Classification of the energy levels using various coupling schemes

3 Classification of the energy levels using various coupling schemes 

In Chapter 9 we discussed the classification of the terms and energy levels of a shell of equivalent electrons using the LS coupling scheme. Here we shall consider the case of two non-equivalent electrons. As we shall see later on, generalization of the results for two non-equivalent electrons to the case of two or more shells of equivalent electrons is straightforward. 

In LS coupling the energy levels of two-electron configuration will be characterized according to Eq. (11.2) by intermediate quantum numbers L, S and resultant momentum J. Usually, instead of LSJ, the notation 2S+1Lj is utilized. Quantum numbers L and S denote the term of the multiplicity 2S + 1, whereas J describes the so-called fine structure (levels) of the term. Each level in accordance with the values of M = —J,—J + 1.J consists of 2J + 1 states. The number of levels of the term equals 2S + 1, i.e. its multiplicity, if L S, and equals 2L + 1, if L S. L acquire integer (whereas S and J may acquire also half-integer) positive values (including L = S = J = 0), however, usually the capital letters of the Latin alphabet are utilized to denote L (as well as small ones for /) in accordance with 

In order to indicate the parity, defined here as (—l),1+ 2, we have to add to the term a special symbol (e.g. for odd configurations the small letter o). Then, for example, the levels of the configuration nsn p will be lP[, 3 0,1,2- Thus, the spectra of two non-equivalent electrons will consist of singlets and triplets. 

Symbols of LS coupling are the most frequently used, partly due to the fact that for an overwhelming majority of neutral atoms and ions of moderate ionization degrees, it is closest to reality, partly traditionally. 

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