuclei into 
two groups, in one of which the mass is odd and in the other even. 
Other evidence suggests that nuclei should be further divided 
according as the charge is odd or even. When the mass and 
charge are both even, the spin is always zero; this statement is 
supported by measurements on more than 30 nuclei. When mass 
is even and the charge odd, the spin is certainly 1 in H 2 and N 14 ; 
of this the alternating intensities of band spectra leave no doubt; 
in Li 6 the absence of hyperfine structure has been taken to in- 
dicate zero spin, but a narrow hyperfine structure can easily be 



CHAP. XX] THE SPIN OF THE NUCLEUS 203 

missed. Nuclei of this type are so unstable that only four ex- 
amples are known. When the mass is odd, the spin is always half 
an odd integer; from time to time, zero moment has been ascribed 
to a nucleus of this type, but in view of the 42 nuclei which con- 
form and the fact that hyperfine structure can always be missed if 
the lines are too blurred or the resolving power too low, they need 
not be further considered; no exception has been established. 

How these regularities are related to be the structure of the 
nucleus can be most profitably considered after the magnetic 
moments have been discussed. 

9. The magnetic moment of the nucleus 

The simplest theory of hyperfine structure ascribes a magnetic 
moment to the nucleus, and argues that when this acts upon an 
electron in its orbit, the electronic term splits. If the coupling of 
the nucleus and electron obeys a cosine law, this hypothesis can 
be shown to predict the doublet formulae, the interval rule and 
the usual magnetic splitting.* 

In particular the displacement of a particular level from the 
centroid will be given by the formula 

v v G = AIJ cos (IJ) 

= %A{F(F+l)-J(J+ !)-/(/+ 1)}, 

where A is the hyperfine interval quotient.* When only one 
electron is active A is identical with a, the electronic interval 
quotient, which is determined by the formula 



1)1838 ' 
for a hydrogen-like orbit, or by 

RaPZfZ* g(I) 
fj __. ___ * _ a __ & _ pm 1 

n** (1 + 1) j(j +1)1838 ' 

for a penetrating orbit. The latter is considered as composed of 
two parts, an inner in which the electron moves as if under the 
influence of a charge Z i , and an outer where the effective charge 
is Z a . n* is the effective quantum number. In theory these 

* Goudsmit, PR, 1931, 37 663; Fermi and Segrd, ZP, 1933, 82 729. 



Element 


Charge 


Mass 


Spin 


Magnetic moments 


H 


1 


1 


\B 




Li 


3 


7 


14 H, B, R 


3-29 S, G; 3-20 F; 3-20 


B 


5 


11 






N 


7 


15 






F 


9 


19 


%H,B 


3 


Na 


11 


23 


14 H, B, R 


2-14 S; 2-09 F; 2-08 


Al 


13 


27 


4// 


1-93 S; 2-1 G; 2-4 


P 


15 


31 


*fl 




Cl 


17 


35 


%IB 








37 






K 


19 


39 


l^R 


0-38, 0-43, -397 






41 


>|and<2J J R 




Sc 


21 


45 


34 // 


3-6 


V 


23 


51 


34 # 




Mn 


25 


55 


2// 




Co 


27 


59 


34 11 


2-5? 


Cu 


29 


63 


nil 


2-74 S 






65 


14 // 


2-74 S 


Ga 


31 


69 


H// 


2-14 S, F; 2-01 G 






71 


lift 


2-74 S; 1-49F; 2-55 G 


As 


33 


75 


14 // 


0-90 S, G 


Br 


35 


79 


14 //, m 








81 


H//, ^? 




Rb 


37 


85 


24 // 


1-49 S; 1-36 F; 1-3 G 






87 


14 ff 


3-06 S; 2-79 F; 2-7 G 


Y 


39 


89 






Cb 


41 


93 


4 // 


3-7 


Ma 


43 









Rh 


45 









Ag 


47 


107 
109 




| <0-24 8 


In 


49 


115 


44 // 


5-25 S; 5-3 F; 5-4 G 


Sb 


51 


121 


24 // 


2-70 S; 2-7 G; 2-75 






123 


24 # 


2-10 S; 2-1 G; 2-0 


I 


53 


127 


44/7, #? 




Cs 


55 


133 


34 // 


2-91 S; 2-63 F; 2-50 


La 


57 


139 


34 # 


2-5 


Pi- 


59 


141 


24 // 




ll 


61 








Eu 


63 








Tb 


65 








Ho 


67 


165 






Tu 


69 


169 






Lu 


71 


175 


34 a 


2-5 


Ta 


73 


181 


34 ff 




Re 


75 


185 


24 // 








187 


2*// 




Ir 


77 


191 


i?# 








193 


|?// 




Au 


79 


197 


14 // 


0-23 S; 1-67 F 


Tl 


81 


203 


i// 


1-47 S; 1-42 F; 1-8 G 






205 


*// 


1-47 S; 1-42 F; 1-8G 


Bi 


83 


209 


4.V /Y 


3-60 S; 3-54 F; 4-0 G 



Fig. 20-30. Protonic nuclei with charge and mass both odd. In the spin column, 
the letters H, B, and R show the method used, hyperfme structure, band spectra 
or atomic rays. In the column of magnetic moments the letters denote the 
authority, S for Schiiler, ZP, 1933, 88 324, F for Fermi and Segre, ZP, 1933, 82 
748, and G for Goudsmit, PR, 1933, 43 638. Figures given without a letter are 
from recent papers which can be traced in the bibliography. 



Element 


Charge 


Mass 


Spin 


Magnetic moments 


H 
Li 
B 

N 


1 
3 

5 

7 


'2 
6 
10 
14 


1 B 
OH 9 ^IR 

1 B 


0-7-0-8 R 
0-7-0-8 R 

^0-2/7 



Fig. 20-31. Deutonic nuclei with charge odd and mass even. For key to letters 
see Fig. 20-30. 



Element 


Charge 


Mass 


Spin 


Magnetic moments 


Be 


4 


9 


i? H 




C 


6 


13 









8 


17 






Ne 


10 


21 






Mg 


12 


25 






Si 


14 


29 






S 


16 


33 






Cr 


24 


53 






Zn 


30 


67 


1* H 




Ge 


32 


73 






Se 


34 


77 






Kr 


36 


83 


^3J H 




Sr 


38 


87 


~$^\\H 


-0-86S 


Mo 


42 


95 










97 






Ru 


44 


99 










101 






Pd 


46 


? 






Cd 


48 


Ill 


\ H 


-0-63 S; -0-53 F; -0-67 G 






113 


i H 


-0-63 S; -0-53 F; -0-67 G 


Sn 


50 


115 










117 


\ H 


-0-95S; -0-89 






119 


i H 


-0-95S; -0-89 






121 






Te 


52 


123 










125 






Xe 


54 


129 


i H 


~" ve l 






131 


1 H 


+ ve) ^ 129 /' Xl81 ~ ~ 


Ba 


56 


135 


2J tL 








137 


2 // 


0-94 S; 1-05 F 


Sm 


62 


? 






Gd 


64 


? 






Dy 


66 


161 










163 






Er 


68 


167 






Yb 


70 


171 










173 






Hf 


72 


? 






W 


74 


183 






Os 


76 


187 










189 






Pt 


78 


195 


i# 




Hg 


80 


199 


i H 


0-55 S; 0-46 F; 0-55 G 






201 


\\ H 


-0-62S; -0-51F; -0-62G 


Pb 


82 


207 


i U 


0-60 S; 0-67 F; 0-60 G 






209 







Fig. 20-32. Neutronic nuclei with charge even and mass odd. For key to letters 
see Fig. 20-30. 



206 HYPERFINE STRUCTURE [CHAP. 

equations offer a simple method of determining the magnetic 
splitting factor </(/), and hence the magnetic moment of the 
nucleus; but in practice a large relativity correction has to be 
made before these formulae can be applied.* A more general 
formula is thus of greater value. 

When several electrons are active the interval quotient can be 
shown to have the value 



where //, is the magnetic moment of the nucleus, and H is the 
magnetic field produced by the electrons at the nucleus. When the 
eigenf unctions of the electrons are known, the field H can be 
calculated, and then the experimental values of the interval 
quotient determine the magnetic moment of the nucleus. 

Whether this theory can be considered satisfactory depends on 
how well nuclear moments agree when calculated from different 
terms of the same spectrum, and from different spectra with the 
same nucleus. That 20 terms distributed among the first three 
spectra of thallium do all give the same magnetic moment is 
therefore encouraging. 

The magnetic moments thus obtained are summarised in 
Figs. 20-30-32. In these figures the nuclear moment is given in 
nuclear magnetons, H, N , where 

eh ji 



M is the mass of the nucleus and p B is the Bohr magneton. 

Of the isotopes of even mass only two magnetic moments are 
known, H 2 and N 14 ; in all the other isotopes the mechanical 
moment is zero, so that there is no hyperfine structure and there- 
fore no evidence. An inspection of the table of isotopes of odd 
mass, however, shows a clear division between those of even and 
odd charge; among the former positive and negative moments 
are equally frequent, the latter being shown empirically by in- 
verted hyperfine terms; moreover, the moment is always less 

* Goudsmit, PR, 1933, 43 636. The precise form the formulae should take 
seems also in doubt. Pauling and Goudsmit, Structure of line spectra, 1930, 
60 and 209, note 1. 



XX] MAGNETIC MOMENT OF THE NUCLEUS 207 

than 1 ; on the other hand, when the charge is odd, the moment is 
always positive, and with two or three exceptions it is greater 
than 1.* 

Though this last statement certainly indicates a tendency, it 
must not be taken quite at its face value, for there are many 
spectra in which spectroscopists have commonly failed to find any 
structure at all; among these are Ni, Pn, Cln, Ki, Kn, Agi and 
Cd n. Band spectra dispose of the hypothesis that the mechanical 
moments of these atoms are all zero; nitrogen, phosphorus and 
potassium all spin. A second alternative is that the magnetic field 
produced by the electrons at the nucleus is very weak, but as 
some of the atoms possess a penetrating s electron such as usually 
produces wide hyperfine intervals, this explanation is improb- 
able. Better is the suggestion that the magnetic moments of these 
nuclei are small; in two elements certainly recent work supports 
this; thus Jones| has shown that in Cdn, though 12 out of the 13 
lines which he examined have no structure, the thirteenth reveals 
the ground, 2 S, term as double and indicates a nuclear magnetic 
moment of 0-625 p, N . In Ki too Jackson and KuhnJ have recently 
shown that if sufficient care is taken, the resonance lines may be 
resolved to a narrow doublet; the lines were obtained from a dis- 
charge tube containing neon at a pressure of a few mm. and 
potassium at a pressure of less than one two-thousandth of a mm. ; 
before entering the spectrograph, the light passed through a ray 
of potassium atoms travelling at right angles across its path. This 
atomic ray passed through a cool tube whose length was twenty 
times its diameter, so that the Doppler width of absorption lines 
was only 1/20 of that obtained with a random distribution of 
velocities. Resolved with a Fabry-Perot etalon, the lines ap- 
peared as a doublet with an interval of 0-015 cm.- 1 

* The magnetic moments have been tabulated by: Fermi and Segre, ZP 
1933, 82 748; Goudsmit, PR, 1933, 43 638; Schiller, ZP 9 1933, 88 324. Schiller 
gives a critical survey of the data and recalculates the values. 

t Jones, Phya. Soc. Proc. 1933, 45 625. 

f Jackson and Kuhn, PUS, 1934, 148 335. 



208 HYPERFINE STRUCTURE [CHAP. 

10. The structure of the nucleus 

At the present day the evidence of hyperfine structure suffices 
to divide the nuclei into four types, though history relates that 
Aston* recognised these types long before hyperfine structure had 
advanced far enough to be of much service. The nuclear type is 
most simply determined by the mass and charge, the crucial 
question being whether each of these is odd or even (Pig. 20-33). 



Nuclear mass 


Even 


Even 


Odd 


Odd 


Nuclear charge 


Even 


Odd 


Even 


Odd 


No. of isotopes 
known 


114 


4 


44 


45 


No. of nuclear 
moments known 


>30 


3 


12 


30 


Value of / 

No. of magnetic 
moments known 






1 or ? 

2 


Half integral 
10 


Half integral 
20 


Values and sign 
of \L 


No evidence, 
probably 





As often - ve 

as +ve; 


Always +ve; 
in all but 4, 


Structure of nu- 
cleus suggested 


Core with 


Core-f 
1 deuton 


Core + 
1 neutron 


Core + 
1 proton 



Fig. 20-33. Frequency of occurrence of the four nuclear types and their pro- 
perties. 

When both mass and charge are even, the nuclear moment is 
always zero; nothing is then known of the magnetic moment, 
though it is commonly assumed zero. This structure is particularly 
stable, Aston's figures showing that more than half the known 
isotopes are built to this plan. 

When the mass is even and the charge is odd, the nucleus is 
usually unstable, though four light isotopes do occur; the heaviest 
of these is N 14 . Of the known mechanical moments, two are of 
magnitude 1 and a third is possibly zero. 

When the mass is odd and the charge even, the mechanical 
moment is half an odd integer; the magnetic moment is as often 
negative as positive, and is always less than one. In terms of the 
number of isotopes known, this nuclear type is less than half as 
stable as the even-even type. 

* Aston, Mass-spectra and isotopes, 1933, 175. 



XX] STRUCTURE OF THE NUCLEUS 209 

Finally, when the mass and charge are both odd, the mechanical 
moment is again half an odd integer, but the magnetic moment is 
always positive and usually greater than 1. This type of nucleus 
is about as stable as the preceding type. Further, of ten of these 
elements, which have two isotopes, nine pairs have the same spin; 
the one exception, rubidium, is exceptional also in being radio- 
active. When two isotopes are of even charge, they do not obey 
this law.* 

These facts are independent of any theory of the structure of 
the nucleus; but to proceed further some simplifying assumptions 
are necessary. A very few years ago, the nucleus was supposed 
constructed of protons and electrons, f and there seemed no 
alternative to allotting the proton a spin of iA/2?r and depriving 
the electron of the spin it has outside the nucleus. But to-day this 
awkward trick of giving the electron different properties in 
different places can be avoided by introducing the neutron, and 
supposing the nucleus built of three bricks only, the proton, the 
neutron and the a-particle. The odd-even rule of mechanical 
moments is then easily explained if both the proton and neutron 
have a spin of %h/27r, while the oc-particle has no spin at all. The 
band spectra of H 1 and He 4 confirm this assignment for they show 
that these nuclei have respectively moments of \ and 0; while the 
moment assigned to the neutron is that suggested by the quantum 
mechanics. % Becoming still more definite, if a nucleus of mass M 
and charge Z is composed of N neutrons, P protons and A 
a-particles, then obviously 



As these equations are indeterminate, there are current at the 
present time two simplifying assumptions; the first due to 
Heisenberg eliminates the a-particles altogether and leaves the 

* Schiiler and Schmidt, ZP, 1935, 94 460. 
t Bryden, PR, 1931, 38 1989; White, PR, 1931, 38 2073a. 
J Temple, PRS, 1934, 145 344. 

Heisenberg, ZP, 1932, 78 156. This theory has been developed by East- 
man, PR, 1934, 46 1. 

CASH 14 



210 HYPERFINE STRUCTURE [CHAP. 

nucleus composed of neutrons and protons only; the second pro- 
posed by Iwanenko and used by Land6* does not allow the 
presence of more than one proton, this one being present when- 
ever the charge is odd. 

For the present purpose, however, the respective merits of 
these two hypotheses are of little account; for both are consistent 
with the assumption that the even-even nucleus is the core from 
which the other three types are formed by the addition of a 
proton, a neutron or a deuton. For convenience we may then 
describe a nucleus with odd mass and odd charge as 'protonic', 
one with odd mass and even charge as ' neutronic ', and one with 
even mass and odd charge as 'deutomV. This hypothesis in its 
simplest form has not thus far been stretched to cover all the 
facts of hyperfine structure, but it has succeeded so well that 
recent papers have agreed that some variation is indicated. 

Consider first the protonic nuclei. t If the mechanical and 
magnetic moments are to be ascribed to a single proton moving 
outside a core in which both moments are zero, the proton is 
best assumed to move in an orbit and to have on this account an 
angular momentum 1, which is always integral; the inherent spin 
of the proton is then written s with value \ , and this is made to set 
parallel or anti-parallel to the orbital vector, so that the resultant 
moment I is half -integral. That the magnetic moments are often 
large suggests that the magnetic moment of the proton is itself 
large; and in fact Stern J has arrived at the same conclusion from 
an entirely independent experiment. Working on the deflection 
of an atomic ray in a magnetic field, he concluded that the 
magnetic moment of the proton is 2| nuclear magnetons, the 
experimental error being given as 10 per cent.; Lande, however, 
in applying this observation to hyperfine structure has found that 
a g factor of 4 fits the facts better than one of 5. 

If the proton revolves about a core, the magnetic moment may 
be calculated by the methods developed by Goudsmit for an 

* Iwanenko, Comptes Rendus, 1932, 195 439; Lande, PR, 1933, 43 620; Inglis 
and Lande, 1934, 45 842 a. 

t Lande, PR, 1933, 44 1028a; Kallmann and Schuler, ZP, 1934, 88 210. 
t Stern, Helv. Phys. Ada, 1933, 6 426. 



XX] 



STRUCTURE OF THE NUCLEUS 



211 



electron; the moment will be gl, where the splitting factor g is 
given by the equation 



9(1) 



21(1+1) 



21(1+1) 

As g (I) is the splitting factor of a revolving particle, its value must 
be 1 ; g (s) is assigned the value 4 for reasons already given. The 
nuclear moments resulting from this system are shown in 
Fig. 20-34. 

The experimental moments do not agree very well with this 
theory, but as no observation can be trusted to less than 10 per 
cent, and the calculations of different authors from the same data 



X 


1J 2| 3J 4 




1 

2 
3 
4 
5 


2 



3 

1 4 
V 5 
V 6 



Fig. 20-34. Protonic nuclei. Magnetic moments dictated by theory. 

show even wider discrepancies, comparison is not easy (Fig. 
20-35). The general tendency of the magnetic moments to increase 
with the spin is well covered by the theory; while if we concen- 
trate attention on the nuclei with a spin of 1, the division into 
seven elements with magnetic moments greater than 2 and three 
elements with moments less than 1 is striking and in accord with 
theory; on the other hand the prediction that for any value of / 
there can be only two values ofp, seems definitely at variance with 
experiment; the range from sodium with an estimated moment 
of 2-14 to lithium with a moment of 3-29 seems to exceed the 
possible error; moreover, there is no doubt that the two gallium 
isotopes have different moments. Ways of circumventing this 
difficulty will, however, be better taken up when the neutronic 
nuclei have been considered. 

14-2 



212 HYPERFINE STRUCTURE [CHAP. 

Land6* has pictured the neutronic nuclei built to a similar 
plan; the mechanical and magnetic moments of the nucleus are 
due wholly to a single neutron, moving with angular- moment 1 
and inherent spin s round an inert core; the inherent spin is again 









Magnetic moment 


Spin 


-Klemcnt 


IMass 










Obs. 


Theory 


i 


F 


19 


3-? 


2 or 




Al 


27 


1-93 






Tl 


203 


1-47 








205 


1-47 




14 


Li 


7 


3-29 


3 or 0-60 




Na 


23 


2-14 






K 


39 


0-38 






Cu 


63 


2-74 








65 


2-74 






Ga 


69 


2-14 








71 


2-74 






As 


75 


0-90 






Kb 


87 


3-06 






Au 


197 


0-23 




21 


Kb 


85 


1-49 


4 or 1-43 




Sb 


121 


2-70 




3J 


Sb 


123 


2-10 


5 or 2-33 




Cs 


133 


2-91 




4* 


In 


115 


5-25 


6 or 3-27 




Bi 


209 


3-60 





Fig. 20-35. Protonic nuclei. Observed magnetic moments compared with 
theory. 



but the magnetic splitting factors are different; an un- 
charged particle will create no magnetic field in its motion so that 
g (I) will be zero, and the nuclear splitting factor g will be simply 



2/7/TT) g (s) ' 

That the magnetic moment of a neutronic nucleus is as often 
negative as positive has been taken to mean that the inherent 
magnetic moment of a neutron is negative, but it would appear 
that equal numbers of positive and negative moments appear 
provided that g (1) is equated to zero; the sign of g (s) is irrelevant. 



Inglis and Lande, PR, 1934, 46 842a. 



XX] 



STRUCTURE OF THE NUCLEUS 



213 



Thus if g (s) is assigned the value 1, so that the magnetic moment 
of the neutron is | a nuclear magneton, the permitted nuclear 
moments are those shown in Fig. 20-36, while if g (s) is given the 
value 1, the numerical values will be unaltered, but the -f and 
signs must be interchanged. 



\ / 


t 


'\ 


i 11 2J 





+ 1 


1 


1 -1- J 


2 


~ i ff "f" 2 


3 


5 



Fig. 20-36. Neutronic nuclei. Magnetic moments dictated by theory. 

That the nuclear moments thus calculated are rather smaller 
than those observed is of no account, for the neutron may easily 
be assigned a larger magnetic moment; but the inequality of the 
positive and negative values is serious, for experiment suggests 
that positive and negative values occur over the same numerical 
range; indeed, all observed moments lie between + J and -I- 1 or 
between | and 1 . Clearly these figures are more in conformity 
with the suggestion that the magnetic moment of the neutron 
is 0-6 JJL and can set itself parallel or anti-parallel to the field, 
there being no orbital motion. Whether the observed moments 
cover too wide a range actually to invalidate this suggestion is 
probably still a matter of opinion. 

