581 



level value in italics), and normally spectral lines are permitted only when terms of dif- 

 ferent parity combine. Furthermore, an overwhelming majority of the transitions between 

 atomic energy levels obey the following rules : 



AR=0 



AL = ± 1 



A/ = 0, ± 1, excepting to 0. 



In complex spectra, especially of heavy elements, intersystem combinations are observed 

 for AR = ± 2, ± 4. Likewise, transitions for AL = give strong multiplets, and transi- 

 tions for which AL = ± 2, ± 3 are observed but usually only faintly. Violations of theA/ 

 rule are extremely rare. Assignment of L values and electron configurations to energy 

 levels implicitly assumes that LS coupling or interaction exists among the individual vec- 

 tors. This means that the individual / vectors are strongly coupled to produce resultant L 

 values of different energies, and the individual s vectors are also strongly coupled to pro- 

 duce resultant 6" values. These L and 5" resultants are then less strongly coupled with each 

 other to produce resultant / values. Other types of coupling such as // or JL are some- 

 times met with and in such cases L loses all or most of its significance. Also when the 

 levels of two like-parity configurations overlap or dovetail, it is practically impossible to 

 distinguish the two configurations or choose the levels that belong to each. However, be- 

 cause LS coupling holds for all the higher elements, predominates in many others, and is 

 either accurately or approximately valid for the ground states of all atoms and ions, it is 

 basic for the standardized notation for spectral terms. Thus, any atomic energy level or 

 spectral term is symbolically represented by four quantities. (1) its principal quantum 

 number n written as a coefficient of the term-type symbol ; (2) its type — S, P, D, F, etc. — 

 where the capital letters stand for azimuthal quantum numbers or orbital angular momenta 

 L = 0, 1,2, 3, etc., respectively; (3) its inner quantum number or total angular momentum 

 / = L -\- S, written as a subscript to the term-type symbol ; and (4) its multiplicity num- 

 ber, R = 2S -\- 1, written as a superior prefix to the term-type symbol. In addition the 

 parity, if the sum of p and / electrons is odd, is indicated by the sign ° attached like an 

 exponent to the term-type symbol. 



For any given spectrum in which energy levels have been established, and in which 

 LS coupling exists, it is possible to assign notation as well as electron configuration without 

 ambiguity. Relative values of / are readily determined from the combining properties of 

 the levels and the selection rule, A/ = 0±1. In terms of odd multiplicity the absolute 

 value of / is fixed by the absence of the transition to which is forbidden. In other cases 

 the absolute value of / can often be deduced from the sum rule (the sum of the intensities 

 of all the lines of a multiplet that belong to the same initial or final state is proportional to 

 the statistical weight 2/ + 1 of the initial or final state respectively), or from the interval 

 rule (the interval between two successive components, / and / -f- 1, of a polyfold term 

 is proportional to / + 1). The most decisive determination of / and L (excepting singlet 

 terms) results from the observation of completely resolved Zeeman patterns since an ex- 

 ternal magnetic field causes each energy level to be split into 2/ + 1 sublevels and the 

 splitting factors indicate L values. 



It is a consequence of atomic structure that long series of spectral terms of the same 

 parity, L, S, J, but increasing n, are observed only in one-electron spectra, as for example 

 to n = 79 in the first spectrum of sodium. Five- six- or seven-electrons provide so many 

 configurations and competing levels that it is often exceedingly difficult to detect the 

 second or any higher members of a spectral series. 



Quantum principles having thus specified the various spectral terms arising from cer- 

 tain electrons, it became possible in 1925 to determine from identified terms the electron 

 configurations of all atoms and ions. By 1950 the ground states of 82 species of neutral 

 atoms and 75 singly ionized atoms had been uniquely determined from spectral structure. 

 Besides disclosing the ground level and normal electron configuration of each atom or 

 ion, the discovery of series relations in atomic spectra has given exact values for many 

 ionization potentials which measure the forces with which the optical electrons are bound 

 to atoms and ions. Furthermore, since the most intense radiations are usually associated 

 with the largest L and / values of low-lying levels, the analysis of spectra has aided in 

 selecting the strongest spectral lines characteristic of atoms and ions. In general, the 

 strongest lines result from s< — >p electron transitions, but do not necessarily end on the 

 ground state. Because these data are of great importance in spectroscopy, atomic physics, 

 chemistry, and astrophysics, they are collected for neutral atoms in Table 623 and for 

 singly ionized atoms in Table 624. 1B3 



193 For more detailed discussions of atomic spectra and complete compilations of atomic energy levels, 

 see the list of references, page 585. 



SMITHSONIAN PHYSICAL TABLES 



