By I.I. Sobel'man
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Extra info for Introduction to the Theory of Atomic Spectra
Energy levels corresponding to definite values of L and S are called spectral terms or simply terms. Capital letters of the Latin alphabet are usually used for denoting terms, as follows L = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 S P D F G H I K L M N 2. Fine structure of terms Just as in the case of the hydrogen atom, relativistic effects, principally spin-orbit interaction, lead to a splitting of the term LS into a number of components, corresponding to different values of the total angular momentum / of the atom.
In the case of two equivalent electrons, the allowed states can be found by means of a simple rule. States (jj)j with / = 2/ — 1, 2/ — 3 are allowed and those with / = 2y, 2/ — 2, 2/ — 4 are forbidden. In the example considered above, when j \ = j 2 = f 1 - 1 =2, 2f-3=0. //-coupling. Electrostatic interaction is always large for equivalent electrons. SYSTEMA1ICS OF THE SPECTRA OF MULTI-ELECTRON ATOMS 35 Allowed levels for a series of configurations jn are given in Table 6. In the event of a given level occurring several times, the level multiplicity is shown below.
This state and the state ML = 0, Ms = \ give the 2 P-term. The remaining states ML = 0, Ms = \ and ML = 0, Ms = ^ correspond to the term 4 S\ Thus, only three terms 2Z>, 2P and 4 5 are possible for the given electron configuration, whereas we obtained twenty-one terms for the configuration of three non-equivalent /^-electrons above. The limitation imposed by the Pauli principle thus considerably reduces the number of possible terms. By the same method, allowed terms can also be found for other configurations /".
Introduction to the Theory of Atomic Spectra by I.I. Sobel'man