In the hope of obtaining better agreement in both protonic and 
neutronic nuclei, Schiller* has proposed the introduction of 
another vector r, which shall combine with the resultant of 1 and 
s to produce I; while Tamm and Altschuler| have proposed that 
in some nuclei two neutrons uncouple from the core, and combine 
freely with the external proton or neutron. Both authors can 
claim that the magnetic moments thus calculated nowhere clash 
with experiment, but both theories give a choice of values, which 
must be considered rather wide when compared with the paucity 

* Schiiler, ZP 9 1934, 88 323. 

t Tamm and Altschuler, Comptes Rendua de VAcad. de Sci. de VU.8.S.R., 
1934, \ 458. 



214 HYPERFINE STRUCTURE [CHAP. XX 

and inaccuracy of the experimental figures. Inglis and Lande* 
have expressed their preference for the solution of Tamm and 
Altschuler, but where rapid advance is likely in the next few 
years, a detailed analysis of what is tentative seems hardly 
justified. 

Thus the deutonic nuclei alone remain to be considered. In 
these the mass is even and the charge odd, so that both a neutron 
and a proton must be added to the core of even mass and even 
charge. If these always combine in the same way to form the 
deuton nucleus of heavy hydrogen, nuclei of this type should 
always have the unit spin of the deuton itself; N 14 actually has 
this spin, but Li 6 has always been assumed to have zero spin. 
Whereas the spins of H 2 and N 14 were obtained from band spectra, 
however, the spin of Li 6 has been obtained only from hyperfine 
structure and signifies therefore only that if the nucleus has a spin 
moment its magnetic moment is very small. Indeed the lines of 
N 14 are also narrow, so that all we know of its magnetic moment 
is that it is certainly less than 0-2 nuclear magneton. Clearly 
band spectra observations which will determine the nuclear 
moments of the two deutonic nuclei Li 6 and B 10 are much to be 
desired. 

BIBLIOGRAPHY 

Much the most thorough article is one by Kallmann and Schiiler in Erg. d. 
Exact. Naturwiss. 1932, 11 134. The treatment is exhaustive, but much has 
been learnt since 1932. 

* Inglis and Lande, PR, 1934, 46 76a. 



CHAPTER XXI 
QUADRIPOLE RADIATION 

1. Forbidden lines 

The transition producing a normal line must satisfy two selection 
rules; Laporte's rule forbids a jump from even term to even term 
and from odd to odd, and a second limits the changes in the 
angular momentum of the atom, J. On occasion, however, lines 
appear which violate these rules; in an electric field, for example, 
both rules are violated, the phenomena being referred to as the 
' completion of the multiplet '. As this has been known for twenty 
years the more recently discovered forbidden lines have been 
frequently ascribed to an unsuspected electric field; the precise 
conditions under which forbidden lines appear are therefore 
important. 

For this purpose the forbidden lines may be classified in three 
divisions: (1) the alkali D->S doublets; (2) the green aurora line 
5577 A. and some nebular lines; (3) the mercury line 8 P 2 -> 1 S , 
2270 A. Of these the last may be dismissed as probably due to the 
interaction between the electrons and the nucleus, the J selection 
rule applying rigidly only to the total angular momentum of the 
atom F.* The two other divisions merit fuller discussion. 

The D->S lines of sodium and potassium seem to have been 
studied for the first time in 1922, when Dattaf showed that they 
are absorbed by a tube of potassium vapour; the lines appeared 
at all pressures used from 2-5 up to 46 mm., while the potassium 
bands, which are known to be sensitive to electrostatic fields, did 
not blur until the pressure rose to 30 mm. At about the same time 
Foote, Mohler and Meggers J showed that the D->S lines are 
emitted in a space shielded from the applied electrostatic field, 
even when the field itself is very weak; though the presence of 
ions in the vapour may be an essential condition of the experi- 

* Rayleigh, PBS, 1927, 117 294; Huff and Houston, PR, 1930, 36 842. 

t Datta, PRS, 1922, 101 539. 

t Foote, Mohler and Meggers, PM, 1922, 43 659. 



216 QUADRIPOLE RADIATION [CHAP. 

ment, it seems more probable that the lines are both radiated and 
absorbed in a field-free space. Later the lines were shown to occur 
also in a newly struck arc;* the arc was struck and rui'i until the 
tips of the electrodes were red hot, when caesium carbonate was 
fused on to both electrodes; thereafter whenever the arc was 
struck, the D -> S lines appeared strong for a few seconds and as 
they faded, the ordinary caesium lines shone forth. 

The next forbidden line to attract attention was the auroral 
Iine5577 A., which McLennanf examined and traced to a forbidden 
transition in the Oi spectrum. As the spectrum of the night sky 
does not contain any nitrogen bands, the potential necessary to 
produce the green auroral line is presumably less than the 11-5 
volts required to produce the most easily excited of these. 
Experiment in the laboratory confirms this hypothesis; in a dis- 
charge tube containing pure oxygen the 5577 A. line is swamped 
by the band spectrum, but if some neon or argon is introduced so 
that when the total pressure is 3 cm. of mercury the partial 
pressure of the oxygen is only 3 mm., the green line comes out 
strongly. Now the inert gases are known to have a very small 
potential drop throughout the discharge, so that the oxygen lines 
produced when the inert gas is in large excess will be limited to 
those of low excitation energy. 

But if the green line is produced by a potential of less than 11-5 
electron volts, the energy which has to be given to the oxygen 
atom must be less than 4-4 volts, for oxygen can be dissociated 
into neutral atoms by light of wave-length 1750 A. corresponding 
to a dissociation potential of 7-1 volts, and other evidence serves 
to confirm this value. The resonance potentials of atomic oxygen 
are, however, 9-11 volts for 5 S<- 3 P and 9-48 for 3 S- 3 P, so that 
an excitation energy of 4-4 volts can hardly cause the atom to 
emit any lines of the triplet or quintet systems. In fact with only 
this potential available, the terms which can be concerned in the 
production of the 5577 A. line seem to be limited to the five 
members of the p 4 configuration, 3 P 2 ,i,oj 1 ^ 2 an d ^Q. 

* Shrum, Carter and Fowler, H. W., PM , 1927, 3 27. 
t McLennan and Shrum, PKS, 1925, 108 501; McLennan, PUS, 1928, 120 
327. 



XXI] FORBIDDEN LINES 217 

Of these low levels 1 D 2 and 1 S are metastable, and if one of 
them is the initial state, the final state must be 1 S or one of the 
3 P components, but even this leaves seven possible transitions. 
To distinguish between them McLennan and his co-workers 
examined the longitudinal Zeeman effect, and found the two 
circularly polarised lines characteristic of a singlet line, a result 
which seems to reduce the seven alternatives to three, namely 
ig _> iD 2 , % ~> 3 P , *D 2 -> 3 P . Of these the last may be rejected 
because in nebular spectra which show the transitions X D 2 -> 3 P 2 l 
occurring strongly, the 1 D 2 -> 3 P line is always so weak that it has 
so far escaped detection; accordingly if the line 5577 A. line is 
iD 2 -> 3 P , two other lines ^^P^ should occur even more 
brightly in positions which can be calculated; but in fact these 
lines do not appear either in the aurora or in oxygen gas excited to 
produce the 5577 A. line. A similar argument applied to 1 S-> 3 P 
transition compels us to reject it too; so that the green auroral 
line may be taken as X D 2 -> 1 S Q without any reference to the theory 
of quadripole radiation; history shows indeed that this evidence 
was accepted in 1928, though only later was the corner stone 
added in an observation of the transverse Zeeman effect, work 
which will be discussed in a later section. 

While McLennan was developing this work on the auroral line, 
Bowen* showed that eight strong nebular lines could be ascribed 
to transitions between various metastable states of oxygen and 
nitrogen (Fig. 21-1). Whereas stellar spectra contain lines 
characteristic of almost all elements, nebulae emit only a few 
lines and of these all that have been assigned arise from the six 
elements H, He, C, O, N and A; thus of a list of 79 lines between 
3300 and 7300 A., 57 have been assigned to these elements. t The 
lines due to hydrogen and helium are of no particular interest, for 
they are simply the lines normally produced in the laboratory, 
but of the lines due to the other elements many are normally 
forbidden. 

That lines forbidden in the laboratory should appear in nebulae 

* Bowen, N, 1927, 120 473. 

t Becker and Grotrian, EEN, 1928, 7 56. A iv lines from Boyce, PR, 1935, 
48401. 



218 QUADRIPOLE RADIATION [CHAP. 

is not difficult to explain. The intensity of a line depends both on 
the transition probability and the concentration of atoms in the 
excited state; in netmlae a low probability may be balanced by a 
high concentration, but this is not usually possible in the labor a- 



Spectrum 


Wave-length 


Transition 


Allowed 
or 
forbidden 


Oi 


6302 
6364 


2p 4 1 T) 2 ->2p 4 3 P 2 
2p 4 1 D 2 ->2p 4 3 Pj 


f. 
f. 


it 


3726 
3729 
4076 

4416 1 

4649 
7325 


2p 3 2 D ir >2p 3 \S H 
2p3 2 D 2r ->2 P 3 \S li 
2p 2 .3d*F H ->2p 2 .3p 4 D 3i ? 
2p 2 .3p 2 D li -^2p 2 .3s 2 P i 
2p 2 .3p 2 D 2i ->2p 2 .3s 2 P li 
2p a .3p*D Jli ->2p 2 .3s*P 2i 
2 p 3 ap-^p 8 2 D 


f. 
f. 
a. 
a. 
a. 
a. 
f. 


Om 


3313 
3342 
3445 
3759 
4363 
4959 
5007 


2p.3p 3 S 1 ->2p.3s 3 P 1 
2p.3p 3 S 1 ->2p.3s 3 P 2 
2p.3p 3 P 2 ->2p.3p 3 P 2 
2p.3p 3 D 3 ->2p.3s 3 P 2 
2p 2 1 S ->2 P 2 iD 2 
2p 2 !D ->2p 2 ?! 
2p 2 1 D 2 ->2p 2 3 P 2 


a. 
a. 
a. 
a. 
f. 
f. 
f. 


Nil 


5755 
6548 
6584 


2p 21 S ->2p 21 D 2 ? 
2p 2 1 D 2 ->2p 2 3 P X 
2p 2 iD 2 ->2p 2 3 P 2 


f. 
f. 
f. 


Nin 


4097 
4102 
4634 
4641 


3p apj.-^Ss 2 Si 
3p 2 Pt->3s 2 S i 
3d 2 D!,->3p 2 Pi 
3d 2 D H ->3p 2 P li 


a. 
a. 
a. 
a. 


A iv 


4711 
4740 


3p 82 D, t ->3p*S lt 
3 P 32 D ir >3p3%I | 


f. 
f. 



Fig. 21-1. Nebular lines. This list is abstracted from one given by Becker 
and Grotrian, EEN, 1928, 7 56; the original gives lines of hydrogen and 
helium as well. 

tory, because atoms leave the excited state by collision. This 
general explanation has received interesting confirmation in a 
comparison of the relative intensities of the magnesium lines 
2852 and 4571 A.* The first is the line 2 *P-> 1 *S, which is very 
intense in the arc, the second 2 3 P X -> 1 1 S, which is very weak. The 
natural lives of the atoms in these initial states, calculated by the 

* Frayne, PE, 1929, 34 590. 



XXI] FORBIDDEN LINES 219 

methods of the quantum mechanics,* are 3. 10~ 9 and 4. 10~ 3 sec. 
respectively, so that if the concentration of tie atoms in the two 
states are* at all comparable, the 2 1 ? line wm appear much the 
more intense. In the arc the number of atoms in the 2 3 P state 
is kept down only by frequent collisions, but if the pressure is 
sufficiently reduced and an inert gas is introduced to prevent the 
magnesium atoms diffusing to the walls, the 4571 A. line should 
increase in intensity. Kinetic theory shows that if the time 
between successive collisions is to be reduced to 10~ 3 sec., the 
vapour pressure must be reduced to 10~ 4 mm.; and in fact the 
vapour pressure of magnesium is of this magnitude at 500 C. 
Working with an electrodeless discharge at this temperature 
Frayne found that the 4571 A. line was fairly prominent and that 
the introduction of 10 mm. of various inert gases increased the 
intensity 50-100 times. In agreement with this work the auroral 
line 5577 A. appears only in the presence of an inert gas, and the 
intensity increases with increase in the diameter of the tube. 

As a general explanation this hypothesis of Bowen's appears 
satisfactory enough, but recent theory shows that it may be made 
much more precise. 

2. Quantum mechanics 

The quantum mechanics shows that the ordinary spectral lines 
arise from a dipole oscillation and that, usually, this alone is 
important; but mathematically it is only the first term in the 
series which arises when the vector potential is developed in 
powers of the atomic radius divided by the wave-length of the 
emitted light; the second and third terms indicate quadripole and 
octapole radiation of much lower intensity. Of these the quadri- 
pole oscillation will be shown responsible for the forbidden lines 
described in the last section; no line has yet been attributed to an 
octapole oscillation. 

In agreement with this theory is the low intensity of the quadri- 
pole lines. Thus experiments in absorption suggest that 12,000 
times as many atoms absorb the 3 2 P - 1 2 S lines of K and 
Rb as absorb the 3 2 D<- 1 2 S lines, the ratio being roughly the 

* Houston, PR, 1929, 33 297. 



220 QUADRIPOLE RADIATION [CHAP. 

same in the two metals;* while Rasetti,f using a more sensitive 
method depending on anomalous dispersion, found the intensity 
ratio of the emitted lines of K to be 1-1.10~ 6 ; and &s Rasetti 
estimates his accuracy as only 50 per cent, this may be considered 
in satisfactory agreement with the theoretical value of 1-5 . 10~ 6 .J 
That the absorption measurements show rather a large error is of 
little account, for the authors themselves insist that their 
estimate was intended to be little more than qualitative. 

The selection rules observed in quadripole lines can be pre- 
dicted from the simple hypothesis that a quadripole line results 
from two simultaneous dipole transitions, though this rough 
analogy is of course a poor substitute for the rigid argument of 
the quantum mechanics. Thus in a dipole jump the siim of the 
orbital vectors 2^ changes always from odd to even or even to 
odd, and accordingly in a quadripole jump the same quantity 
changes from even to even or odd to odd; in particular a quadri- 
pole line may be emitted when the jump is between two terms of 
the same configuration. Again in a dipole line 

AJ = or 1, 
so that in a quadripole line we expect 

AJ = or 1 or 2. 

And in fact all known lines do satisfy this condition. 

In practice the quadripole selection rules are not used like the 
dipole rules to predict which lines will appear, since so few of the 
lines allowed have yet been produced; rather do they serve to 
determine whether an observed line arises from a dipole or a 
quadripole transition, and for this in a field-free space the 
Laporte rule is crucial; if a transition is known to start from one 
term and end in another, then it can be written down at once as 
a dipole or a quadripole. But so often one cannot be certain 
whether there is a stray electric field or not, and then the Laporte 
rule cannot be trusted; instead one has to examine the Zeeman 
effect and let it decide. 

* Sowerby and Barratt, PRS, 1926, 110 190. 
f Rasetti, Accad. Lincei, Atti, 1927, 6 54. 
j Stevenson, PKS, 1930, 128 591. 



XXI] ZEEMAN EFFECT 221 

3. Zeeman effect 

In the Zeeman splitting of quadripole, as of dipole, lines, the 
term displacements are simple fractions of the Lorentz unit, 

m 7 > so that the change in energy &E of any state may 

be written &E/hc = Mgo 

where g has the normal Lande values given by 



~ .......... 2J(J+l) 

But whereas in a dipole line the transitions are governed by the 
selection rule 



in quadripole lines AM ^ 2. 

And the polarisation rules too are different, as the summary given 
in Pig. 21-2 shows; in particular, when the pattern is viewed at an 
angle of 45 to the field, components appear which are invisible 
when the line of sight is parallel or perpendicular to the field. 



Transition 



A M = - 2 

AM +2 



m 


Polarisation when viewed 


Across 
field 


Diagonal 
at 45 


Parallel 
to field 


2 


or 


1. ell. 





2 


CT 


r. ell. 





1 


77 


cr 


1. circ. 


1 


7T 


a 


r. circ. 







7T 






Fig. 21-2. Quadripole radiation. Transitions permitted in a magnetic field and 
the polarisation of the line produced. 

Applied to a singlet line, such as the green auroral line, this 
theory shows that the Zeeman pattern should be that shown in 
Fig. 21-3; thus when viewed parallel to the field the Zeeman 
pattern of a dipole and a quadripole line are identical, a fact which 
explains why McLennan* was able to confirm the identification of 
the 5577 A. line as due to 1 D 2 -> 1 S before the quadripole theory 
was developed, though later Frerichs and Campbellf showed that 

* McLennan, McLeod and Ruedy, PM, 1928, 6 558; Sommer, ZP, 1928, 
51 451. 

f Frerichs and Campbell, PR, 1930, 36 1460. 



222 QUADRIPOLE RADIATION [CHAP. 

it arises in a quadripole transition; for McLennan viewed the pat- 
tern along the field axis, while Frerichs and Campbell viewed 
it transversely. The latter obtained a beautiful confirmation of 
theory, finding two TT components at a distance of one, and two a 
components at a distance of two, Lorentz units, all four lines 
being of equal intensity (Fig. 21-3). 



la ) perpendicular 



(Mparallel 



45 



7T 
<J 



Ot. 



Fig. 21-3. Zeeman pattern of a quadripole singlet line, when viewed (a) per- 
pendicular, (6) parallel, (c) at 45, to the field. The intensities are proportional 
to the lengths of the verticals. 

A more rigorous because more complex confirmation of theory 
has been obtained by Segre and Bakker, who measured both the 
Zeeman and Paschen-Back splitting of SD alkali doublets,* and 
contrasted these with the splitting of the mercury line 3680 A.; 
this line arises as 7p 3 P 2 ->6p 3 P 2 and is normally forbidden, but 
it appears in an electric field, f 

The Zeeman effect of the SD doublet was demonstrated with a 
field of 7500 gauss applied to the potassium lines 
4d 2 D 2 ^->4s 2 S^ 4642-27 A. | 
4d 2 D u ->4s 2 Sj 4641-77 A. j 
with an interval of 2-325 cm.- 1 



* Segre and Bakker, ZP, 1931, 72 724. 
t Bakker and Segre, ZP, 1932, 79 655. 



XXI] ZEEMAN EFFECT 223 

For this doublet the theoretical patterns are: 

(1) When observed parallel to the field, 

SD^-^S* 4.8/5 
2 D U -> 2 S^ 1.7/5 
all components being circularly polarised. 

(2) When observed transverse to the field, 

2 D 2i -> 2 S* (4). (8). 10. 14/5 

2 I>H-> 2 S* (1). (7). 11/5. 

The figures in brackets measure TT components, the other figures 
a components. 

(3) When observed at an angle of 7r/4 to the field, 

2 D 2 i-> 2 S t (2). 4. 8. 10. 14/5 

2 D u -> 2 Sj 1. (3). 1.11/5. 

The figures in italics are elliptically polarised with an axis ratio 
of A/2 : 1 between the or and TT axes. The intensities in these 
simple transitions may be obtained from the polarisation rule 
and the sum rule of Burger and Dorgelo (Fig. 21-4). Fig. 21-5 







'Bit 


->S 




D H -+S 






M 


i 


1* 


i 


H 


2t 


M 


gM 


t 




.V 


* 


t 


3 


k 


[ 


-i(2) 


I(D 


-*<3) 


tW 


2 (5) 


-i 


-1 


H3) 


V (4) 


*(2) 


Vd) 





Fig. 21-4. The displacements and in brackets the intensities of the Zeeman com- 
ponents of a D->S doublet. 

shows that the experimental results are in complete agreement 
with theory. 

The Zeeman effect thus satisfactorily confirmed, Segre and 
Bakker changed from potassium to sodium, in which the two 
lines lie so close together that they were not resolved in the instru- 
ment used. The pattern should then be (1).2/1, when observed 
transverse to the field. Experiment confirmed this Paschen- 
Back effect (Fig. 21-6) though the photographs are somewhat 




wx 



(a) 





(b) (c) 

Fig. 21-5. The 4642-41 A., D-^S, doublet of potassium. In each figure the 
photometer curve appears above and the theoretical splitting below. The in- 
tensity scale is arbitrary, but the same in all figures. The 2 D 2 j-> 2 S| line is on the 
left, and the 2 D 1 ^-> 2 S^ line on the right. At the foot the scale is shown by two 
lines of length 0-1 A. and 1 cm." 1 The three figures show respectively (a) the 
doublet in the absence of a magnetic field, (6) the a components viewed per- 
pendicular to a field of 7500 gauss, and (c) the n components viewed from the 
same direction. (After Segre and Bakker, ZP, 1931, 72 728.) 



CHAP. XXI] ZEEMAN EFFECT 225 

distorted by the appearance of bands due to the sodium molecule; 
but if the intensities observed in the absence of a field are com- 
pared witR those obtained with a field, the lines can be dis- 
tinguished. Not content with these successes the authors measured 






U 



(a) (b) (c) 

Fig. 21-6. Paschen-Back effect in the 3427 A. 3 2 D^1 2 S, line of sodium. 
Figure a is taken in the absence of a magnetic field, b and c in a field of 16,100 
gauss; b shows the a components viewed perpendicular to the field, c the rr com- 
ponents viewed in the same direction. The appearance of the Na 2 bands con- 
fuses the pictures a little, but it is the changes which occur between a on the one 
hand and 6 and c on the other which are of importance. (After Segre and 
Bakker, ZP, 1931, 72 731.) 

the potassium doublet in an * intermediate field ', the splitting and 
intensity having been calculated by Milliaiizuk* with the help of 
Darwin's work on the gross Paschen-Back effect. A field of 
17,800 gauss was used giving the ratio o m /Ai/ a value of 0-35, and 
again satisfactory agreement was obtained. 

