212 
THE QUANTUM [xv. 4 
4. Multiplicity of Spectral Terms 
The four chief spectral series may be written (p. 51) 
P (m) = iS — mV 
S (m) = iP — mS 
D (m) = iP — mD 
F (m) = 2D — mV 
Here D(2), for example, indicates the line in the Diffuse or D 
series for which m = 2, while 2D is equivalent to the term 
N/(2+D) 2 . 
These formulae represent the four chief series of a " singlet ” 
system, but in many cases spectral lines occur as doublets (as 
in the case of the D-lines of sodium), triplets, etc. ; thus the 
terms from which the spectral lines are derived are two-fold, 
three-fold, etc. In forming the possible combinations we must 
take into account this “ multiplicity ” of the terms, though it 
must be observed that some of the components which are pos 
sible algebraically are inadmissible physically. The S term is 
always simple (one-fold), whereas the P term, D term and the F 
term have larger multiplicity and may be two-fold, three-fold, 
etc. This similarity of subdivision which is found for the various 
terms is called the permanency of the multiplicities. The problem 
of accounting for these multiplicities stands in intimate relation 
ship to the problem of the anomalous Zeeman effect. In both 
cases the existence of an intra-atomic magnetic field has been 
postulated to account for the observed results. This explana 
tion is in harmony with the fact that multiplicity and valency 
vary together : we find doublets in the case of uneven valency, 
and triplets in the case of odd valency. As valency is associated 
with the number of outer electrons of the atom, the origin of 
the inner magnetic field appears to be related to the number of 
those outer electrons. By work on these lines Lande * and also 
Sommerfeld f have been able to co-ordinate the phenomena con 
nected with the multiplet structure of spectral terms and the 
general Zeeman effect. Mention must also be made of the sug 
gestive work of Heisenberg. £ 
It would appear then that doublet separations, such as are 
observed in the spectra of the alkali elements, are manifestations 
of what is practically a Zeeman effect produced by an internal 
atomic magnetic field. To account for the observed separations, 
the fields, for some atoms at least, must be exceedingly high (of 
the order io 6 or 10 7 gausses). When the external field is great 
as compared with the internal, theory shows that for doublets 
* Lande, Zeits. f. Physik, vol. 15, p. 189 ; vol. 19, p. 122, 1923. 
f Sommerfeld, Ann. d. Physik, vol. 73, p. 209, 1924. 
I Heisenberg, Zeits. /. Physik, vol. 8, pp. 257, 273, 1922.