8o 
THE QUANTUM 
[V-4 
single spectral line, because we must now take into consideration 
not only single electrons, but an atomic system comprising a 
considerable number of electrons. In this case the atom must 
be regarded, at least from one standpoint, as a complete and 
independent system. It may be remarked here that results 
of a similar character have been found in the formation of band 
spectra, the individual lines of which are now associated with 
changes in the energy of rotation and configuration of molecules. 
For further information on this important subject reference 
may be made to the Bulletin of the National Research Council 
(No. 57) on Molecular Spectra in Gases (1926). 
In the theory of Heisenberg and Hund (published in 1925) 
five quantum numbers are used to specify an electron orbit, 
viz. n, k lt k 2 , m lt m 2 ; but of these five numbers only four are 
independent. The principal quantum number n retains the 
same meaning as in Bohr’s central orbit theory. If k denotes, as 
is customary, the azimuthal quantum number, k x = k — and 
k 2 may be either k t — | or k x + f, so that either k 2 = k — 1 
or k 2 = k. Finally m x and m 2 are the magnetic quantum numbers 
for weak and strong fields respectively. 
Three quantum numbers are required to specify a spectro 
scopic term, these are denoted by r, l, and j, and may be identified 
respectively with the multiplicity, the group quantum number, 
and the inner quantum number referred to in the previous 
chapter.* The main object of the theory is to deduce the values 
of these term numbers, r, l, j, from the quantum numbers of 
those electrons which are in uncompleted groups. This is 
done by employing a set of rules, partly theoretical, partly 
empirical, which serve to determine the possible states of the 
system. 
Probably the most important principle limiting the number 
of possible electronic orbits is that enunciated by Pauli. It 
may be stated as follows : Four independent quantum numbers 
being required to determine uniquely an electronic orbit, two 
electrons cannot move in orbits characterized by exactly the 
same four quantum numbers. Thus there cannot be more than 
one electron in each uniquely defined quantum state, or in 
other words, there is only one possible electronic orbit of a given 
size, shape and position. It can be shown that this principle 
leads to the scheme of electron distribution proposed by Main 
Smith and by Stoner. 
The actual procedure followed in determining the terms is 
somewhat lengthy, and for examples reference must be made 
* As different conventions have been used for the absolute values to 
be assigned to the quantum numbers, some care is needed in dealing with 
the results of various authors.