Finally Segre and Bakkerj examined the 7p 3 P 2 -> 6p 3 P 2 line 
of mercury in order to show that it arises, not as a quadripole 
transition, but as a dipole conditioned by the electric field. The 
quantum mechanics makes this probable, for a rough calculation 
shows that the quadripole term in the radiation of a forbidden 
line is usually larger than the dipole produced by an electric field, 
but this is not true when a state with which both levels may com- 

* Milianczuk, ZP, 1932, 74 825. 

t Segre and Bakker, ZP, 1932, 79 655. 

CASH 15 



226 QUADRIPOLE RADIATION [CHAP 

bine lies close to one of them;* and in mercury the 7p 3 P 2 tern 
lies at a distance of only 188 cm." 1 from the 6d 3 D 2 term. 

An electric field modifies the ordinary selection rule ; when th< 
pattern is viewed transverse to the magnetic field, TT component! 



M 


2 


- 1 1 


2 


Mg of 7p 3 P 2 
Mg of 6p 3 P 2 


-3 
-3 


-H o ii 

-1J li 


3 
3 


Pattern if a dipole 


(0) (3) 3 (5/2 


Pattern if a quadripole 


(3) 6/2 



Fig. 21-7. Theoretical Zeeman pattern of the 3680 A., 7p 3 P 2 -^6p 3 P 2 , line o 
Hg I, when viewed perpendicular to the magnetic field, if it arises as (a) a dipol 
transition conditioned by an electric field; (b) a quadripole transition. 



<r 



3-8 



1-9 



13 



14-7 



Fig. 21*8. Theoretical intensities of the Zeeman components of the 3680 A. line 
of Hg i, if it arises as a dipole in an electric field. The line is viewed transverse 
to the field. (After Segre and Bakker, ZP, 1932, 79 655.) 

arise from transitions in which A M is or 1 and o- components 
when M is 0, 1 or 2; so that the pattern should be 
(0) (3) 3 6/2 (Fig. 21-7) and intensity calculations show that 
of these components the undisplaced line is far the strongest 
(Fig. 21-8). In contrast the selection rules of a quadripole line 
allow 77 components to arise only when AJtf" is 1 and a com- 
ponents only when AJf is 2, so that the pattern predicted is 
(3) 6/2. The photometer curve reveals simply a strong central 
line, but as there seems no doubt that the resolving power was 
sufficient to have separated the side components of a quadripole 
line, this may be taken as proof that the transition is a dipole. 
* Huff and Houston, PR, 1930, 36 842. 



XXI] ZEEMAN EFFECT 227 

4. Intensities 

Theory has been able to predict the intensities of normal 
quadripole* multiplets,* but very little has been confirmed by 
experiment. In part this is due to the difficulty of producing 
quadripole lines in the laboratory, and in part to the restriction 
of theory to multiplets arising from Russell-Saunders coupling, a 
restriction which implies the exclusion of all inter-system lines; 
no general theory of the latter has yet been developed, so that the 
intensity of each separate line has to be calculated. 

BIBLIOGRAPHY 

There are two important articles, the first by Becker and Grotrian "Uber die 
galaktischen Nebel und den Ursprung der Nebellinien" in Erg. d. Exact. 
Naturwiss. 1928, 7 8, and the second by Rubinowicz and Blaton on "Die 
Quadrupolstrahlung " in Erg. d. Exact. Naturwiss. 1932, 11 170. The second 
of these deals with the theory more thoroughly than here. 

* Rubinowicz and Blaton, EEN, 1932, 11 176. 



15-2 



CHAPTER XXII 
FLUORESCENT CRYSTALS 

1. The energy levels of crystals 

Though the energy levels of many gases and vapours are now well 
known, the energy levels of solids are the hills of an unexplored 
land; for only two routes have yet led to quantitative results, and 
both of these are of limited value. X-ray levels do change from 
one chemical compound to another,* but as 15,000 calories corre- 
spond to a shift of between 0-1 and 0-01 X. unit or 10~ 4 of the 
energy involved, the measurements have to be very accurate. 
The light scattered in the Raman effect, f on the other hand, is 
accurate enough, but it reveals only certain energy states out of 
the many which exist. 

A third route runs through the absorption and fluorescent 
spectra of crystals, though as yet this has given hardly any 
quantitative results. At room temperature the lines are blurred 
by the agitation of the molecules, for the levels of one ion are split 
by the electric field of the ions which surround it, but the lines 
sharpen as the temperature is reduced. Much valuable work has 
been done in liquid air, but Spedding and his co-workers in 
California are rapidly making this of little more than historic 
interest by their work in liquid hydrogen. 

Many absorption lines are of course due to molecular vibra- 
tions, but in the last five years evidence has accumulated to show 
that in the rare earths and the phosphors of chromium at least, 
many lines arise as electronic transitions within the atom. This 
evidence is both simpler and more conclusive in chromium. 

2. Fluorescence and phosphorescence 

When a solution of chlorophyll is illuminated with a beam of 
violet or ultra-violet light, a green band can be seen from all 

* Siegbahn, Spektroskopie der Rontgenstrahlen, 1931, 278. 

f Kohlrausch, Der Smekal-Raman-Effekt, 1931. Placzek, Rayleigh Streuung 
und Raman-Effekt, 1934. Symposium at Faraday Congress by Raman, Wood, 
Cabannes and others, Trans. Far. Soc. 1929, 25 781. Dadieu and Kohlrausch, 
"Raman effect in organic chemistry", JOS A, 1931, 21 286. 



CH. XXII] FLUORESCENCE AND PHOSPHORESCENCE 229 

sides; this is an example of fluorescence. Again, in time past 
luminous paints consisted of impure barium sulphide; if first 
exposed to sunlight, this remains visible in the dark for some 
hours; it is said to phosphoresce. Fluorescence is distinguished 
from phosphorescence by the persistence of the latter after the 
exciting rays have been extinguished. To-day, however, this 
distinction does not seem of great importance; it is probably 
related to the fact that only solids phosphoresce, though solids, 
liquids and gases may all fluoresce. 

In general fluorescence and phosphorescence may both be 
excited by cathode rays and X-rays as well as by light. When 
light is used, however, the wave-length of the exciting beam must 
be shorter than the wave-length of the light emitted; this law, 
discovered in 1853 by Sir George Stokes,* is simply explained by 
the quantum theory; energy may be lost between absorption and 
emission, it cannot be gained. This must not be taken to mean, 
however, that all wave-lengths shorter than those emitted are 
equally effective; on the contrary, a fluorescent solution or crystal 
absorbs only certain bands, and these are characteristic of the 
substance. The emission spectrum too is typically independent of 
the exciting source. 

Many organic substances, such as quinine sulphate and eosin, 
fluoresce; but in these the cause is undoubtedly molecular. Of 
more interest here are the solid phosphors, a group of substances 
which are conveniently divided under five heads : the phosphors 
of chromium, the phosphors of the rare earths, the uranyl salts, 
the Lenard phosphors and the platino -cyanides. The phos- 
phorescence of the first two has recently been shown to originate 
within the atom, and the evidence deserves detailed considera- 
tion. The phosphorescence of the other three may be atomic in 
origin, but no evidence is yet forthcoming; accordingly they are 
treated much more briefly. 

3. Chromium phosphors 

Many naturally occurring stones, such as the ruby, sapphire, 
red spinell, alexandrite and topaz, emit a red fluorescence. This 

* Stokes, Roy. Soc., Phil. Trans., 1853, 142 463; 1853, 143 385. 



230 FLUORESCENT CRYSTALS [CHAP. 

spectrum was thoroughly studied at a time when a ruby was sup- 
posed to consist of almost pure aluminium oxide, the odd 1 per 
cent, of chromium oxide being regarded as an unimportant 
impurity. Of recent years however the ruby has been imitated in 
the laboratory, and the chromium oxide, though present in such 
a small proportion, has been proved an essential constituent; for 
without it the aluminium oxide is not fluorescent, while with it 
the artificial ruby exhibits a spectrum identical with that of the 
natural stone. 

In preparing one of the chromium phosphors in the laboratory 
a few drops of a chromium salt solution are added to the salt of 
some other metal, such as calcium nitrate, and heated twice to a 
temperature of about 1400 C. The spectrum of this phosphor 
does not depend on the amount of chromium, though it is 
brightest with a few parts per thousand present. But the oxide 
must be an intrusion in the regular lattice of the bedding; mixed 
crystals of KA1(SO 4 ) 2 . 12H 2 and KCr(S0 4 ) 2 . 12H 2 show no 
phosphorescence, whatever the proportions of chromium and 
aluminium;* moreover, the Cr 2 3> or some molecule which con- 
tains it such as MgCr 2 4 , must be isomorphous with the material 
in which it is bedded, for Deutschbein has shown that chromium 
fluoresces in: 

aA! 2 3 which is isomorphous with Cr 2 3 ; both trigonal. 
MgAl 2 4 MgCr 2 4 ; regular. 

ZnGa 2 O 4 ,, ,, ZnCr 2 O 4 ; ,, regular. 

BeAl 2 4 ,, BeCr 2 4 ; ,, rhombic. 

MgO because it forms mixed crystals withMgCr 2 O 4 ; ,, regular. 
On the other hand, chromium does not fluoresce in: 
yA! 2 O 3 because it is not isomorphous with Cr 2 3 , the one being 
regular and the other trigonal; 

BeO because it forms no mixed crystals with BeCr 2 O 4 , the former 
being hexagonal and the latter rhombic. f 

That Cr 2 3 must be isomorphous with the bedding means 
presumably that the outer electrons must not be much distorted; 

* Deutschbein, AP, 1932, 14 713. 
t Deutschbein, PZ, 1932, 33 874. 



XXII] 



CHROMIUM PHOSPHORS 



231 



and in fact the spectrum of the ruby is very sharp and bright, 
for the Cr 2 O 3 molecule fits easily into the ocAl 2 O 3 lattice. On the 
other hand, in Mg 2 Ti0 4 when the distortion is greater, the 
spectrum is more diffuse; moreover, the unaided eye notices that 
the phosphorescent light is much weaker. 




Fig. 22*1. Spectra of some chromium phosphors. The lines shown black are those 
emitted at 186 C. ; those shown in outline appear in absorption at low tem- 
peratures, but in emission only at high temperatures. Comparison of the spectra 
in A1 2 O 3 and Ga 2 O ;{ , crystals belonging to the same system, shows that the 
principal doublet appears in both, but with fivefold greater interval in Ga 2 O 3 ; 
the two strongest subsidiary lines are also more widely separated in Ga 2 O 3 . The 
spectra in the regular crystal system MgO, MgAl 2 O 4 , ZnAl 2 O 4 show greater 
symmetry and a much smaller doublet interval, the doublet of MgO being still 
unresolved. (After Deutschbein, PZ y 1932, 33 876.) 

Whether the chromium phosphors are excited by cathode rays, 
X-rays or ultra-violet light, the spectrum produced is always the 
same; moreover, the emission spectrum is very like that produced 
in absorption. In both the lines are easily divided into three 
groups; first, principal lines, which are intense, sharp and only 
some half-dozen in number; second, subsidiary lines, which are 
weaker and more numerous; and third, bands, which are weak 
and often lie near the lattice bands of the pure bedding. Plate V 
shows these three in the emission spectrum of chromium bedded 



232 FLUORESCENT CRYSTALS [CHAP. 

in aluminium oxide; at the short wave-length end of the spectrum 
lies the principal doublet, which is here some thousand times 
over-exposed. Then follow on the long wave-length #ide a few 
weaker but very sharp subsidiary lines, while beyond again lie 
some diffuse bands. That this type is general Fig. 22-1 shows. 

All the chrome phosphors have one or two principal lines in the 
red, while several exhibit also a group of three lines in the blue 
(Fig. 22-2). Moreover, examination of a series of alums of the 



7000 6000 5000 A 


Tern 
Cr 

I 


is of 

IV 

?*<> 
^H, . 

JG> 
'^ 4 - 

&<* 

^ 


V 
cm^l 

25000 
20000 
15000 
10000 
5000 



AUO, 


II I 


Ga 2 0, 




MgO 




MgAl 2 4 




ZnAl 2 4 




MgGa 2 4 




ZnGa 2 4 




BeAl 2 4 | HI 


Al 2 Si0 5 I I 


[Al(OH,F)] 2 Si0 4 II 


Be^^SiO^ I 


CajCAl.CrMSiO^ || 


TiMg 2 4 


* 


KCr(S0 4 ) 2 -t-12H 2 | 


Term difference of Cr 3 * 


\ III 


Combination 2 G Vp _Aj *jj 2 H-* 4 F $# 


V 14,000 16.000 18,000 20.000 22.000cm.' 



Fig. 22-2. Principal emission and absorption lines of some chrome phosphors 
compared with the term differences of Cr iv. (After Deutschbein, PZ, 1932, 
33 877.) 

types RCr(S0 4 ) 2 .12H 2 O and RCr(Se0 4 ) 2 . 12H 2 O, where R is 
variously K, Rb, Tl and (NH 4 ), shows that in liquid air all absorb 
a strong doublet near 6700 A. (Fig. 22-3).* Other chromium com- 
pounds are not of course so regular as these, but most show line 
absorption. f The frequencies of these lines, and especially of the 
phosphorescent lines, are comparable with term differences found 
in an analysis of the Criv spectrum; in this the 3d 3 configuration 
produces a 4 F ground term and above it metastable 2 G and 2 H 

* Sauer, AP, 1928, 87 197. 

t Snow and Rawlins, Camb. Phil. Soc. Proc. 1932, 28 522; Joos and 
Schnetzler, Z. Phys. Chem. 1933, B, 20 1. A paper on KCr(S0 4 ) 2 .12H 2 by 
Spedding and Nutting, J. Chem. Phys. 1934> 2 421, appeared after this section 
was written. 



XXII] CHROMIUM PHOSPHORS 233 

terms; in the vapour these terms do not combine, but in the 
phosphors the mechanism is probably not a pure dipole, so that 



6800 



6700 



6600 



6500 



6400 A 



I 




18C 



7-8 



11-12 




-78C 



6800 



-190C 




67 00 



6600 



6500 



6400 A 



Fig. 22-3. Absorption curves of RbCr(Se0 4 ) 2 .12H 2 Oat 18, - 78 and -190 C. 
Crystal thickness about 4 mm. (After Saner, AP, 1928, 87 219.) 

the transitions may reasonably be allowed. At any rate, Fig. 22-2 
shows that the frequencies agree so remarkably that the identifica- 
tion can hardly be doubted; the red principal lines are there 



234 FLUORESCENT CRYSTALS [CHAP. 

shown to arise in the 2 G-> 4 F transition and the blue lines in 
2 H-> 4 F;* the precise transitions to which the individual lines are 
to be assigned are not yet clear, but as the doublet of chrome alum 
is still strong at 195 and is not fading out, the two highest 
levels of the ground term, 4 F 4i and 4 F 3 ^, lying at 950 and 550 cm." 1 
above ^j, may be reasonably excluded. The Boltzmann dis- 
tribution would allow very few atoms in these states at so low 
temperature, and the law so admirably explains the fading of 
certain lines in samarium that it can hardly be in error. f 

Like the principal lines, the subsidiary do not change greatly 
when the temperature is reduced from 20 to 195C.; they 
grow rather sharper, and the whole spectrum has its wave-length 
reduced by a few angstroms, J but they do not otherwise change 
much in position or intensity. They appear both in phosphor- 
escent and absorption spectra, but they occupy very different 
positions in different beddings; the positions, however, are 
characteristic of the crystal lattice, not of the anion; indeed with 
practice the lattice type can be recognised from the look of the 
spectrum. This would seem to suggest that the subsidiary lines 
are Stark components produced by the electric fields of the ions 
in the crystal lattice; but if the atomic states are split by a strong 
electric field all components should be Stark components, and it 
is not easy to see why the half-dozen lines should be so much 
stronger than any others. Again, is it mere chance that nearly all 
subsidiary lines are of shorter wave-length than the principal 
lines ? One might assume that some Cr 2 3 molecules are lumped 
together, and that these produced different lines to those spread 
evenly through the bedding of say A1 2 O 3 ; but if the fields of 
Cr 2 3 and A1 2 3 are different, as is probable, we should expect all 
fields from that characteristic of Cr 2 3 to that characteristic of 
A1 2 3 , and then the lines would be diffuse not sharp; accordingly 
one must suppose the Cr 2 O 3 molecules spread evenly through the 
A1 2 3 lattice like currants in a cake. The electric field is then 
effectively that of the A1 2 O 3 lattice. 

* Deutschbein, ZP, 1932, 33 877. 
t Spedding, PR, 1933, 43 143 a. 
J Deutschbein, AP, 1932, 14 720. 



XXII] CHROMIUM PHOSPHORS 235 

The bands are considerably more complicated than either the 
principal or the subsidiary lines, for they are not the same in 
emission ar*d absorption, and grow more complex if the tempera- 
ture is raised. At low temperatures, however, the emission spec- 
trum consists only of a long wave-length band lying in the red and 
infra-red; while the absorption spectrum consists of a short wave- 
length band lying in the blue. If the principal lines, which lie 
between these two bands, are unaltered electron transitions, and 
the bands conform to Stokes's law, these facts are easily ex- 
plained; the absorption bands must lie on the high-frequency side 
of the principal lines, and the emission bands on the low-frequency 
side.* At room temperature emission still occurs chiefly in the 
red and infra-red, but some diffuse bands appear on the violet 
side of the principal lines ; these short-wave or ' anti-Stokes ' bands 
must be emitted by molecules passing from an excited state to 
one of low energy, so that their intensity should be proportional 
to the number of molecules in the excited state; this number is 
determined by the Boltzmann law and decreases rapidly with 
decrease of temperature. Again, in the absorption spectrum there 
appear at room temperature bands of wave-length longer than 
the principal lines; these anti-Stokes absorption bands can be 
explained in the same way as the anti-Stokes emission bands, 
they are due to absorption by molecules which are already in an 
excited state, f 

The frequencies of some of the stronger bands are also of 
interest. The Raman spectrum of pure aA! 2 3 reveals a lattice 
frequency of 417 cm." 1 Now in the emission spectrum of a ruby, 
the principal doublet and a strong band lie at 14,416 and 
14,006 cm." 1 respectively; thus in the phosphor a band occurs 
with a frequency difference slightly less than that of pure A1 2 3 , 
410 instead of 417 cm." 1 This relationship is not uncommon in 
the chrome phosphors, and is accounted due to a decrease in the 
lattice frequency caused by the introduction of the chromium 
oxide molecules.* 

* Deutschbein, ZP, 1932, 77 490. 

t For the effect of a magnetic field on the lines of a ruby: Du Bois and Elias, 
AP, 1908, 27 233, 1911, 35 617; Du Bois, PZ, 1912, 13 128. 



236 FLUORESCENT CRYSTALS [CHAP. XXII 

4. Rare earth phosphors 

As long ago as the eighties of last century Crookes* showed, 
during the course of his pioneer work on high vacuaf that when 
rare earth minerals are irradiated with cathode rays, they emit a 
strong phosphorescent spectrum ; but his work is only of historic 
interest, because very few of his rare earth preparations were pure. 
More recent work shows that salts, which are colourless like those 
of lanthanum, gadolinium and ytterbium, exhibit no after-glow; 
but the smallest trace of active impurity makes the substance 
phosphorescent; 4.10~ 6 gm. of samarium in 1 gm. of calcium 
oxide is sufficient to produce a red after-glow, while the spectrum 
is brightest if the active earth is present in a proportion of only 
1 per cent.; thus the smallest trace of dysprosium in yttrium, or 
of terbium in gadolinium, can easily be detected.! 

Naturally occurring fluorites too have long been known to 
exhibit blue, yellow and green fluorescence, when excited with 
radium; but little progress was made until synthetic calcium 
fluoride was used and 1/10 per cent, of a rare earth added. Then 
it was shown that the blue band appears only when europium is 
present, and the yellow-green band only when ytterbium. The 
active agent of the red band has not yet been traced ; all other rare 
earths are inactive. As europium and ytterbium are the two rare 
earths which most readily become divalent, J and the fluor- 
escence may be excited by heating the activated fluorite in a 
reducing flame, the transition from tri- to divalent form is clearly 
linked with the fluorescence. 

Of all the rare earth phosphors, samarium has been most 
thoroughly studied (Fig. 22-4); as elsewhere the spectrum is much 
the same if excited by ultra-violet light instead of by cathode rays . 
The lines are somewhat sharper than those of the chromium 
phosphors, especially at room temperature; while at low tem- 
peratures even naturally occurring fluorspar emits lines which 
are as sharp as the D lines of a flame poor in sodium. || Again rare 

* Crookes, Chem. Soc. J. 1889, 55 255. 

t Urbain, Chem. Rev. 1924, 1 167. 

J Jantsch and Klemm, Z. /. anorg. und allgem. Chemie, 1933, 216 80. 

Haberlandt, Karlik and Przibram, Akad. Wiss. Wien, Ber. 1934, 143 151. 

!| Tomaschek, AP t 1927, 84 329, 1047. 



<J 



o 

VN 

u-\ 




300 cm: 1 

Tomaschek, 


- 




o 

\r\ 


o 

O 
(M 


T 


o 
o 

CM 


o 

T 




T - 

. 




T 




o 

\r\ 

7 










4 




MMMl 


.: .... 


~ 





"""' 


Ij ^5 

I 






s 




= 


^-*-**m 




- 


i 




I 

03 

C 




__L-a 


^ 
4 


- 






- 


















1 






















"&, 






















-75 






















~^S 






















V^ w 






















S 












1 




...... 








.2 




o 






4 










-= 


MBMBI 


> 











~i 


*1 




MiBIMH 



















^ 







r_ = 


- 


T3 
dS 


= 


-_ij 




- 




rium bedd 




J 


















efi 






















O 02 






















Jn " 






















" 1 












- 




_ 





M 


02 


o 


~= 




< 








- 


~ fmtm 




1 


o 








* 





""* 


_ 








g 


<p 






.^ 


. i 




- 








i-23 







-=f 


Ja 


- 


-^ 










8 




_zz 


__"-" 


"^ 


^ 


^ 




^ 


, 









CO "I 




"3 


" 


- j^ 

CO 




- CO 

3f 


O 
-co 

cS 


O 
-co 

CO 




-*< 

-0 GS1 
VTs C<| 

s 



238 FLUORESCENT CRYSTALS [CHAP. 

earth compounds need not be isomorphous with the bedding, and 
this can very probably be related to the sharpness of the lines. In 
contrast to the chromium phosphors, however, a phosphorescent 
spectrum of the rare earths is usually much more complicated than 
the absorption spectrum.* This may be ascribed to two causes; 
first absorption lines all arise in levels less than 500 cm." 1 above 
the ground term, but emission lines may end in much higher 
levels; and second all absorption lines arise in atomic transitions, 



300 



200 



100 - 



Sulphides 




300 



200 



100 - 



Be Mg Ca 



Sr 



Ba 



Oxides 




20 



40 



Be Mg Ca 

_l I U 



Sr 



Ba 



20 



40 



Fig. 22-5. Term displacements of samarium and praseodymium phosphors, 
when bedded in the sulphides and oxides of the alkaline earths. The heavier the 
rare earth and the smaller the diameter of the alkaline earth atom, the greater 
the displacement. (After Tomaschek, PZ, 1932, 33 878.) 

while some emission lines arise in the rare earth molecule and 
others in the lattice of the bedding. 

In the rare earth phosphors the vibrations of the bedding 
lattice are rather slower than those calculated for the pure 
crystal, and this is significant for the rare earth molecules may be 
supposed to act as inert loads. If this explanation is correct, the 
change of frequency should be greater the larger the rare earth 
and the smaller the bedding molecule; these predictions experi- 

* Spedding, PR, 1933, 43 



XXII] 



RARE EARTH PHOSPHORS 



239 



ment confirms. The praseodymium ion has a diameter 3 per cent, 
greater than the samarium ion, and the change of frequency is 
slightly groater ; barium oxide has a larger diameter than calcium 



cm: 1 16,000 17,000 18,000 


a 


A-X 


type 


MgO 


II i i 


4-21 


2*10 




CaO 


II II 


4-80 


2-38 




SrO 


;| I I | 


5-15 


2-59 


il 










'SH 


BaO 


, 1 ll 1 |l 1 I 


5-50 


2-77 


O 


MgS 


li 1 1 il 


5-19 


2-52 


O 

g 


CaS 


1 1 


5-69 


2-80 




SrS 


n i ii 


6-01 


3-00 


M 


BaS 


in i 


6-37 


3-18 




CaF 2 


1 l! 1 


5-45 


2-36 




SrP 2 


i i i 


5-78 


2-50 


0) 


BaF 2 


i i i 


6-19 


2-68 


'2 

o 


Zr0 2 


,111, n ,i 


5-10 


2-21 


1 


Ce0 2 


,, u i 


5-40 


2-34 




Th0 2 


".if. i 


5-57 


2-42 




A1 2 3 


IN 1 ,1 


5-15 


1-84 
1-99 


,s 










W 7 


Ga 2 0, 


III ,i 1 


5-28 






Li 2 S0 4 


II 1 








CaS0 4 


II II A , 








SrSO, 


, ill .1 








BaSQ, 


.III II 








A. 6200 6000 5800 5600 A 



Fig. 22-6. The two short wave line groups of some samarium phosphors 
arranged by the crystal type of bedding, a is the lattice constant and A-X the 
distance between the electropositive and electronegative centres in the lattice ; 
both are in angstroms. (After Tomaschek, PZ 9 1932, 33 880.) 

oxide, and the change of frequency produced by bedding sam- 
arium in it is much less (Fig. 22-5).* 

Though in their general features the spectra of samarium in 



* Tomaschek, PZ, 1932, 33 878. 



240 FLUORESCENT CRYSTALS [CHAP. 

different beddings are similar, a closer examination reveals many 
differences. Thus in Fig. 22-6 a series of spectra are arranged 
according to their crystal types, the figures alongside being the 
lattice constant a and the distance between the positive and 
negative ions, both in angstroms. The crystal type is here 
revealed as an important influence, but in fact this is clearer 
still in the original photographs,* for in them a practised eye 
can recognise the crystal type at a glance. t 

With so few principal lines in the samarium emission spectrum, 
one naturally asks whether they may not be interpreted, like the 
principal lines of the chromium phosphors, as electronic transi- 
tions within the ion. As the spectrum of samarium vapour has 
not been analysed, the way is by no means clear; but the fact that 
the rare earths do not have to be isomorphous with their bedding, 
suggests that the outer electrons can hardly be concerned; rather 
are the transitions likely to occur between different terms of the 
4f /l configuration, the brightest lines arising between terms of the 
same multiplicity. If transitions between the 4f n and 4f )l ~ l . 5d 
configurations are responsible for some lines, as Laporte has 
suggested, they are likely to be much more diffuse than the lines 
arising within the 4f n configuration; indeed it is tempting to 
identify a diffuse spectrum, photographed beside the sharp one 
by Fagerberg in neodymium and by Tomaschek J in samarium, 
with these predicted lines. 

Assuming that the principal lines arise within the 4f H con- 
figuration, their positions can be calculated by the method which 
Goudsmit developed. This method gives the extreme intervals 
of the various terms, if the coupling is Russell-Saunders, and the 
individual terms can then be interpolated with the interval rule. 
The calculations are laborious, but the results are eminently 
satisfactory, especially in praseodymium, whose emission spec- 
trum has been recently measured by Evert |). The lines shown in 

* Photographs, AP, 1927 84 Taf. ix-xi. Cf . Z. Elect. 1930, 36 737. 

f Tomaschek, PZ, 1932, 33 879. 

J Tomaschek, PZ, 1932, 33 882. 

Goudsmit, PR, 1928, 31 948, and chapter xvm of this book. 

|| Evert, AP, 1932, 12 144. 



PLATE VIII 

1. Fluorescent spectra of samarium bedded in various sulphates at 20 and 
150C. At room temperature the lines are so blurred that the photo- 
graphs do little more than show that the positions of the multiplets are 
independent of the bedding, but they sharpen as the temperature is 
reduced. The samarium lines are much sharper in La 2 (SO 4 ) 3 than in any 
other bedding, probably because lanthanum like samarium is trivalent. 
(After Tomaschek, AP, 1927, 84, Taf. X, XI.) 

2. DF quintet from the iron arc. This multiplet arises as 3d 6 . 4s ( 4 P) 4p 8 F 
-*3d 6 .4s 25 D. (Lent by Prof. H. Dingle.) 



Plate VIII 




XXII] BARB EARTH PHOSPHORS 241 

Fig. 22-7, taken from left to right, arise in transitions between 

the following values of J: 

for 3 F-> 3 H: 4-6, 3-5, 2-4, 4-5, 3-4, 4-4, 

for iG-^H: 4-5, 4-4. 

Since quadripole transitions are probable, J has been allowed to 

change by two units. These predictions are compared with the 

phosphorescent spectrum of the metal plotted above the line, and 

the absorption spectrum plotted below. 

Besides praseodymium satisfactory agreement is obtained in 
neodymium and erbium, spectra arising from 3 and (14 3) 
electrons respectively. In samarium only the terms of highest 
multiplicity have yet been calculated, for when there are five elec- 
trons the work becomes very heavy, but the 6 F-> 6 H transition 
accounts apparently for three strong lines in the infra-red. 

5. Uranyl salts* 

Like the rare earths the uraiiyl salts are fluorescent in their own 
right, and are not dependent on the crystal in which they happen 
to be embedded; but fluorescence is a property of the uranyl 
radical UO 2 , not of the uranium atom, for salts in which uranium 
is quadrivalent do not fluoresce. On the other hand the absorption 
spectra of all uranium compounds are so similar, that the uranyl 
radical cannot be considered peculiar in the energy it absorbs, but 
only in re-emitting some of this energy as visible light. 

At room temperature and viewed in a spectroscope of low re- 
solving power, both the fluorescent and absorption spectra of 
uranyl salts consist of bands. In the emission spectra some seven 
or eight bands appear in the yellow and red, while in absorption 
a smaller number appear in the green and blue ; the emission band 
of shortest wave-length coincides with the longest absorption 
band. The emission bands are equally spaced in the scale of 
frequency; the interval varies a little from salt to salt, but is 
never far from 830 cm." 1 Again, all emission bands show the same 
variation in intensity, but the intensity distribution in absorption 
bands is quite different (Fig. 22-8). 

* Pringsheim, Fluorescenz und Phosphorescenz, 1928, 238; Nichols and 
Howes, The fluorescence of the uranyl salts, Carnegie Institute Publication, 
1919, No. 298. 

CASH 16 



242 



FLUORESCENT CRYSTALS 



[CHAP. 



SH 
W 



XXII] 



UKANYL SALTS 



243 









1 


>.s 

^ Is 

-*^ 03 









t 


fl 








r 


If 













.a & 




k 








O w 

00 2 


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0' 


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. 


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=: 


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. Multiplets of 
ie line is the ph< 
(After Tomasc; 






. 


1 1 


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*H 




C/Q 





^ > ^ 

Eb <1 "5 



16-2 



244 



FLUORESCENT CRYSTALS 



[CHAP. 




6400 6000 



4400 A. 



Fig. 22-8. Spectra of uranyl potassium sulphate at 25 C. I, the fluorescent 
spectrum showing the intensity increasing towards the blue ; II, the absorption 
spectrum showing the intensity decreasing towards the blue. The three marked 
with arrows appear in both emission and absorption. (After Pringsheim, 
Fluorescenz und Phosphor escenz, 1928, 241.) 



r 




i 



i 



5200 



5100 A. 



Fig. 22-9. Structure of a single fluorescent band of uranyl sulphate. The curve 
gives the intensity at room temperature ; the lines are those observed at 185 C. 
(After Pringsheim, Fluorescenz und Phosphor -escenz, 1928, 243; and Wick, PR, 
1918, 11 126.) 



ill 1 H i; i 


i 

lull 






Hill! 

5500 5 

1 


ill; ill 1: 

000 


1 illill 

A. 


BOO 1900 2000 


Z100 cm. 1 



_A 
v 



Fig. 22-10. Spectra of uranyl potassium chloride at 186 C. The fluorescent 
lines are shown above the horizontal, the absorption lines below. The lines are 
polarised parallel and perpendicular to the principal axis of the crystal; the 
ordinary spectrum is shown by full and the extraordinary by dotted lines. The 
lengths of the lines indicate intensities. (After Pringsheim, Fluorescenz und 
Phosphorescenz, 1928, 243.) 



XXII] URANYL SALTS 245 

At low temperatures high resolution splits these bands into a 
number of components; indeed in liquid hydrogen, at 20 A., 
many linas are as fine as the lines of a spark spectrum 
(Fig. 22.9). But rather curiously even these sharp lines show 
no trace of broadening in a magnetic field of 2500 gauss. In both 
emission and absorption spectra many lines are polarised parallel 
or perpendicular to the principal axis; in Fig. 22-10 these lines 
are represented by continuous and dotted lines respectively, and 
their different positions show that when the phosphorescent 
spectrum is viewed through a nicol prism, two entirely different 
spectra appear as the nicol is rotated. 

The spectra of the uranyl salts resemble those of chromium 
sufficiently closely to make one wonder whether the frequencies 
of the strong lines are not equally significant, but as yet none of 
the higher spark spectra of uranium has been analysed. 


6. Lenard phosphors 

Many phosphorescent compounds, whether occurring natur- 
ally as minerals or artificially produced, consist of a crystalline 
salt carrying a trace of some other substance which will not fit 
into the crystal lattice; the intruding substance is commonly 
a metal, and the greater number of these phosphors may be 
regarded as members of a family of which the alkaline earth 
sulphides activated by a heavy metal may be considered the 
prototype. Having been exhaustively studied by Lenard and his 
school, they are commonly known as Lenard phosphors. 

As the intruding metal seems responsible for the fluorescence, 
one might have hoped for a line spectrum, instead of the broad 
bands actually observed, though as many workers have used 
spectroscopes of low resolving power combined with a slit 1 mm. 
wide the evidence is not so extensive as could be desired. When 
a substance exhibits several bands these often behave inde- 
pendently when a change is made in the wave-length of the 
exciting light or in the temperature; some bands fade and others 
grow brighter. Further, the positions of the bands change when 
either the active element or the bedding is changed.* 

* Pringsheim, Hb. d. Phys. 1929, 21 600. 



246 FLUORESCENT CRYSTALS [CHAP. XXII 

Like the Lenard phosphors the platino-cyanides phosphoresce 
only when bedded in some inert material; neither the pure salts 
nor their solutions are themselves phosphorescent; but the 
phosphorescence appears so regularly that it has been attributed 
to the platino-cyanide molecule in the absence of other evidence. 
The details of the emission spectra depend largely on the crystal 
type, and change when water of crystallisation is added. The 
polarisation depends on the polarisation of the incident light. 

At room temperature the emitted light lasts a very short time; 
but if a body at 250 C. is illuminated, it phosphoresces only 
when allowed to warm up. In this the platino-cyanides are like 
the Lenard phosphors. 

BIBLIOGRAPHY 

The most thorough study of the older work is Lenard, Schmidt u. Tomaschek, 
" Phosphorescenz und Fluorescenz ", Handbuch der Experimental Physik, 1928, 
23. This fills two large volumes; briefer summaries have been provided by: 
Pringsheim, Fluorescenz und Phosphor escenz, 1928; Pringsheim, "Lumin- 
escenzspektra ", Handbuch der Physik, 1929, 21 574. 

The newer work of Spedding, Tomaschek and Deutschbein, with which this 
chapter is chiefly concerned, does not seem to have been written up. 



APPENDIX V 
KEY TO REFERENCES 

The periodicals, in which most papers appear, I have cited by the 
capitals introduced by Gibbs, the less common by the usual abbrevia- 
tions. A key to the former is given here ; a key to the latter may be 
found in Science Abstracts. 

AJ Astrophysical Journal. 

AP Annalen der Physik. 

BSJ Bureau of Standards, Journal of Research. 

EEN Ergebnisse der Exacten Naturwissensehaften. 

JOS A Journal of the Optical Society of America. 

N Nature. 

Nw Naturwissenschaften. 

PM Philosophical Magazine. 

PR Physical Review. 

PES Proceedings of the Royal Society, London, series A. 

PZ Physikalische Zeitschrift. 

ZP Zeitschrift fur Physik. 

An author's initials are not given in the text unless two authors of 
the same name occur; but all authors are given their initals in the 
index. 



APPENDIX VI 
BIBLIOGRAPHY 

The bibliography is divided into three sections : 

A. Books of reference. 

B. Spectra of the elements. 

C. Hyperfine structure of the elements. 

In the last two sections I follow Bacher and Goudsmit in arranging 
the elements in the alphabetical order of their chemical symbols. 

A. Books of reference 

The following books are frequently needed for reference, because they 
contain experimental data conveniently arranged. Books dealing 
with a particular subject are discussed at the end of the chapter on 
that subject. 

1. Gibbs, J. C. * A complete bibliography of individual spectra for the years 
1920-1931.' Rev. Mod. Phys. 1932, 4 278. 

2. Bacher, R. F. and Goudsmit, S. Atomic energy states, 1932. The terms 
of all known spectra, but no wave-lengths. 

3. Kayser, H. and Konen, H. Handbuch der Spektroskopie, vol. vm, 1932. 
A complete review of the first nineteen elements in alphabetical order; that is 
A, Ag, Al, As, Au, B, Ba, Be, Bi, Br, C, Ca, Cd, Ce, Cl, Co, Or, Cs, Cu. Wave- 
lengths, terms, magnetic splitting factors and hyperfinc structure are all given 
with a bibliography. 

4. Grotrian, S. Graphische Darstellung der Spektren von Atotmn mil ein, zwei 
und drei Valenzelektronen, 1928. The energy diagrams of vol. n show the 
transitions which produce all the strong lines. 

5. Fowler, A. Report on series in line spectra, 1922. Paschen, F. and Gotze, 
R. Seriengesetze der Linienspektren, 1922. Both books contain lists of terms and 
lines for the elements of the first three columns. 

B. The spectra of the elements 

These lists are select; where one paper provides a satisfactory sum- 
mary, earlier papers are not cited. The papers deal chiefly with the 
analysis into systems of terms, but papers on intensities and the 
Zeeman effect have been included when they deal with a particular 
spectrum. 

When one of the books of reference, Kayser and Konen, Grotrian 
and Fowler, deals with a spectrum, I have included the author's 
name in the bibliography, as these sources are too easily overlooked. 

The abbreviations are those used in the text. 



BIBLIOGRAPHY OF THE ELEMENTS 249 

A: Argon 18 

A Kayser and Konen. 

A i Meissner, ZP, 1926, 39 172, 40 839. Terms and lines. 

Dorgelo and Abbink, ZP, 1927, 41 753. Extension in ultra-violet. 

Gremmer, ZP 9 1928, 50 716. Extension in infra-red. 

Rasmussen, Nw, 1930, 18 1112. Bergmann series. 

Terrien and Dijkstra, J. de Phys. 1934, 5 443. Zeeman effect. 

Pogany, ZP, 1935, 93 364. Zeeman effect. 

Boyce, PR, 1935, 48 396. Extreme ultra-violet. 
A ii Compton, Boyce and Russell, PR, 1928, 32 179. Extreme ultra-violet. 

Bakker, de Bruin and Zeeman, ZP, 1928, 51 114, 52 299; K. Akad. 
Amsterdam, 1928, 31 780. Zeeman effect. 

de Bruin, ZP, 1930, 61 307; K. Akad. Amsterdam, 1930, 33, 198. 
Complete term scheme and lines. 

Boyce, PR, 1935, 48 396. Extreme ultra-violet. 
A m Keussler, ZP, 1933, 84 42. Lines and terms. 

Boyce, PR, 1935, 48 396. Extreme ultra-violet. 

Boyce, PR, 1936, 49 351. Intersystem lines. 
A iv Boyce and Compton, Proc. Nat. Acad. Sci. 1929, 15 656. Lines and terms. 

Boyce, PR, 1935, 48 396. Extreme ultra-violet. 
Ag: Silver 47 
Ag Kayser and Konen. 
Ag i Fowler. Grotrian. 

Blair, PR, 1930, 36 1531. Extension of series. 
Ag ii Shenstone, PR, 1928, 31 317. Terms and lines. 

Blair, PR, 1930, 36 173. Two new terms. 

Gilbert, PR, 1935, 47 847. High terms. 
Ag m Gilbert, PR, 1935, 47 847. Lines and terms. 
Al: Aluminium 13 
Al Kayser and Konen. 

Al i Fowler. Grotrian. 
Al ii Sawyer and Paschen, AP, 1927, 84 1. Terms and classified lines. 

Ekefors, ZP, 1928, 51 471. New ultra-violet lines. 
Al m Paschen, AP, 1923, 71 152. Terms and lines. 

Ekefors, ZP, 1928, 51 471. New terms. 

Al iv Edlen and Ericson, Comptes Rendus 1930, 190 1 16, 173. Resonance lines. 
Al v Ibid. 
Al vi Ibid. 
As: Arsenic 33 
As Kayser and Konen. 
As i Meggers and de Bruin, BSJ, 1929, 3 765. Lines and terms. 

Rao, K. R., PRS, 1929, 125 238. Lines and terms. 

Rao, A. S., Proc. Phys. Soc. 1932, 44 243. 
As ii Rao, A. S., Proc. Phys. Soc. 1932, 44 343. 
As m Lang, PR, 1928, 32 737. Series. 

Rao, K. R., Proc. Phys. Soc. 1931, 43 68. Series. 
As iv Sawyer and Humphreys, PR, 1928, 32 583. 
As v Ibid. 



250 BIBLIOGRAPHY 

As: Arsenic 33 (conl.) 

As vi Borg and Mack, PR, 1931, 37 470. Series. 

Au: Gold 79 

Au Kayser and Konen, 

Au I Grotrian. 

McLennan and McLay, PRS, 1926, 112 95. Terms and lines. 

Symons and Daley, Proc. Phys. Soc. 1929, 41 431. eeman effect. 
Au ii McLennan and McLay, T. Roy. Soc. Canada, 1928, 22 103. Terms and 
lines. 

Sawyer and Thompson, PR, 1931, 38 2293. Ground term. 

Mack and Fromer, PR, 1935, 48 357. Pt I isoelectronic sequence. 

B: Boron 5 

B Kayser and Konen. 

B I Bowen, PR, 1927, 29 231. Terms and lines. 

Smith and Sawyer, JOSA, 1927, 14 287. Series. 

B ii Bacher and Goudsmit, 1932. Terms from unpublished material. 
B m Ibid. 

Edlen, ZP, 1931, 72 763. Ground term. 
B iv Edl6n, N, 1931, 127 405. 
Ba: Barium 56 
Ba Kayser and Konen. 
Ba i Fowler. Grotrian. 

Russell and Saunders, AJ, 1925, 61 38. 
Ba ii Fowler. Grotrian. 

Kasmussen, ZP, 1933, 83 404. New terms. 
Be: Beryllium 4 
Be Kayser and Konen. 

Be I Paschen and Kruger, AP, 1931, 8 1005. Series extended. 
Be ii Ibid. 
Be m Edlen and Ericson, ZP, 1930, 59 656. Series. 

Edlen, N, 1931, 127 405. 
Be iv Edlen and Ericson, ZP, 1930, 59 656. 

Edlen, N, 1931, 127 405. 
Bi: Bismuth 83 
Bi Kayser and Konen. 
Bi i Thorsen, ZP, 1926, 40 642. Terms and lines. 

Toshmwal, PM , 1927, 4 774. Terms and lines. 

Zeeman, Back and Goudsmit, ZP, 1930, 66 1. Interpretation of low 

terms. Zeeman effect. 

Bi ii McLennan, McLay and Crawford, PRS, 1930, 129 579. Series. 
Bi in Lang, PR, 1928, 32 737. Series. 

Bi vi Mack and Fromer, PR, 1935, 48 357. Pt I isoelectronic sequence. 
Br: Bromine 35 
Br Kayser and Konen. 

Br i Kiess, C. C. and de Bruin, BSJ, 1930, 4 667. Lines and terms. 
Br ii Deb, PRS, 1930, 127 197. Series. 
Br in Ibid. 



OF THE ELEMENTS 251 

Br: Bromine 35 (cont.) 

Br iv Deb, PRS, 1930, 127 197. Series. 

Br v Ibid. 



C: Carbon 6 
C Kayser and Konen. 

C i Hopfield, 3>R, 1930, 35 1586. lonisation potential. 

Paschen and Kruger, AP, 1930, 7 1. Terms and lines. 

Birkenbeil, ZP, 1934, 88 1. Extension in infra-red. 
C ii Fowler and Selwyn, PRS, 1928, 120 312. Terms and lines. 

Bowen, PR, 1931, 38 128. 

Edlen, ZP, 1935, 98 561. New terms. 
C in Bacher and Goudsmit, using unpublished material. 

Bowen, PR, 1931, 38 128. Extension and revision of series. 

Edl6n, ZP, 1931, 72 559. Series. 
C iv Edlen and Stenman, ZP, 1930, 66 328. Term system. 

Bacher and Goudsmit, using unpublished material. 
Ca: Calcium 20 
Ca Kayser and Konen. 
Ca I Fowler. Grotrian. 

R%ssell and Saunders, AJ, 1925, 61 38. Displaced terms. 

Back, ZP, 1925, 33 579. Zeenmn effect. 

Russell, AJ, 1927, 66 191. New terms. 
Ca ii Fowler. Grotrian. 

Saunders and Russell, AJ, 1925, 62 1. Terms and lines. 

Russell, AJ, 1927, 66 283. 
Ca in Bowen, PR, 1928, 31 497. 
Ca iv Ibid. 
Ca v Ibid. 
Cb: Columbium 41 
Cb i Meggers, J. Wash. Acad. Sci. 1924, 14 442. Zeeman effect. 

Meggers and Kiess, C. C., JO8A, 1926, 12 417. Lines and terms. 

King and Meggers, PR, 1931, 37 226. Furnace spectrum. 

Meggers and Scribner, BSJ, 1935, 14 629. New terms. 

Cb ii Meggers and Kiess, C. C., JOSA, 1926, 12 417. Multiplets and Zeeman 
effect. 

King and Meggers, PR, 1931, 37 226a. Furnace spectrum. 

Meggers and Scribner, BSJ, 1935, 14 629. New terms. 
Cb m Gibbs and White, PR, 1928, 31 520. Multiplets. 

Eliason, PR, 1933, 43 745. New multiplets. 
Cb iv Gibbs and White, PR, 1928, 31 520. Multiplets. 
Cd: Cadmium 48 
Cd Kayser and Konen. 
Cd i Fowler. Grotrian. 

Ruark, JOSA, 1925, 11 199. Higher terms added. 
Cd ii McLennan, McLay and Crawford, T. Roy. Soc. Canada, 1928, 22 45. 

Takahashi, AP, 1929, 3 27. Series. 
Cd m Gibbs and White, PR, 1928, 31 776. Multiplets. 



252 BIBLIOGRAPHY 

Ce: Cerium 58 

Ce Kayser and Konen. 

Ce i Karlson, ZP, 1933, 85 482. Terms and lines. 

Ce ii Haspas, ZP, 1935, 96 410. Terms and Zeeman effect. 

Ce in Kalia, Indian J. Phys. 1933, 8 137. Terms and lines. 

Ce iv Gibbs and White, 1929, 33 157. Doublets of stripped atoms. 

Badami, Proc. Phys. Soc. 1931, 43 53. Lines and terms. 

Lang, Can. J. Research, 1935, A 13 1. New terms. 

Lang, PR, 1936, 49 552 a. Ground term. 
Gl: Chlorine 17 
Cl Kayser and Konen. 

Cl I Kiess, C. C. and de Bruin, BSJ, 1929, 2 1117. Lines and terms. 
Clil Bowen, PR, 1928, 31 34; 1934, 45 401. New lines and terms. 

Murakawa, ZP, 1931, 69 507. Terms and lines. 

Murakawa, ZP, 1935, 96 117. New terms. 

Clni Bowen, PR, 1928, 31 34; 1934, 45 401. Lines and terms. 
Cl iv Ibid. 
Cl v Ibid. 

Cl vi Bowen and Millikan, PR, 1925, 25 591. Lines and terms. 
Cl vn Bowen and Millikan, PR, 1925, 25 295. Lines and term 
Co: Cobalt 27 
Co Kayser and Konen. 

Co i Catalan, ZP, 1928, 47 89. Terms and classified lines. 

Catalan, An. Soc. fis. y quim. (Madrid), 1929, 27 832. 
Co ii Findlay, PR, 1930, 36 5. Lines, terms and Zeeman effect. 
Co v Gilroy, PR, 1931, 38 2217. V i isoelectronic sequence. 
Cr: Chromium 24 
Cr Kayser and Konen. 

Cr i Kiess, C. C., BSJ, 1930, 5 775. Terms and lines. 

Allen and Hesthal, PR, 1935, 47 926. Intensities. 
Cr ii Kromer, ZP y 1928, 52 531. Zeeman effect. 

Kiess, C. C., BSJ, 1930, 5 775. Terms and lines. 

Gilroy, PR, 1931, 38 2217. V I isoelectronic sequence. 
Cr in White, PR, 1929, 33 914. Ti i isoelectronic sequence. 
Cr iv White, PR, 1929, 33 676. Sc I isoelectronic sequence. 
Cr v White, PR, 1929, 33 543. Ca i isoelectronic sequence. 
Cr vi Gibbs and White, PR, 1929, 33 157. Doublets of stripped atoms. 
Cs: Caesium 55 
Cs Kayser and Konen. 

Cs i Fowler. Grotrian. 
Cs ii Bacher and Goudsmit, 1932, using unpublished material. 

Laporte, Miller and Sawyer, PR, 1931, 37 845; 1932, 39 458. 

Olthoff and Sawyer, PR, 1932, 42 766. Analysis extended. 
Cu: Copper 29 
Cu Kayser and Konen. 
Cui Sommer, ZP, 1926, 39 711. Zeeman effect. 

Bacher and Goudsmit, 1932, using unpublished material. 
Cu ii Shenstone, PR, 1927, 29 380. Terms and lines. 

Bacher and Goudsmit, 1932, using unpublished material. 



OF THE ELEMENTS 253 

Eu: Europium 63 

Eu i Russell and King, PR, 1934, 46 1023. Low terms. 
Eu ii Albertson, PR, 1934, 45 499 a. Low terms. 

F: Fluorine 9 

F i Bowen, PR, 1927, 29 231. Ground state from ultra-violet lines. 

Dingle, PTtS, 1928, 117 407. Terms and lines. 

Edlen, ZP, 1935, 98 445. New terms. 
F ii Dingle, PRS, 1930, 128 600. Series. 
Fm Dingle, PRS, 1929, 122 144. Series. 
F iv Bowen, PR, 1927, 29 231. 
F vi Edlen, ZP, 1934, 89 179. 
F vn Edlen, ZP, 1934, 89 179. 
Fe: Iron 26 
Fe i Laporte, ZP, 1924, 23 135, 26 1. Classification and Zeeman effect. 

Laporte, Proc. Nat. Acad. Sci. 1926, 12 496. Series. 

Moore and Russell, AJ, 1928, 68 151. Terms. 

Burns and Walters, Alleghany Observatory Publications, 1929, 6 159. 
Fe ii Russell, AJ, 1926, 64 194. Terms and classified lines. 

Meggers and Walters, Bur. of Standards, Sci. Pap. 1927, 22 205. Low 



Dobbie, PRS, 1935, 151 703. New terms. 

Fe iv Gilroy, PR, 1931, 38 2217. V i isoelectronic sequences. 
Fe v White, PR, 1929, 33 914. Ti I isoelectronic sequences. 
Fe vi Bowen, PR, 1935, 47 924. 

Ga: Gallium 31 

Ga i Grotrian. 

Sawyer and Lang, PR, 1929, 34 718. Lines and terms. 
Ga ii Sawyer and Lang, PR, 1929, 34 712. Series. 
Ga in Lang, PR, 1927, 30 762. 
Ga iv Mack, Laporte and Lang, PR, 1928, 31 748. 
Gd: Gadolinium 64 

Gd i Albertson, PR, 1935, 47 370. Ground term. 
Ge: Germanium 32 
Ge i Gartlein, PR, 1928, 31 782. Lines and terms. 

Rao, K. R., PRS, 1929, 124 465. Lines and terms. 
Ge ii Lang, PR, 1929, 34 697. Lines and terms. 

Gartlein, PR, 1931, 37 1704a. Series. 
Ge in Lang, PR, 1929, 34 697. Series. 
Ge iv Lang, PR, 1929, 34 697. Series. 
Ge v Mack, Laporte and Lang, PR, 1928, 31 748. Lines and terms. 

H: Hydrogen 1 

H i Fowler. Grotrian. 

Bracket, AJ, 1922, 56 154. A new series. 

Pfund, JOSA, 1924, 9 139. A new series. 

Hansen, AP, 1925, 78 558. Fine structure. 

Houston, AJ, 1926, 64 81. Fine structure. 

Kent, Taylor and Pearson, PR, 1927, 30 266. Fine structure. 



254 BIBLIOGRAPHY 

H: Hydrogen 1 (cont.) 

H I Houston and Hsieh, PR, 1934, 45 263. Intervals of Balmer lines. 

Williams and Gibbs, PR, 1934, 45 491 a. Correction to R tt . 
He: Helium 2 
He I Fowler. Grotrian. 

Burger, ZP, 1929, 54 643. Intensity. 

Hopfield, AJ, 1930, 72 133. Ultra-violet series 

Kruger, PR, 1930, 36 855. New lines classified. 

Gibbs and Kruger, PR, 1931, 37 1559. Structure of 3888 A. line. 
He II Fowler. Grotrian. 

Paschen, AP, 1927, 82 689. Fine structure. 

Kruger, PR, 1930, 36 855. New lines classified. 
Hf : Hafnium 72 

Hf I Meggers and Scribner, BSJ, 1930, 4 169. Terms and lines. 
Hf ii Meggers and Scribner, JOS A, 1928, 17 83. Terms. 

Meggers and Scribner, BSJ, 1934, 13 625. Terms, intensities and 

Zeeman effect. 
Hg: Mercury 80 
Hg i Fowler. Grotrian. 

Takamine and Suga, Inst. Phys. and Chem. Tokio, 1930, 13 1. Ne^ 

series in infra-red. *' 

Hg ii Paschen, Berlin Akad. Sitz. 1928, 32 536. Terms and lines. 

McLennan, McLay and Crawford, PRS, 1931, 134 41. Terms and lines 
Hg in McLennan, McLay and Crawford, T. Roy. Soc. Canada, 1928, 22 247. 
Terms and lines. 

Mack and Fromer, PR, 1935, 48 357. Pt I isoelectronic sequence. 

I: Iodine 

1 1 Evans, PRS, 1931, 133 417. Lines and terms. 

Deb, PRS, 1933, 139 380. Lines and terms. 

I iv Krishnaniurty, Proc. Phys. Soc. 1936, 48 277. Lines and terms. 
In : Indium 49 
In I Fowler. Grotrian. 

Sawyer and Lang, PR, 1929, 34 718. New terms. 

Lansing, PR, 1929, 34 597. New terms. 

Lang, PR, 1930, 35 126a. lonisation potentials. 
In ii Bacher and Goudsmit, 1932, using unpublished data. 
In in Lang, Proc. Nat. Acad. Sci. 1927, 13 341; 1929, 15 414. 

Rao, K. R., Narayan and Rao, A. S., Indian J. Phys. 1928, 2 482. 
In iv Gibbs and White, PR, 1928, 31 776. Some multiplets. 
Ir: Iridium 77 
Ir I Meggers and Laporte, PR, 1926, 28 642. Low levels. 

Albertson, PR, 1932, 42 443 a. Low terms. 

K: Potassium 19 

Ki Fowler. Grotrian. 

Ferschmin and Frisch, ZP, 1929, 53 326. Doublet structure of D terms, 
Edlen, ZP, 1935, 98 445. Doublets resolved. 



OF THE ELEMENTS 255 

K: Potassium 19 (cont.) 

K II Bowen, PR, 1928, 31 497. Terms and lines. 

Whitford, PR, 1932, 39 898. Zeeman effect. 
K m de Bpuin, ZP, 1929, 53 658. 

Ram, Indian J. Phys. 1933, 8 151. 
K iv Bowen, P, 1928, 31 497. One multiplet. 

Ram, Indian J. Phys. 1933, 8 151. 
Kr: Krypton 36 
Kr i Gremmer, ZP, 1929, 54 215. Lines and terms. 

Meggers, de Bruin and Humphreys, BSJ, 1929, 3 129; 1931, 7 643. 
Lines and terms. 

Pogany, ZP, 1933, 86 729. Zeeman effect. 
Kr ii Bakker and de Bruin, ZP, 1931, 69 36. Zeeman effect. New terms. 

de Bruin, Humphreys and Meggers, BSJ, 1933, 11 409. 
Kr m Deb and Dutt, ZP, 1931, 67 138. Series. 

Humphreys, PR, 1935, 47 712. Lines and terms. 

La: Lanthanum 57 

La i Meggers, BSJ, 1932, 9 239. Lines and Zeeman effect. 

Russell and Meggers, BSJ, 1932, 9 625. Lines and terms. 
La ii Resell and Meggers, BSJ, 1932, 9 625. Lines and terms. 
La in Russell and Meggers, BSJ, 1932, 9 625. Lines and terms. 
Li: Lithium 3 
Li i Fowler. Grotrian. 
Li ii Werner, N, 1925, 116 574; 1926, 118 154. Series. 

Schiiler, ZP, 1926, 37 568; 1927, 42 487. Fine structure. 

Ericson and Edlen, ZP, 1930, 59 656. Ground term. 
Li m Edlen and Ericson, ZP, 1930, 59 656. Two lines. 

Gale and Hoag, PR, 1931, 37 1703a. New lines. 
Lu: Lutecium 71 

Lu i Meggers and Scribner, BSJ, 1930, 5 73. Lines and terms. 
Lu ii Ibid. 
Lu in Ibid. 

Mg: Magnesium 12 

Mg i Fowler. Grotrian. 

Bowen and Miliikan, PR, 1925, 26 150. PP' multiplets. 
Mg ii Fowler. Grotrian. 
Mg m Mack and Sawyer, Science, 1928, 68 306, 1761. Series. 

Edlen and Ericson, Comptes Rendus, 1930, 190 116. Doublet. 
Mgiv Edlen and Ericson, Comptes Rendus, 1930, 190 173. Extreme ultra- 
violet. 

Mack and Sawyer, PR, 1930, 35 299. Screening doublets. 
Mg v Ibid. 
Mn: Manganese 25 

Mn i McLennan and McLay, T. Roy. Soc. Canada, 1926, 20 89. Lines and 
terms. 

Russell, AJ, 1927, 66 184, 347. Configurations assigned. 

Seward, PR, 1931, 37 344. Intensities. 



256 BIBLIOGRAPHY 

Mn: Manganese 25 (cont.) 
Mn ii KusseU, AJ, 1927, 66 233. 

Duffendack and Black, PR, 1929, 34 42. Lines and terms. 

Seward, PR, 1931, 37 344. Intensities. 
Mnm Gibbs and White, Proc. Nat. Acad. Sci. 1927, 13 525. Multiplets. 

Gilroy, PR, 1931, 38 2217. Lines and terms. f 
Mn iv White, PR, 1930, 33 914. Ti i isoelectronic sequence. 
Mn v White, PR, 1929, 33 678. Sc I isoelectronic sequence. 

Bowen, PR, 1935, 47 924. New terms. 
Mn vn Gibbs and White, Proc. Nat. Acad. Sci. 1926, 12 676. 
Mo: Molybdenum 42 
Mo i Catalan, An. Soc. fis. y quim. (Madrid), 1923, 21 213. Lines and terms. 

Wilhelmy, AP, 1926, 80 305. Zeeman effect. 

Meggers and Kiess, JOS A, 1926, 12 417. Lines and terms. 
Mo ii Meggers and Kiess, JOS A, 1926, 12 417. Lines and terms. 

Wilhelmy, AP, 1926, 80 305. Zeeman effect. 
Mo iv Eliason, PR, 1933, 43 745. Multiplets. 
Mo v Trawick, PR, 1935, 48 223. Sr i isoelectronic sequence. 

N: Nitrogen 7 

N i Ingram, PR, 1929, 34 421. Terms and lines. 

Hopfield, PR, 1930, 36 789. Adds some higher terms. 

Ekefors, ZP, 1930, 63 437. Lines and terms. 

Stucklen and Carr, PR, 1933, 43 944. One term. 
N n Fowler, A. and Freeman, PRS, 1927, 114 662. Lines and terms. 

Bowen, PR, 1927, 29 231. Lines and terms. 

Freeman, PRS, 1929, 124 654. New terms. 

Bowen, PR, 1929, 34 534. Series. 

N m Freeman, PRS, 1928, 121 318. Lines and terms. 
N iv Freeman, PRS, 1930, 127 330. Lines and terms. 

Edlen, N, 1931, 127 744. Singlets. 

Bacher and Goudsmit, using unpublished material. 
N v Edlen and Ericson, ZP, 1930, 64 64. Series. 
Na: Sodium 11 
Na i Fowler. Grotrian. 

Ferschmin and Frisch,ZP, 1929, 53 326. Doublets structure of D terms. 
Na ii Bowen, PR, 1928, 31 967. Lines and terms. 

Frisch, ZP, 1931, 70 498. Lines and terms. 

Vance, PR, 1932, 41 480. Lines and terms. 

Na m Edlen and Ericson, Comptes Rendus, 1930, 190 173. Extreme ultra- 
violet. 

Mack and Sawyer, PR, 1930, 35 299. New lines and levels. 

Vance, PR, 1932, 41 480. Lines and terms. 

Soderqvist, ZP, 1932, 76 316. Lines and terms. 
Na iv Vance, PR, 1932, 41 480. 
Ne: Neon 10 
Ne i Paschen, AP, 1918, 60 405. 

Paschen and Gotze. 



OF THE ELEMENTS 257 

Ne: Neon 10 (cont.) 

Ne i Back, AP, 1925, 76 317. Zeeman effect. 

Lyman and Saunders, Proc. Nat. Acad. Sci. 1926, 12 92. Low levels. 

Gremier, ZP, 1928, 50 716. New levels from infra-red lines. 

Murakawa and Iwama, Inst. Phys. and Ghem. Tokio, 1930, 13 283. 

Zeeman effect. 

Ne ii Russell, Compton and Boyce, Proc. Nat. Acad. Sci. 1928, 14 280. Lines 
and terms. 

Frisch, ZP, 1930, 64 499. Two new terms. 

de Bruin and Bakker, ZP, 1931, 69 19. Zeeman effect. 
Ne in Boyce and Compton, Proc. Nat. Acad. Sci. 1929, 15 656. Series. 

de Bruin, ZP, 1932, 77 489. New lines and terms. 

Keussler, ZP, 1933, 85 1. Ground term. 

Ne iv Boyce and Compton, Proc. Nat. Acad. Sci. 1929, 15 656. Series. 
Ni: Nickel 28 
Ni i Russell, PR, 1929, 34 821. Lines and terms. 

Ornstein and Buoma, PR, 1930, 36 679. Intensities. 

Marvin and Baragar, PR, 1933, 43 973. Zeeman effect. 
Ni n Shenstone, PR, 1927, 30 255. Lines, terms and Zeeman effect. 
^ Menzies, PRS, 1929, 122 134. Ground term. 

Orifctein and Buoma, PR, 1930, 36 679. Intensities. 
Ni vi Gilroy, PR, 1931, 38 2217. V i isoelectronic sequence. 

O: Oxygen 8 

O i Hopfield, PR, 1931, 37 160. Lines and terms. 

de Bruin, N, 1932, 129 469. 

O n Russell, PR, 1928, 31 27. Terms and lines. 
O in Fowler, A., PRS, 1928, 117 317. Lines and terms. 

Freeman, PRS, 1929, 124 654. Series. 
O iv Bowen, PR, 1927, 29 231. 

Freeman, PRS, 1930, 127 330. 
O v Edlen, N, 1931, 127 744. Singlets. 

Bacher and Goudsmit, 1932, using unpublished material. 
O vi Edlen and Ericson, ZP, 1930, 64 64. Li-like spectra. 
Os: Osmium 76 
Os i Meggers and Laporte, PR, 1926, 28 642. Six low levels. 

P: Phosphorus 15 

P i Kiess, C. C., BSJ, 1932, 8 393. Lines and terms. 

Robinson, PR, 1936, 49 297. New terms. 
P n Bowen, PR, 1927, 29 510. Lines and terms. 

Robinson, PR, 1936, 49 297. New terms. 
P in Millikan and Bowen, PR, 1925, 25 600. Lines and terms. 

Saltmarsh, PRS, 1925, 108 332. Higher terms. 

Bowen, PR, 1928, 31 34. New lines. 

Bowen, PR, 1932, 39 8. New terms. 
P iv Bowen and Millikan, PR, 1925, 25 591. Terms and lines. 

Bowen, PR, 1932, 39 8. New terms. 
P v Millikan and Bowen, PR, 1925, 25 295. Lines and terms. 

CASH 17 



258 BIBLIOGRAPHY 

Pb: Lead 82 

Pb I Gieseler and Grotrian, ZP, 1925, 34 374; 1926, 39 377. Series. 

Back, ZP, 1926, 37 193. Zeeman effect. 

Bacher and Goudsmit, 1932, using unpublished material 
Pb n Gieseler, ZP, 1927, 42 265. Lines and terms. 
Pb in Smith, PR, 1929, 34 393; 1930, 36 1. Terms and lines. 

Green and Loring, PR, 1932, 41 389. Zeeman effect. 
Pb IV Smith, PR, 1930, 36 1. Lines and terms. 
Pb v Mack, PR, 1929, 34 17. Lines and terms. 

Mack and Fromer, PR, 1935, 48 357. Pt I isoelectronic sequence. 
Pd: Palladium 46 

Pd I Shenstone, PR, 1930, 36 669. Lines, terms and Zeeman effect. 
Pd ii Shenstone, PR, 1928, 32 30. Lines and terms. 

Blair, PR, 1930, 36 173. New terms. 
Pt: Platinum 78 

Pti Haussmann, AJ, 1927, 66 333; PR, 1928, 31 152. Zeeman effect and 
terms. 

Livingood, PR, 1929, 34 185. Lines and terms. 

Ra: Radium 88 

Ra I Rasmussen, ZP, 1934, 87 607. 

Ra n Fowler. 

Rasmussen, ZP, 1933, 86 24. 
Rb: Rubidium 37 
Rb i Fowler. Grotrian. 

Ramb, AP, 1931, 10 311. Doublets resolved. 
Rb ii Laporte, Miller and Sawyer, PR, 1931, 38 843. Series. 
Re: Rhenium 75 

Re I Meggers, BSJ, 1931, 6 1027. Lines and terms. 
Rh: Rhodium 45 

Rh I Sommer, ZP, 1927, 45 147. Lines, terms and Zeeman effect. 
Rh II Bacher and Goudsmit, 1932, using unpublished material. 
Rn: Radon 86 

Rn I Rasmussen, ZP, 1933, 80 726. Lines and terms. 
Ru: Ruthenium 44 

Ru i Sommer, ZP, 1926, 37 1. Lines, terms and Zeeman effect. 
Ru n Meggers and Shenstone, PR, 1930, 35 868. 

Bacher and Goudsmit, 1932, using unpublished material. 

S: Sulphur 16 

S i Frerichs, ZP, 1933, 80 150. Lines and terms. 

Meissner, Bartelt and Eckstein, ZP, 1933, 86 54. Additional terms. 

Ruedy, PR, 1933, 44 757. New terms. 
S n Ingram, PR, 1928, 32 172. Lines and terms. 

Gilles, Ann. de Phys. 1931, 15 267. Terms. 

Bartelt and Eckstein, ZP, 1933 86 77. New terms. 
S in Ingram, PR, 1929, 33 907. Lines and terms. 
S iv * Millikan and Bowen, PR, 1925, 25 602. Lines and terms. 



OF THE ELEMENTS 259 

S: Sulphur 16 (cont.) 
S iv Bowen, PR, 1928, 31 38. New terms. 

S v Millikan and Bowen, PR, 1925, 25 591, 26 150. Lines and terms. 
S vi Millilsan and Bowen, PR, 1925, 25 295. Doublet Laws. 
Sb: Antimony 51 

Sb i McLennan and McLay, T. Roy. Soc. Canada, 1927, 21 63. Lines and 
terms. 

Lowenthal, ZP, 1929, 57 822. Zeeman effect and new terms. 
Sb n Lang and Vestine, PR, 1932, 42 233. Terms. 
Sb m Lang, PR, 1930, 35 445. Terms and lines. 

Sb iv Green and Lang, Proc. Nat. Acad. Sci. 1928, 14 706. Lines and 
terms. 

Badami, Proc. Phys. Soc. 1931, 43 538. Series. 
Sb v Lang, Proc. Nat. Acad. Sci. 1927, 13 341. Series. 

Badami, Proc. Phys. Soc. 1931, 43 538. Series. 
Sc: Scandium 21 
Sc i Russell and Meggers, Bur. Stand., Sci. Papers, 1927, 22 329. Lines and 

terms. 

Sc n Russell and Meggers, Bur. Stand., Sci. Papers, 1927, 22 329. Lines and 
^ terms. 

Russell and Meggers, BSJ, 1929, 2 733. Comparison with Y. 
Sc in Russell and Lang, A J , 1927, 66 13. Lines and terms. 

Smith, Proc. Nat. Acad. Sci. 1927, 13 65. Extension of series. 
Sc iv Majumdar and Toshniwal, N, 1928, 121 828. Screening doublets. 
Se: Selenium 34 
Se i McLennan, McLay and McLeod, PM , 1927, 4 486. Lines and terms. 

Gibbs and Ruedy, PR, 1932, 40 204. New terms. 
Se ii Badami and Rao, K. R., PRS, 1933, 140 387. Lines and terms. 

Martin, PR, 1935, 48 938. Lines and terms. 

Se iv Pattabhiramayya and Rao, A. S., Indian J. Phys. 1929, 3 531. Series. 
Se v Sawyer and Humphreys, PR, 1928, 32 583. Series. 
Se vi Sawyer and Humphreys, PR, 1928, 32 583. Series. 
Si: Silicon 14 
Si i Fowler, A., PRS, 1929, 123 422. Lines and terms. 

Kiess, C. C., BSJ, 1933, 11 775. New terms. 
Si n Fowler, A., Phil. Trans. R.S. 1925, 225 1. Series. 

Bowen and Millikan, PR, 1925, 26 150. PP multiplets. 

Bowen, PR, 1928, 31 34. Series. 
Si m Fowler, A., Phil. Trans. R.S. 1925, 225 1. Series. 

Sawyer and Paschen, AP, 1927, 84 1. Comparison with Al n. 
Si iv Fowler, A., Phil. Trans. R.S. 1925, 225 1. Series. 
Si v Edlen and Ericson, Comptes Rendus, 1930, 190 116. Doublets. 
Sm: Samarium 62 

Sm i Albertson, PR, 1935, 47 370. Ground term. 
Sn: Tin 50 
Sn i Back, ZP, 1927, 43 309. Lines, terms and Zeeman effect. 

Green and Loring, PR, 1927, 30 575. Terms, lines and Zeeman effect. 

Bacher and Goudsmit, 1932, using unpublished material. 

17-2 



260 BIBLIOGRAPHY 

Sn: Tin 50 (cont.) 
Sn ii Grotrian. 

Green and Loring, PR, 1927, 30 574. Lines, terms and Zeeman effect. 

Narayan and Rao, K.R., ZP, 1927, 45 350. Terms. 

Lang, PR, 1930, 35 445. Lines and terms. 
Sn in Gibbs and Vieweg, PR, 1929, 34 400. Cd i isoelectronic sequence. 

Green and Loring, PR, 1931, 38 1289. Multiplets and Zeeman effect. 
Sn iv Rao, K. R., Narayan and Rao, A. S., Indian J. Phys. 1928, 2 476. 

Series. 

Sn v Gibbs and White, Proc. Nat. Acad. Sci. 1928, 14 345. Series. 
Sr: Strontium 38 
Sri Fowler. Grotrian. 

Russell and Saunders, AJ, 1925, 61 39. Lines and terms. 
Sm Fowler. Grotrian. 

Ta: Tantalum 73 

Ta i McLennan and Durnford, PRS, 1928, 120 502. Zeeman effect. 

Kiess, C. C. and Kiess, H. K., BSJ, 1933, 11 277. Lines and terms. 
Te: Tellurium 52 

Te i Bartelt, ZP, 1934, 88 522. Lines and terms. 
Te m Krishnamurty, PRS, 1935, 151 178. Lines and terms. 
Te iv Rao, K. R., PR8, 1931, 133 220. Lines and terms. 
Te v Gibbs and Vieweg, PR, 1929, 34 400. Cd i isoelectronic sequence. 
Te vi Lang, Proc. Nat. Acad. Sci. 1927, 13 341. Lines and terms. 

Rao, K. R., PRS, 1931, 133 220. Lines and terms. 
Ti: Titanium 22 
Ti i Russell, A J, 1927, 66 347. Lines and terms. 

Harrison, JOSA, 1928, 17 389. Intensities. 

White, PR, 1929, 33 914. Ti i isoelectronic sequence. 
Ti n Russell, AJ, 1927, 66 283. Lines and terms. 
Ti m Russell and Lang, AJ, 1927, 66 13. Terms. 
Ti iv Russell and Lang, AJ, 1927, 66 13. Terms. 
TI: Thallium 81 
TI i Fowler. Grotrian. 
TI n McLennan, McLay and Crawford, PRS, 1929, 125 570. Lines and terms. 

Smith, PR, 1930, 35 235. Extension of series. 

Ellis and Sawyer, PR, 1936, 49 145. New lines and terms. 
TI m McLennan, McLay and Crawford, PRS, 1929, 125 50. Lines and terms. 
TI iv Rao, K. R., Proc. Phys. Soc. 1929, 41 361. Terms. 

Mack and Fromer, PR, 1935, 48 357. Pt i isoelectronic sequence. 

V: Vanadium 23 

V i Bacher and Goudsmit, 1932, using unpublished material. 

Gilroy, PR, 1931, 38 2217. New lines and terms. 
V n Meggers, ZP, 1925, 33 509; 39 114. Lines, terms and Zeeman effect. 

Russell, AJ, 1927, 66 184, 194. Terms named. 

White, PR, 1929, 33 914. New terms and lines. 
V iii White, PR, 1929, 33 672. Sc i isoelectronic sequence. 



OF THE ELEMENTS 261 

V: Vanadium 23 (cont.) 

V IV White, PR, 1929, 33 542. Ca I isoelectronic sequence. 

V v Gibbs and White, PR, 1929, 33 157. Doublets of stripped atoms. 

W: Tungsten 74 

W i Beining, ZP, 1927, 42 146. Zeeman effect. 

Bacher aftd Goudsmit, 1932, using unpublished material. 

Laun, PR, 1935, 48 572 a. New terms. 
W ii Beining, ZP, 1927, 42 146. Zeeman effect. 

Xe: Xenon 54 

Xe i Rasmussen, ZP, 1932, 72 779. 

Humphreys and Meggers, BSJ, 1933, 10 139. Lines and terms. 

Pogany, ZP, 1935, 93 364. Zeeman effect. 

Xe ii Humphreys, de Bruin and Meggers, BSJ, 1931, 6 287. Lines and terms. 
Xe in Deb and Dutt, ZP, 1931, 67 138. 

Y: Yttrium 39 

Y i Meggers and Russell, BSJ, 1929, 2 733. Lines and terms. 

Y n Meggers and Russell, BSJ, 1929, 2 733. Lines and terms. 

^ ni Meggers and Russell, BSJ, 1929, 2 733. Lines and terms. 



Zn: Zinc 30 
Zn i Fowler. Grotrian. 

Sawyer, JOSA, 1926, 13 431. PP multiplets. 
Zn ii Lang, Proc. Nat. Acad. Sci. 1929, 15 414. Lines and terms. 

Takahashi, AP, 1929, 3 27. Lines and terms. 
Zn in Laporte and Lang, PR, 1927, 30 378. Series. 
Zr: Zirconium 40 
Zn Kiess, C. C. and Kiess, H. K., BSJ, 1931, 6 621. Lines, terms and 

Zeeman effect. 
Zr ii Kiess, C. C. and Kiess, H. K., BSJ, 1930, 5 1205. Lines, terms and 

Zeeman effect. 

Zr m Kiess, C. C. and Lang, BSJ, 1930, 5 305. Lines and terms. 
Zr iv Kiess, C. C. and Lang, BSJ, 1930, 5 305. Lines and terms. 

C. The hyper fine structure of the elements 

Ag Tolansky, PPS, 1933, 45 559. No hyperfine structure in Ag I. 

Williams and Middleton, N 9 1933, 131 691. No hyperfine structure found. 

Jackson, N, 1933, 131 691. No hyperfine structure found. 

Hill, PR, 1934, 46 536. No hyperfine structure found. 
Al Gibbs and Kruger, PR, 1931, 37 656a. No hyperfine structure in 4 lines. 

White, PR, 1931, 37 1175a. Interpretation of Gibbs and Kruger. 

Tolansky, ZP, 1932, 74 336. Narrow lines suggests g (I) small. 

Williams and Sabine, PR, 1933, 43 362 a. No hyperfine structure in Al m. 

Paschen and Ritschl, AP, 1933, 18 867. Hyperfine structure of Al n 
shows / = J. 

Brown and Cook, PR, 1934, 45 731a. Work of Paschen shows ^=2-4. 



262 BIBLIOGRAPHY 

As Tolansky, PBS, 1932, 137 541 ; ZP, 1933, 87 210. / = 1J in As n. 
Rao, A. S., ZP, 1933, 84 236. / is 1 J in As n. 
Crawford and Crooker, N, 1933, 131 655. As iv confirms. 
Tolansky and Heard, PUS, 1934, 146 818. Intensities of As n con- 

firm. 
Ba Ritschl and Sawyer, ZP, 1931, 72 36. Resonance lines of Ba n. 

Kruger, Gibbs and Williams, PR, 1932, 41 322. /=2'in 135 and 137. 
Be Kruger and Wagner, PE, 1932, 41 373 a. Three lines of Be i and two lines 

of Be n appear sharp. 

Parker, PE, 1933, 43 1035a. / is probably . 
Bi Goudsmit and Back, ZP, 1927, 43 321 ; 1928, 47 174. Hyperfine structure 

in magnetic field shows / = 4J. 

McLennan, McLay and Crawford, PRS, 1930, 129 579. Bi n and Bi m. 
Zeeman, Back and Goudsmit, ZP, 1931, 66 1. Magnetic analysis of Bi I. 
Fisher and Goudsmit, PE, 1931, 37 1057. Analysis of partially resolved 

patterns. 

Br de Bruin, N, 1930, 125 414. Hyperfine structure shows /= 1. 
Tolansky, PRS, 1932, 136 585. Confirms de Bruin. 
Brown, PR, 1932, 39 777. Band spectrum shows /= 1| or 2 in Br 79 and 

Br. 

Cb Ballard, PR, 1934, 46 806. / = 4|; ^ = 3-7. r 

Gd Schiller and Bruck, ZP, 1929, 56 291. Hyperfine structure shows 7 = 

hi even and / = in odd isotopes. 

Schiiler and Keyston, ZP, 1931, 71 413. Abnormal intensities. 
Jones, Proc. Phys. Soc., 1933, 45 625. In Cd n p, is -0-625. 
Schiiler and Westmeyer, ZP, 1933, 82 685. Isotope displacement in 
Cdn. 
Cl Elliott, PRS, 1930, 127 638. Band spectrum shows / = 2. 

Tolansky, ZP, 1931, 73 470; 1932, 74 336. Hyperfine structure shows 

ju, is small; isotope displacement. 
Go Grace, PR, 1933, 43 762a. / is probably 3J. 

More, PR, 1934, 46 470. /=% ^ is between 2 and 3. 
Kopfermann and Rasmussen, ZP, 1935, 94 58. / = 3| confirmed. 
Gs Jackson, PRS, 1934, 143 455. Hyperfine intensity ratio shows / = 3J. 
Granath and Stranathan, PR, 1934, 46 317. ^ is 2-45. 
Kopfermann, ZP, 1932, 73 437. / = 3J in Cs n. 
Cohen, PR, 1934, 46 713. Atomic ray shows / = 3. 
Heydenburg, PE, 1934, 46 802. Polarisation of resonance radiation 

shows n between 2-40 and 2-52. 

Jackson, ZP, 1935, 93 809. Intensity ratios in 4555 A line. 
Granath and Stranathan, PE, 1935, 48 725. Hyperfine structure shows 

p between 2-4 and 3-0. 

Gu Ritschl, ZP, 1932,79 1. /is 1 in both isotopes. Cu i. Isotope displace- 
ment. 
Schiiler and Schmidt, ZP, 1936, 100 113. ^ = 2-5 in 63 and /z=2-6 in 65 

Electric quadripole moment. 

Eu Schiller and Schmidt, ZP, 1935, 94 457. / = 2J in 151 and 153; both 
pa are positive; /i 151 : fc 153 = 2-2. Abnormal intervals. 



OF HYPEEFINE STRUCTURE 263 

F Gale and Monk, PR, 1929, 33 114. Band spectrum shows / = . 

Campbell, ZP, 1933, 84 393. In F I, / = J. 

Brown and Bartlett, PR, 1934, 45 527. /* is about 3/^ v . 
Ga Jacksgn, IP, 1932, 74 291. Resonance lines of Ga i. 

Campbell, A; 1933, 131 204. /= 1| in 69 and 71 from Ga n. 
H 1 Kapuscinski and Eymers, PRS, 1929, 122 58. Band spectrum shows 
/ = *. * 

Rabi, Kellogg and Zacharias, PR, 1934, 46 157. /* for proton is 3-25. 
H 2 Urey, Brickwedde and Murphy, PR, 1932, 40 1. Mass effect in Balmer 
lines. 

Murphy and Johnston, PR, 1934, 46 95. Band spectrum shows /= 1. 

Estermann and Stern, N, 1934, 133 911. p is 0-7^. 

Rabi, Kellogg and Zacharias, PR, 1934, 46 163. /* for deuton is 

0-75 + 0-2. 
Hg Schiiler and Keyston, ZP, 1931, 72 423. Hg I. Isotope displacement. 

Schiiler and Jones, ZP, 1932, 74 631. Hg n. Isotope displacement. 

Schiiler and Jones, ZP, 1932, 77 801. Irregularities. 

Mrozowski, Acad. Pol. Sci. et Lettres, 1931, 9 464. 2537A. line. 

Inglis, ZP, 1933, 84 466. Magnetic wandering of 2537 A. line. 

Schiiler and Schmidt, ZP, 1935, 98 239. Asymmetry of electric field of 

J^SOl. 

Venkatesachar and Sibaiya, Indian Acad. of Sci. Proc. 1934, 1 8. 

Hypcrfine structure of Hg IT. 
I Loomis, PR, 1927, 29 112. Band spectrum shows / is large. 

Tolansky, PRS, 1935, 149 269. Hyperfine structure of I n shows 

/ = 2J. 

Tolansky, PRS, 1935, 152 663. 1 1 confirms. A perturbed term. 
Strait and Jenkins, PR, 1936, 49 635 a. Alternating intensities confirm 

J = 2*. 
In Jackson, ZP, 1933, 80 59, Hyperfine intensity ratio shows 7 = 4. 

Paschen, Sitz. d. Preusz. Akad. d. Wiss. Phys.-Math. 1934, 456. De- 

partures from interval rule in In n. 
Ir Schiiler and Schmidt, ZP, 1935, 94 460. / is probably in 191 and 

193. 

K Loomis and Wood, PR, 1931, 38 854. Band spectrum shows /> . 
Schiiler, ZP, 1932, 76 14. Isotope displacement. 
Fermi and Segre, ZP, 1933, 82 749. Hyperfine structure cannot be re- 

solved. 

Frisch, P.Z. Sowjetunion, 1933, 4 557. 30 lines of K n are single. 
Jackson and Kuhn, PRS, 1934, 148 335. Hyperfine structure of re- 

sonance lines shows / ^ 2 . 
Millman, Fox and Rabi, PR, 1934, 46 320. Splitting of atomic rays gives 



Millman, PR, 1935, 47 739. /> 4 in K 41 . 

Fox and Rabi, PR, 1935, 48 746. Atomic ray shows ^ = 0-379 in K 39 



Kr Kopfermann and Wieth-Knudsen, ZP, 1933, 85 353. Work on Kr i 
shows in Kr 83 /is ^ 3 J and /* probably negative. 



264 BIBLIOGRAPHY 

La Anderson, PR, 1934, 45 685; 46 473. Hyperfine structure shows 7 = 3 

and /x = 2-5. 
Crawford, PR, 1935, 47 768. Hyperfine structure of La I confirms 

Anderson. , 

Li Schiiler, AP, 1925, 76 292; ZP, 1927, 42 487. Hyperfine structure of 

Li ii. 
Harvey and Jenkins, PR, 1930, 35 789. Band spectAim shows 7=1J 

in Li 7 . 

Hughes and Eckart, PR, 1930, 36 694. Mass effect. 
van Wijk and van Koeveringe, PRS, 1931, 132 98. Band spectrum shows 

7=4 in Li 7 . 

Giittinger and Pauli, ZP, 1931, 67 743. Perturbations in Li n. 
Goudsmit and Inglis, PR, 1931, 37 328 a. Hyperfine structure of Li 11. 
Granath, PR, 1932, 42 44. From 5485 A. of Li n, 7= 1 and /A = 3-29/^. 
Gray, PR, 1933, 44 570. 7= 1J confirmed. 
Ladenburg and Levy, ZP, 1934, 88 449. Alternating intensities suggest 

7 = 2JinLi. 
Fox and Rabi, PR, 1935, 48 746. Atomic ray shows /> 1 in Li 6 and 

^ = 3-20^1 Li. 
Fock and Petrashen, P.Z. Sowjetunion, 1935, 8 547. Theory suggest * 

^ = 4-57. r 

Bartlett and Gibbons, PR, 1936, 49 552 a. Comment on Fock and 

Petrashen. 

Schtiler and Schmidt, ZP, 1936, 99 285. If 7 = 1 in Li 6 , then ^ = 0-6. 
Lu Schiiler and Schmidt, ZP, 1935, 95 265. 7 = 3J, deviations from interval 

rule. 
Mg Murakawa, ZP, 1931, 72 793. Absence of hyperfine structure in Mgi 

suggests 7 = 0. 
Jackson and Kuhn, PRS, 1936, 154 679. Isotope displacement in 

resonance line. 

Mn White, PR, 1929, 34 1404. Hyperfine structure shows 7 - 2J. 
White and Ritschl, 1930, 35 1146. Vector coupling in Mn I. " 
N Ornstein and van Wijk, ZP, 1928, 49 315. Band spectrum shows 

7 = 1. 
Bacher, PR, 1933, 43 1001. Magnetic moment of nucleus ^0-2^ since 

lines very fine. 

Na Frisch, P.Z. Sowjetunion, 1933, 4 559. Lines of Na n show 7= 1-J. 
Rabi and Cohen, PR, 1933, 43 582. Atomic rays show 7= 1J. 
van Atta and Granath, PR, 1933, 44 61 a. /x = 2-6/z A . 
Joffe, PR, 1934, 45 468. Band spectrum shows 7= 1J. 
Rabi and Cohen, PR, 1934, 46 707. Atomic ray shows 7= 1 \. 
Larrick, PR, 1934, 46 581. Polarisation of resonance radiation explained 

by 7 = 14. 
Fox and Rabi, PR, 1935, 48 746. Method of "zero moments" shows 



Ne Nagaoka and Mishima, P. Imp. Acad. Tokio, 1929, 5 200; 1930, 6 143. 

Mass effect and magnetic splitting. 
Bartlett and Gibbons, PR, 1933, 44 538. Isotope displacement theory. 



OF HYPERFINE STRUCTURE 265 

P Herzberg, PR, 1932, 40 313. Band spectrum. 

Ashley, PR, 1933, 44 919. Band spectrum shows /=. 

Jenkins, PR, 1935, 47 783 a. Alternating intensities confirm Ashley. 
Pb Muraka.wa, ZP, 1931, 72 793. 7 = for 206 and 208, but for 207. 

Kopfermann, ZP, 1932, 75 363. Isotope displacements. 

Schiller and Jones, ZP, 1932, 75 563. Hyperfine structure shows new 
isotope. * 

Rose and Granath, PR, 1932, 40 760. Isotope displacements. 

Dickinson, PR, 1934, 46 498. Isotope displacements. 

Rose, PR, 1935, 47 122. Isotope displacements reviewed. 
Pr White, PR, 1929, 34 1397. In Pr n, / = 2J. 
Pt Puchs and Kopfermann, Nw, 1935 ,23 372. 

Jaeckel and Kopfermann, ZP, 1936, 99 492. / = in Pt 195 ; isotope 
displacements. 

Jaeckel, ZP, 1936, 100 513. Confirms / = J. 

Kopfermann and Krebs, ZP, 1936, 101 193. Isotope proportions present. 
Rb Kopfermann, ZP, 1933, 83 417. Rb n shows /= 1J in 87 and 2J in 85. 
/i 87 is twice ^ 85 . No isotope displacement. 

Jackson, ZP, 1933, 86 131. Confirms Kopfermann. 

Zeeman, Gisolf and de Bruin, N, 1931, 128 637. Zeeman effect of 
hyperfine structure shows / = 2J. 

Meggers, King and Bacher, PR, 1931, 38 1258. Hyperfine structure 
shows / = 2J in both isotopes. 

Sommer and Karlson, Nw, 1931, 19 1021. Confirms Meggers. 
Sb Tolansky, PRS, 1934, 146 182. J = 2J in 121 and 123; 



Crawford and Bateson, Can. J. Research, 1934, 10 693. Sb in shows 

/ = 2| in 121 and 3J in 123; /J t m = 4-0, ju 123 = 3-2. 

Sc Kopfermann and Rasmussen, ZP, 1934, 92 82. 7 = 3 and /x = 3-6. 
Se Rafalowski, Acta Phys. Polonica,, 1933, 2 119. Lines are single. 
Olsson, ZP, 1934, 90 134. Band spectrum shows 7=0 in Se 80 . 
Sm Schiiler and Schmidt, ZP, 1934, 92 148. Isotope displacements. 
Sn Tolansky, PRS, 1934, 144 574. Sn n shows / = in 117 and 119; 
fji is 0-89/Lt v in both. One line of Sn I confirms /. Isotope displace- 
ment. 
Sr Benson and Sawyer, PR, 1933, 43 7 66 a. No hyperfine structure wider 

than 0-05 cm.- 1 

Ta Gisolf and Zeeman, N, 1933, 132 566. Hyperfine structure shows / = 3J. 
McMillan and Grace, PR, 1933, 44 949. Hyperfine structure shows 

/ = 3J. 

Te Rafalowski, Acta Phys. Polonica, 1933, 2 119. Lines are single. 
Tl Sehiiler and Keyston, ZP, 1931, 70 1. Isotope displacement. Tl i, 

Tin. 

Crooker, PM, 1933, 16 994. Paschen-Back effect. 
Wills, PR, 1934, 45 883. ^ = 2-7. A perturbed term. 
V Kopfermann and Rasmussen, ZP, 1935, 98 624. Hyperfine structure 

shows / = 3J. 
W Grace and White, PR, 1933, 43 1039a. No value of /. Lines complex. 



266 BIBLIOGRAPHY 

Xe Kopfermann and Rindal, ZP, 1933, 87 460. /= in 129 and 1 in 131. 

/Lt 129 is negative, ju 131 is positive. ^129/^131 is !!. No isotope displacement. 
Gwynne-Jones, PR8, 1934, 144 587. Xe i confirms. 

Y Kruger and Challacombe, PR, 1935, 48 Ilia. Earlier report incorrect. 
Zn Schtiler and Brack, ZP, 1929, 56291. No hyperfine structure found. Zit I. 
Murakawa, ZP, 1931, 72 793. Absence of hyperfine structure in Zn i 

suggests 7 = 0. * 

Schtiler and Westmeyer, ZP, 1933, 81 565. Zn n shows isotope displace- 
ment. In Zn 67, 1=1%. 

Billeter, Helv. Phys. Acta, 1934, 7 413. No hyperfine structure found in 
resonance line. 



SUBJECT INDEX 



Numbers in Clarendon refer to the second volume. 



Absorption spectra, 68 

rare earths, 81 

X-rays, 193 

Alkaline earths, arc and spark spectra, 
46 

inter-system lines, 57 

interval rule, 63 

isoelectronic spectra, 212 

jj coupling, 142 

singlets and triplets, 47 
Alkalis, doublet series, 23, 31-2 

doublet intensities, 107 

forbidden lines, 215 

isoelectronic spectra, 212 
ernating intensities, 200-2 
lumim'um. 224 

absorption spectrum, 68 

displaced terms, 7 

displacement law, Al in, 177 

Land6's doublet formula, 215 

perturbed series, 151 
Analysis, hyperfine, 189 

multiplet, 48 

series, 18 

Zeeman, 99 
Angstrom unit, 5 
Anomalous Zeeman effect, 85, 144 
Antimony, 28-32 

fluorescence, 80 
Arc spectra, 46 
Argon, 39-44 

ionized, 38, 145 

level diagram, 40 

nebular lines, 218 
Arsenic, 28-32 
Atomic magnetism, atomic rays, 129 

electronic theory, 129 

paramagnetic ions, 135 
Atomic rays, 129 

nuclear spin, 201 

velocity selector, 200 
Atomic volumes, 161 
Auroral line, 35, 215-17 

Balmer series, 2, 5, 7, 9 

fine structure, 41 

reversal, 69 
Band spectra, 172 

nuclear spin, 201 



Bands, anti-Stokes, 233 

in phosphores, 233 
Barium, 46-58, 50 

abnormal intensities, 135 
Bergmann series, 22 
Beryllium, 46-58 

displaced terms, 6 

Moseley diagram, 204 
Bismuth, 28-32 

hyperfine structure, 169-70, 181-3, 
185 

magnetic moment, 133 

X-ray spectrum, 197-8 
Bohr magneton, 87, 128, 130 
Boltzmann distribution law, 70, 85, 234 
Boron, 22-4 
Bromine, 36-9 

Cadmium, 46-58 

displaced terms, 7 

hyperfine structure, 170-1, 207 

ionised, 67 

magnetic moment, 132 
Caesium, 18-39, 50 

doublet structure, 30 

intensities, 107-8 

level diagram, 39 

series, 39 
Calcium, 46-58, 50 

diffuse triplets, 56 

displaced terms, 1 

doublet limit, 158 

effective quantum numbers, 51 

intensities, 102 

ionised, 178, 205 

level diagrams, 50, 52, 2 

perturbed series, 151 

series, 48 
Carbon, 24-8 
Catalysts, 188 
Centroid of a multiplet, 65 
Cerium, 53, 78 
Chlorine, 36-9 

hyperfine structure, 207 

level diagram, 37 
Chromium, 57-8 

g factors, 125 

intensities, 106 

intervals, 148-9 



268 



SUBJECT INDEX 



Chromium (cont.) 

phosphores, 229-32 

Zeeman patterns, 117 
Cobalt, 61, 63 

intensities, 106 

magnetic moment, 134 
Coloured ions, 188 
Columbium, 54, 57 

Zeeman patterns, 103 
Column III, 22-4 

IV, 24-8, 140-2 

V, 28-32 

VI, 33-4 

Combination of electrons, energy rules, 
15 

equivalent electrons, 11 

inverted terms, 17 

unlike electrons, 9 
Combination principle, 21, 24 
Configurations, 179-93 

elements tabulated, 194-5 
Copper, 66-9 

g factors, 155 

level diagram, 69 

magnetic moment, 132 

perturbed series, 1514 

Zeeman patterns, 103-4, 118 
Correspondence principle, 13, 36, 93 
Coupling, deviations from Russell- 
Saunders, 43-4, 122 

jj, 28, 136-^-3 

Russell-Saunders, 3-5, 22 
Covalency, 167, 172 
Crystals, energy levels, 228 

Deutonic nuclei, 205, 214 
Diamagnetism, 127 
Diffuse series, 18 

doublets, 31, 34, 37 

formula, 23 

Stark effect, 158 

triplets, 54-6 

Zeeman types, 83 
Displaced terms, alkaline earths, 1 

Be and Mg, 6 

Zn, Cd and Hg, 7 

Displacement law for spectra, 175-8 
Displacements, atomic, 19, 128, 133 

electronic, 19, 128-33, 147-50 

in electric field, 145, 157-60 

in magnetic field, 112, 124 

sum rule, 124, 126 
Distribution law, Boltzmann's, 70, 85, 

234 
Doublet formulae, irregular, 206 

Lande's, 212-16 

regular, 208 



Doublet formulae (cont.) 

screening, 206 

Sommerfeld's, 210-11 

spin, 208 
Doublet series, 23, 31-2 * 

Earth metals, 22-4 
Effective nuclear charge, 203 
Effective quantum number, 22 
Electric field, see Stark effect, 144 
Electron, in nucleus, 209-10 

magnetic moment of, 96 

mass of, 14, 44, 84 
Electron impact, 76 
Electron orbits, 10-13, 26-8, 207 
Electron theory of magnetism, 127 
Electronic angular momentum, see J, 

34 

Electronic displacements, 147-50 
Electronic structures, 179-95 
Electro valency, 167 

Energy of interaction of two vectors, 
orbital and spin vectors, 65 

in strong magnetic field, 112 ***'' 

in weak magnetic field, 9f 
Energy rules, multiplet, 15 
Enhanced lines, 46 
Equivalent electrons, 11 
Erbium phosphores, 242 
Erect terms, 35 
Europium, hyperfine structure, 199 

phosphores, 236 

valency, 78 
Excitation, by electron impact, 76 

by monochromatic light, 78 

potentials, 73 

Exclusion principle, periodic system, 
201 

combination of electrons, 11, 17 

Fine structure, constant, 210 

of helium, 44-5, 60-1 

of hydrogen, 40-4 
Fluorescence, in crystals, 228 

hyperfine, 192 

in vapours, 80 

Fluorescent crystals, chromium phos- 
phores, 229 

energy levels, 228 

Lenard phosphores, 245 

platino- cyanides, 246 

rare earth phosphores, 236 

uranyl salts, 241 
Fluorine, 36-9 
Fluorite, 236 

Forbidden lines, 27, 151, 215 
Frame elements, 184 



SUBJECT INDEX 



269 



Fundamental series, 22 
doublets, 32, 37 
formula, 23 
triplets, 57 



g, 3ee Magnetic splitting factor, 90 
Gadolinium, 83 
Gallium, 22-4- 

nucleus, 211 
F, see Displacement 
Germanium, 24-8 
Gold, 66-7 

magnetic moment, 132 
Ground terms, 68 

elements tabulated, 194 

long periods, 187, 45-7 

rare earths, 192, 80 

short periods, 183 

Hafnium, 53-4 

Halogens, 36 

Heavy hydrogen, 15, 167 

nucleus, 206, 214 
*afelium, 59-62 

ionised, 44, 44-5 

level diagram, 59 

Stark effect, 151-4 
Hydrogen atom, Bohr's theory, 10 

electron orbits, 28 

magnetic moment, 132 

mechanical moment, 11 

wave mechanics, 15 

Hydrogen spectrum, Balrner's series, 2, 
5, 13 

fine structure, 40-3 

series, 5 

Stark effect, 145-51 
Hyperfine structure, empirical, 166 

intensities, 183 

isotope displacement, 187 

nuclear mass, 167 

Paschen-Back effect, 173 

vector model, 168 

Zeeman effect, 173 

Indium, 22-4 

absorption spectrum, 69-70 
Inert gases, 36-41 

diamagnetism, 139 

g factors, 146-7 

intervals, 127 

Inner quantum number, see J, 34 
Intensities, alkali doublets, 107 

experimental, 90 

hyperfine, 183-7 

iron-frame elements, 104 

jj coupling, 150 



Intensities (cont.) 

normal multiplet, 35, 91 

quadripole, 227 

raies ultimes, 120 

sum law, 93, 135 

super multiplet, 101 

tables, 95-9 

X-ray, 196 

Zeeman, 98, 108 

Zeeman tables, 112-15 
Intermediate magnetic fields, 116 
Inter-system lines, 57 

jj coupling, 28 

Zeeman effect, 116 
Interval quotient, 65 
Interval rule, 63 

hyperfine, 173 

hyperfine perturbed, 197-9 

perturbation, 155 
In variance, of g sum, 123, 123-6 

of T sum, 124, 126 
Inverted terms, 35, 16-20 
Iodine, 36-9 

jj coupling, 142 

lonisation potentials, from electron im- 
pact, 72 

from series limit, 20-1 

long periods, 187, 189 

rare earths, 192, 74 

short periods, 182-3 
Iron, 59-61 

magnetic moment, 132 
Iron-frame elements, ground terms, 
46 

compared with other frames, 70-4 

paramagnetic ions, 140-3 
Irregular doublet law, 206 
Isoelectronic sequences, Moseley law, 
203-5 

screening doublets, 206-8 

spin doublets, 211-12 
Isotope displacement, 187-97 

Jj definition, 34 

orientation in magnetic field, 88, 129- 
31 

series limit, 159 
jj coupling, 28, 136-43 

intensities, 150 

Krypton, 39-44 

Lande's doublet formula, 212 
Lanthanum, 50, 53 

g factors, 155 
Lead, 24-8 

fluorescence, 79 



270 



SUBJECT INDEX 



Lead (cont.) 

isotope displacements, 197 

magnetic moment, 133 
Lenard phosphores, 245 
Level diagrams, optical, 11, 24 

X-ray, 197-8 
Limit, calculation of series, 20 

displaced, 3 

multiplet, 31, 42, 159 
Lithium, 18-39 

hyperfine structure, 166, 168 

level diagram, 25 

Moseley diagram, 204 

nucleus, 214 

series, 19 

Zeeman patterns, 105 
Long periods, analysis, 48 

configurations, 48 

ground terms, 45 

individual spectra, 49-70 

in periodic system, 1837 

three rows compared, 704 
Lorentz unit, 84 
Lutecium, 50, 53 

hyperfine structure, 199 

Magnesium, 46-58 

displaced terms, 6 

intensities, 218 

intervals, 150 

ionised, 177 

Paschen-Back effect, 115, 117 

Zeeman effect, 105, 119 
Magnetic field, see Zeeman effect, 82 
Magnetic moment, of atoms, 132-4 

of electrons, 96 

of ions, 135-43 

of nucleus, 203 

Magnetic splitting factor, atomic rays, 
131 

definition, 90 

sum law, 123 

tabulated, 92-3, 100-1 
Magnetism, 187 
Manganese, 58-9 

intensities, 100, 106 

Zeeman effect, 116 

Mass effect in hyperfine structure, 167 
Matching strong and weak terms, 118 
Mercury, 46-58 

absorption spectrum, 70-2 

displaced terms, 7 

excitation potentials, 75 

forbidden line, 215 

hyperfine intervals, 197-9 

hyperfine structure, 190-2 

intensities, 101-3 



Mercury (cont.) 

ionised, 67 

isotope displacements, 193-5 

level diagram, 53 

magnetic moment, 132 

quadripole radiation, 222 

resonance radiation, 79 

Zeeman effect, 118^ 
Molecules, symmetrical, 2012 
Molybdenum, 57-8 

intervals, 148-9 
Moseley 's law, optical, 199 

X-ray, 203-5 
Multiplets, 62 

analysis, 48 

intensities, 94^-9 
Multiplicities in iron row, 175 

Nebular lines, 217 
Neodymium phosphores, 242 
Neon, 39-43 

absorption spectrum, 69 

hyperfine structure, 168 

intervals of s terms, 134 

jj coupling, 141 

series limits, 43, 159-60 

Stark effect, 155 
Neutronic nuclei, 205, 212-13 
Neutrons in nucleus, 20910 
Nickel, 63-5 

g factors, 155 

intensities, 1056 

magnetic moment, 134 

Stark effect, 158-60 
Nitrogen, 28-32 

inverted terms, 20 

level diagram, 29 

nebular lines, 218 

nucleus, 206-7, 214 

triplet limit, 32 
Normal Zeeman triplet, 134 
Notation in complex spectra, 49 
Nucleus, electric field of, 200 

magnetic moment of, 203-6 

spin of, 200 

structure, 208 

types of, 204-5, 208 

One line spectra, 76 

Orbits, exclusion principle, 201 

general atom, 26-8 

hydrogen, 10-13 
Orbital vector, 26 
Oxygen, 33-5 

auroral line, 216-17 

intensities, 101 

level diagram, 33 



SUBJECT INDEX 



271 



Oxygen (cont.) 

magnetic moment, 134 
nebular lines, 218 
Paschen-Back effect, 106, 115 



Pafladium, 63-5 

Palladium frame elements, 188 

ground terms, 47 

paramagnetism, 143 
Paramagnetism, classical theory, 136-8 

frame elements, 140-3 

gases, 138 

Langevin's theory, 127 

rare earths, 138-40 
Partial Paschen-Back effect, 115 

intensities, 118-19 
Paschen-Back effect, empirical, 105 

hyperfine structure, 173 

intermediate fields, 117 

in variance of g sum, 123 

invariance of F sum, 125 

matching strong and weak terms, 

119 
partial effect, 115 

quadripole, 225 

vector model, 111 
Penetrating orbits, 27 
Periodic system, 161-202 

displacement law, 175 

electronic structures, 179 

exclusion principle, 201 

rare earths, 75 

valency, 166 
Periodic table, 163, 165 
Perturbation, 150-7 

hyperfine, 197-8 
Phosphores, chromium, 229 

Lenard, 245 

rare earth, 236 
Phosphorescence, 228-9 
Phosphorus, 28-32 

hyperfine structure, 207 
Photometry, 90 
Platino- cyanides, 246 
Platinum, 66 
Platinum frame elements, 189 

ground terms, 47 

paramagnetism, 143 
Polarisation in, Paschen-Back effect, 
112-13 

quadripole radiation, 220 

Stark effect, 148, 154 

Zeeman effect, 112, 109 
Potassium, 18-39, 50 

displacement law, 178 

electron impact, 78 

forbidden lines, 215 



Potassium (cont.) 

g sum, K n, 126 

hyperfine structure, 207 

magnetic moment, 132, 138 

Moseley diagram, 205 

quadripole line, 222-5 

Stark effect, 178 
Praseodymium phosphores, 238, 240, 

243 
Principal series, 18 

doublets, 31, 36 

formula, 23 

triplets, 51, 55 

Zeeman types, 83 
Protonic nuclei, 204, 210-12 
Protons in nucleus, 209-10 

Quadripole radiation, forbidden lines, 
215 

intensities, 227 

polarisation rule, 221 

quantum mechanics, 219 

selection rules, 220 

Zeeman effect, 221 

Quantum mechanics, hyperfine per- 
turbation, 199 

Paschen-Back effect, 117 

quadripole radiation, 219 

valency, 172 

Zeeman effect, 97 
Quantum of action, 10 

Radium, 46-58, 50 
Raies ultimes, 120 
Raman spectra, 228, 235 
Rare earths, 75-89 

absorption spectra, 81 

arc and spark spectra, 79 

configurations, 190-2 

in periodic system, 75 

ionisation potentials, 192 

paramagnetism, 138 

phosphores, 236, 242-3 

valency, 77 
Regular doublets, 208 
Resonance potentials, 72 
Resonance radiation, 78 
Rhenium, 59 
Rhodium, 63 
Rubidium, 18-39, 50 

electron impact, 78 

g sum, Rb n, 126 

nucleus, 209 
Russell-Saunders coupling, 3-5, 22 

deviations from, 122 
Ruthenium, 59, 61 

T sum, 132 



272 



SUBJECT INDEX 



Rydberg constant, 2 
for helium, 14 
for hydrogen, 12 
for other atoms, 19 

Samarium, 859 

phosphores, 236-40, 243 
valency, 78 
Scandium, 503 

ionised, 178, 205 
Screening, constant, 203 

doublet, 206 

Selection rules, displaced terms, 4 
for J, 57 
for L, 26 

Paschen-Back, 112-13 
quadripole, 220 
Stark, 148, 154 
X-ray, 196 
Zeeman, 89 
Selenium, 33-5 
Self- reversal, 18, 69 
Serial number, 19, 23, 49 
Series, 5, 18 
formula, 18-21 
intensities, 104 
limits, 10-11, 21, 158-65 
Sharp series, 18 
doublet, 31, 36 
formula, 21-3 
Stark effect, 158 
triplet, 54-5 
Zeeman types, 83 
Short periods, 181-3 
deep terms, 14 
elements, 21 
ground terms, 16-18 
irregularities, 22 
Silicon, 24-8 

doublet limit, 160 
ionised, 177 
level diagram, 25 
Silver, 66-7 

hyperfine structure, 207 
magnetic moment, 130-2 
Singlet spectra, 47 
Sodium, 18-39 

absorption spectrum, 68 

controlled electron impact, 77 

D lines in magnetic field, 106-10, 112- 

13 

displacement law, 177 
fluorescence, 79-81 
forbidden lines, 215 
Lande's doublet formula, 215 
level diagram, 33 
magnetic moment, 132 



Sodium (cont.) 

nuclear spin, 201 

Paschcn-Back effect, 115 

quadripole lines, 223-5 

Stark effect, 155 

Zeeman patterns, 85 
Spark spectra, 46 
Spectroscopic terms, <32 
Spin doublets, 208 

X-ray, 130 
Spin of nucleus, 200 
Spinning electron, doublet series, 32 

Zeeman effect, 94 
Stark effect, 144-60 

experimental, 144 

forbidden lines, 215 

in crystals, 234 

in hydrogen, 145 

in other elements, 151 
Stationary states, 3, 10 
Statistical weight of a term, 66 
Stripped atoms, 207 
Strong field, 106 
Strontium, 46-58, 50 

intensities, 102 

perturbation, 157 
Sulphur, 33-5 
Sum rules, g sum, 123 

T sum, 126 

intensity, 135 
Super multiplet, intensities, 101 

Tellurium, 33-5 
Temperature class, 49 
Terbium, valency, 78 
Terms, 3, 9, 11 
Thallium, 22-4 

absorption, 69-70 

fluorescence, 79 

hyperfine structure, 172-89 

intensities, 108 

isotope displacement, 194 

level diagram, 23 

magnetic moment, 132 

nucleus, 206 
Tin, 24-8 

magnetic moment, 133 
Titanium, 53-4 

g factors, 155 

T sum, 132 

intensities, 101, 106 

ionised, 178, 205 
Transition elements, 184 
Triplet terms, 49 
Tungsten, 58 

Uranyl salts, 241 



SUBJECT INDEX 



273 



Valency, 166-75 

rare earths, 77 
Vanadium, 54, 57 
Vector model, alkali doublets, 29 

combination of several electrons, 9 

displaced terms, 3 

general coupling, 135 

hyperfine intervals, 199 

hyperfine structure, 168, 172 

hyperfine Zeeman effect, 173 

interval rule, 65 

jj coupling, 27-8 

Paschen-Back effect, 111-12 

Stark effect, 157 

Zeeman effect, 88-9 

Wave mechanics, 3 

hydrogen atom, 15 

hyperfine structure, 176, 179 
Wave numbers, 5 
Weak field, 106 

X-rays, 193-200, 228 
^dpin doublets, 209-11, 130 
Xenon, 39-48 

Stark effect, 156-7 



Ytterbium, phosphores, 236 

valency, 78 
Yttrium, 50, 53 

Zeeman effect, 82-104 

analysis, 99 

anomalous types, 85 

hyperfine, 173 

intensities, 98, 108-20 

magnetic splitting factors, 92-3, 
100-1 

normal triplet, 82 

quadripole, 221 

quantum theory, 86 

spinning electron, 94 

unresolved patterns, 106 
Zinc, 46-58, 67 

displaced terms, 7 

Lande's doublet formula, 215 

magnetic moment, 132 
Zirconium, 53-4 

doublet limit, 161 

g factors, 154, 156 

intensities, 106 



CAS n 



AUTHOR INDEX 



Numbers in Clarendon refer to the second volume. 



Albertson, W., 79 

Allen, J. S. V., 106 

Altschuler, S., 213 

Andrade, E. N. da C., 69, 78, 81 

Arnot, F. L., 81 

Aston, F. W., 188, 208 

Backer, B. F., short periods, 44; long 

periods, 74; hyperfine structure, 

173, 199 
Back, E., Paschen-Back effect, 104-6, 

115-18, 126; g factors, 147; hyper- 
fine structure, 169, 178, 180, 187 
Bakker, C. J., halogens, 36; g sum, 

125; quadripole Zeeman effect, 
* 222-6 
Balmer, J. f., 2, 5 
Barratt, S., 220 
Bartlett, J. H., 150 
Bear, R. S., 85, 88-9 
Bechert, K., 150 
Becker, F., 217, 227 
Becquerel, J., 82-3 
Blair, H. A., 104, 125 
Blaton, J., 227 
Bohr, N., 3; H atom 10 f.; He ion, 14; 

selection rule, 89; Stark effect, 157; 

periodic table, 163-4, 180-91 ; rare 

earths, 75, 79 

Boltzmann, L., 2, 70, 85, 234 
Born, M., 175, 202 
Bourland, L. T., 143 
Bowen, I. S., doublet laws, 204, 207, 

212; nebular lines, 217-19 
Boyce, J. C., nitrogen, 20; nebular lines, 

217-19 

Brackett, F. S., 7 
Bragg, W. H., 202 
Bragg, W. L., 202 
Breit, G., matching terms, 120; isotope 

displacements, 194-7; nuclear spin, 

201 

Brickwedde, F. G., 167 
Briick, H., 170-1 
Bryden, S. D., 209 
Buoma, T., 106 
Burger, H. C., helium, 60; intensities, 

101-4; Zeeman intensities, 108-10; 

photometry, 121 



Cabannes, J., 228 
Cabrera, P., 139 
Campbell, J. S., 84, 221 
Capel, W. H., 139 
Carter, N. M., 27, 216 
Casimir, H., 199, 200 
Chalk, L., 149, 150 
Charola, F., 80 
Chenault, R. L., 8 
Coelingh, M., 102 
Cohen, V. W., 131, 200-1 
Compton, K. T., 20 
Cotton, A., 84 
Condon, E. U., 158-9 
Crookes, W., 236 
Curie, S., 127 
Curtis, W. E., 7 

Dadieu, A., 228 

Darwin, C. G., Paschen-Back effect, 117; 
quantum mechanics, 211; Paschen- 
Back intensities, 118 

Darwin, K., 109-10 

Datta, S., 215 

Davis, B., 74-5 

de Boer, J. H., 167, 172, 202 

de Broglie, L., 15 

de Bruin, T. L., 36, 125 

de Gramont, A., 120 

de Haas, W. J., 139 

Dennison, D. M., 200 

Deutschbein, O., rare earths, 83; chrome 
phosphores, 230-5 

Dewar, J., 2 

Dickinson, R. G., 201 

Dijkstra, H., 147 

Dirac, P. A. M., 93 

Dobson, G. M. B., 90 

Dorgelo, H. B., 91-3, 109 

du Bois, H., 235 

Eastman, E. D., 209 
Eckart, C., 167 
Ehrenfest, P., 82 
Elias, G. J., 235 
Eliason, A. Y., 95, 150 
Epstein, P. S., 147 
Evans, E. J., 14, 168 
Evans, S. F., 142 



276 



AUTHOR INDEX 



Evert, H., 240 
Eymers, J. G., 102 

Fagerberg, S., 240 

Fermi, E., 108, 203-7 

Fersehmin, A., 40 

Filippov, A., 107 

Fisher, R. A., 104 

Foote, P. D., 215, 8 

Fortrat, R., 68 

Foster, J. S., 149-51, 155 

Fowler, A., helium, 14; series laws, 21; 

doublet series, 31; Moseley's law, 

205; carbon, 28 
Fowler, H. W., 27, 216 
Franck, J., 76, 81 
Frank, A., 139 
Fraser, R. G. J., 129-30, 143 
Fraunhofer, J., 68 
Frayne, J. G., 218-19 
Freed, S., 139, 83-5 
Frerichs, R., intensities, 106, 121; 

auroral line, 221 
Fridrichson, J., 76 
Frisch, S., 40 
Fiichtbauer, C., 71, 107 

Gale, H. G., 15 

Gebauer, R., 145 

Gehrcke, E., 84 

Gerlach, W., 129, 132-3, 138 

Gibbons, J. J., 197 

Gibbs, R. C., H a , 43; He atom, 61; 
doublet laws, 208, 212-16; f elec- 
trons, 14; cerium, 80 

Gotze, R., 23, 1 

Goucher, F. S., 74-5 

Goudsmit, S. A., spinning electron, 32-4; 
fine structure of hydrogen, 40-5; 
He atom, 58; Paschen-Back effect, 
111; doublet laws, 209-10, 216; 
short periods, 44; long periods, 74; 
combination of electrons, 20; g y 126, 
143; T sum, 130-2; jj coupling, 
142; perturbation, 156; hyperfine 
structure, 169, 173, 180, 199; nuclear 
moments, 203-7; rare earth phos- 
phores, 240 

Grace, N. S., 43, 197 

Granath, L. P., 168 

Grebe, L., 197 

Green, J. B., Paschen-Back effect, 117; 
doublet laws, 216; perturbation, 
155; hyperfine structure, 175-7, 
183-6 

Griffith, I. 0., 90, 121 

Grotrian, W., hydrogen, 40; helium, 40, 



58; aluminium, uo; muium, iv, 
Stark effect, 155; Moseley diagrams, 
205; nebular lines, 217, 227 
Guthrie, A. N., 143 

Haberlandt, H., 236 

Hansen, G., helium, 41, 60; hyperfine 
structure, 168 

Harkness, H. W., 156, 160 

Harrison, D. N., photometry, 90, 121 

Harrison, G. R., intensities, 106, 135 

Heard, J. F., 156, 160 

Heisenberg, W., hydrogen, 40; helium, 
61; Paschen-Back effect, 117, 120; 
intensities, 91, 111; nuclear struc- 
ture, 209 

Heitler, W., 174 

Hellmann, H., 202 

Herlihy, J., 108 

Hertz, G., 69, 76, 206 

Hesthal, C. E., 106 

Hevesy, G. v., 75, 81, 89 

Hill, E. L., 185 

Hiyama, S., 145 

Hoag, J. B., 15 

Honl, H., 93, 111 

Hopfield, J. J., 35 

Houston, W. V., hydrogen, 41-3; 
helium, 60; Lorentz unit, 84; per- 
turbed # factors, 155, 178; quadri- 
pole radiation, 215, 219, 226 

Howes, H. L., 241 

Hsieh, Y. M., 43 

Hiibner, H. J., 107 

Huff, L. D., 215, 226 

Hughes, D. S., 167-8 

Hund, F., electronic structures, 193; 
energy rules, 15; combination of 
electrons, 20; short periods, 24-36, 
44; inert gases, 42; long periods, 
74; series limit, 160-3 

Idei, S., 200, 206 

Inglis, D. R., perturbed, terms, 156; 

nucleus, 210, 212, 214 
Ishida, Y., 145 
Iwama, T., 147 
Iwanenko, D., 210 

Jack, R., 102 
Jackson, B. A., 207 
Janes, R. B., 143 
Jantsch, G., 236 
Jenkins, H. G., 120 
Jevons, W., 174, 202, 201 
Jog, D. S., 28 
Johnson, M. H., 106, 135 



AUTHOR INDEX 



277 



Jones, E. G., 197-8, 207 

Joos, G., 107, 232 

Jordan, P., hydrogen, 40; energy levels, 

81; Paschen-Back effect, 117, 120; 

Zeeman intensities, 111 

Kalia, P. N., 79 

fcallmann, H., hyperfine structure, 

194-6, 210, 214 
Karlik, B., 236 
Karlson, P., 79 
Kassner, L., 147 
Kast, W., 157 
Kayser, H., 214 
Kellogg, J. M. B., 201 
Kent, N. A., 41 

Keyston, J. E., 171, 185-91, 193 
Kiess, C. C., g factors, 90, 100; zirconium, 

106; perturbation, 154; series limit, 

161 

Kiess, H. K., 106, 154 
King, A. S., 46, 49, 79 
Klemm, W., 236 
X*ch, J., 151 

Kohlrausc 1 ! , K. W. F., 228 
Kohn, H., 107 
Kossell, W., 169, 176, 186 
Kramers, H. A., 147, 154 
Kromer, E., 125 
Kronig, R. de L., intensities, 93, 104, 

150; Zeeman intensities, 111 
Kruger, P. G., 61 
Kuhn, H., 207 
Kurt, E. (X, 134 

Ladenburg, R., 71, 155 

Land6, A., selection rule, 57; interval 
rule, 63; g factors, 90; Zeeman 
effect, 104; T sum, 125; doublet 
formula, 212; oxygen, 35; neon, 41; 
g sum, 125; nucleus, 210-14 

Lang, R. J., 80, 161 

Langer, R. M., 152 

Langevin, P., 127 

Langstroth, G. 0., 135, 156 

Laporte, O., interval rule, 64; para- 
magnetic ions, 141; raies ultimes, 
121; g sum, 126; perturbation, 156; 
selection rule, 220; rare earth 
phosphores, 240 

Lenard, P., 73, 246 

Leu, A., 132-3 

Lewis, G. N., 170 

Liveing, G. D., 2 

London, F., 174 

Lorentz, H. A., 82, 84 

Loring, R. A., 155 



Lo Surdo, A., 145 
Lyman, T., 7, 58, 39 

McLennan, J. C., 35, 216, 221 

McLeod, J. H., 221 

Mack, J. E., 162 

Masaki, O., 40 

Meggers, W. F., g factors, 90, 100; in- 
tensities, 104; raies ultimes , 121; 
g sum, 125; F sum, 132; forbidden 
lines, 215 

Meissner, K. W., caesium, 38; rubidium, 
40; neon, 69; atomic rays, 130 

Mendeteeff, D., 162, 165 

Mensing, L., 117 

Metcalfe, E. P., 70 

Meyer, S., 139 

Milianczuk, B., 225 

Miller, G. R., 126 

Millikan, R. A., doublet laws, 204, 207. 
212; displaced terms, 6 

Minkowski, R., 147, 160 

Mishima, T., 168 

Mitchell, A. C. G., 81 

Mohler, F. L., 79, 215 

Moll, W. J. H., 121 

More, K. R., 197 

Moseley, H. G. J., 199, 203 

Mrozowski, S., 192 

Mulliken, R. S., 174 

Murakawa, K., 147 

Murphy, E. J., 167 

Nagaoka, H., 168 
Newman, F. H., 77 
Nichols, E. L., 241 
Nutting, G. C., 84, 232 

Ornstein, L. S., intensities, 101-4, 106; 
Zeeman intensities, 108-10; photo- 
metry, 121 

Paschen, F., hydrogen, 7; serial num- 
bers, 23; helium, 45, 58; Paschen- 
Back effect, 105-6, 115; oxygen, 
35; neon, 39, 42; perturbed series, 
151 

Pauli, W., matching terms, 119; g sum, 
124; Stark effect, 158; exclusion 
principle, 201; g sum, 125; hyper- 
fine structure, 166, 168 

Pauling, L., doublet laws, 209, 216; 
combination of electrons, 20; T 
sum, 132; jj coupling, 142 

Pearson, H., 41 

Pfluger, A., 71 

Pfund, A. H., 7 



278 



.TJTHOR INDEX 



Phipps, T. E., 134 

Piccardi, G., 192, 75 

Pickering, W. H., 14 

Placzek, G., 228 

Planck, M., 10 

Poetker, A. H., 7 

Pogany, B., 42, 145-7 

Preston, T., 85, 105 

Pringsheim, P., absorption spectra, 69, 

78, 81; fluorescence, 241, 244-6 
Przibram, K., 236 



Rabi, I. I., atomic rays, 129, 131, 143; 

nuclear spin, 200-1 
Raman, C. V., 228 
Ramb, R., 40 
Ramsauer, G., 155 
Rasetti, F., 107-8, 220 
Rawlins, F. I. G., 232 
Rayleigh, Lord, 80-1, 215 
Ritz, W., 3, 21, 24 
Rolla, L., 192, 75 
Roschdostwenski, D., 107-8 
Rosenthal, A. H., 36 
Rowles, W., 155 
Ruark, A. E., 180, 202 
Rubinowicz, A., 89, 227 
Ruedy, J. E., 221 
Rumer, G., 174 
Rump, W., 79 
Runge, C., 58, 85, 214 
Russell, H. N., series laws, 21; notation, 

34; unresolved patterns, 104; 

matching terms, 120; xenon, 158; 

displaced terms, 1, 5; notation, 4; 

combination of electrons, 10; euro- 
pium, 79; intensities, 93, 104-5; 

g sum, 125; F sum, 132; perturbed 

series, 151, 154 
Rydberg, J. R., Rydberg constant, 2; 

series formula, 18; combination 

principle, 21, 24 
Ryde, J. W., 120 
Ryde, N., 156 

Saha, N. K., 83 

Sambursky, S., 108 

Sauer, H., 232-3 

Saunders, F. A., 1, 5, 39 

Sawyer, R. A., 7, 126, 151 

Scheffers, H., 130 

Schlapp, R., 151 

Schmidt, T., isotope displacements, 
195; hyperfine structure interval 
rule, 199; nuclear structure 209; 
fluorescence, 246 



Schnetzler, K., 232 

Schrodinger, E., 149 

Schiiler, H., hyperfine structure, 
lithium, 166; vector model, 170-1; 
intensities, 185-7; isotope dis- 
placement, 189-97; perturbation, 
197-9; nucleus, 204-5, 209-10 
213-14 

Schuster, A., 2 

Scribner, B. F., 121 

Segre, E., nuclear moments, 203-7; 
quadripole radiation, 222-6 

Selwyn, E. W. H., 205 

Seward, R. S., 106 

Sexl, T., 200 

Shane, C. S., 15, 43 

Shenstone, A. G., unresolved patterns, 
104; notation, 34,4; inverted terms, 
19; g sum, 125; F sum, 132; per- 
turbation, 151, 154-5; series limit, 
161 

Sherman, A., 202 

Shrum, G. M., 27, 216 

Sidgwick, N. V., 167, 172, 202 

Siegbahn, M., 200, 202, 228 

Slater, J. C., 58, 174, 130 

Smith, D. M., 120 

Snow, C. P., 232 

Sommer, L. A., 221 

Sommerfeld, A., intensity rule, 35; H I 
and He n, 40-5; Paschen-Back 
effect, 115; matching terms, 119; 
paramagnetism, 141; displacement 
law, 176; doublet laws, 210-11, 
216; intensities, 91-3 

Sowerby, A. L. M., 220 

Spedding, F. H., H a , 15, 43; para- 
magnetism, 139; rare earths, 83-9; 
chromium compounds, 232-4; rare 
earth phosphores, 238 

Spencer, J. E., 89 

Stark, J., 144-5, 150, 160 

Stern, O., 129, 132, 210 

Stevenson, A. F., 220 

Stokes, G. G., 229 

Stoner, E. C., 136, 143 

Stoney, G. J,, 2 

Takamine, T., 158-9, 8 
Tamm, I., 213 
Taylor, J. B., 132 
Taylor, L. B., 41 
Temple, G., 209 
Terenin, A., 80 
Terrien, J., 147 
Thomas, E., 168 
Thornton, R. L., 149 



AUTHOR INDEX 



279 



Tomaschek, R., rare earths, 83; fluor- 
escence, 242-3, 246; rare earth 
phosphores, 236-40 
Traubenberg, H. R. v., 145 
Turner, L. At, 34, 4 
[Vyman, F., 120 

Uhlenbeck, G. E.,<fcpmnmg electron, 32; 
H I and He n, 40-5; helium, 58; 
doublet laws, 210; g factor, 143 

Unsold, A., 45 

Urbain, G., 236 

Urey, H. C., periodic system, 180, 202; 
combination of electrons, 20 ; hyper- 
fine structure, 167 

Van Arkel, A. E,, 167, 172, 202 
Van Geel, W. C., 117, 110, 116-21 
Van Lohuizen, T., 87 
Van Vleck, J. H., 138-9, 143, 202 
Van Wijk, W. R., 101 
Venkatesachar, B., 70 
Voigt, W., 105-6, 108, 117 
f 9n Baeyer, A., 84 

& 
Weiss, P., 84 



Wentzel, G., 196, 5 

West, G. D., 15 

Weyl, A., 174 

Whiddington, R., 13 

White, H. E., doublet laws, 208, 212, 

216; combination of electrons, 14; 

cerium, 80; intensities, 95, 150; 

perturbation, 151; series limit, 163 
Whitford, A. E., 126 
Wick, F. G., 244 
Wiersma, E. C., 139 
Wilber, D. T., 14 
Williams, J. H., 43 
Williams, S. E., 108 
Wolff, H. W., 107 
Wood, R. W., 68, 79, 228 
Wrede, E., 132 
Wulff, J., hyperfine structure, 175-8, 

183-7 

Zacharias, J. R., 201 
Zahrahnicek, J., 211 
Zeeman, P., Zeeman effect, 82, 104; 

aluminium, 36 ; hyperfine structure, 

169, 180 
Zemansky, M. W., 81 



CAMBRIDGE: PRINTED BY w. LEWIS, M.A., AT THE UNIVERSITY PRESS