Russell-Saunders coupling for

Note that we have ignored spin. If we include spin, then the following rules become a complete set (at least for Russell-Saunders coupling for the one-electron atom) ... 

A second approximation neglects coupling between the spin of an electron and its orbital momentum but assumes that coupling between orbital momenta is strong and that between spin momenta relatively weak but appreciable. This represents the opposite extreme to the 77-coupling approximation. It is known as the Russell-Saunders coupling approximation and serves as a useful basis for describing most states of most atoms and is the only one we shall consider in detail. 

The bond diagrams provide an obvious simple method of determining the allowed spectral terms for equivalent electrons with Russell-Saunders coupling, which may be convenient for the reason that it separates states of different multiplicity at the start. 

Table IV-3.—The Lani> (/-Factor for Russell-Saunders Coupling...

We now consider many-electron atoms. We will assume Russell-Saunders coupling, so that an atomic state can be characterized by total electronic orbital and spin angular-momentum quantum numbers L and S, and total electronic angular-momentum quantum numbers J and Mj. (See Section 1.17.) The electric-dipole selection rules for L, J, and Mj can be shown to be (Bethe and Jackiw, p. 224)... 

For convenience, the states that may arise by Russell-Saunders coupling from all dn configurations are listed in Table 9.1. For quantitative applications of ligand field theory we must know not only the nature of the states but also their relative energies in a particular ion. For a great number of the ions of practical interest these energies are known from experimental measurements. The standard tabulation of such data is C. E. Moore s Atomic Energy Levels. t... 

If the approximation is made that HL > //ER, then we have the reverse of the Russell-Saunders coupling scheme. The individual electron total angular momenta, specified by /, couple together to give the total angular momentum for the set of electrons. The equivalent of equation (33) becomes... 

Relaxation of the rules can occur, especially since the selection rules apply strongly only to atoms that have pure Russell-Saunders (I-S) coupling. In heavy atoms such as lanthanides, the Russell-Saunders coupling is not entirely valid as there is the effect of the spin-orbit interactions, or so called j mixing, which will cause a breakdown of the spin selection rule. In lanthanides, the f-f transitions, which are parity-forbidden, can become weakly allowed as electric dipole transitions by admixture of configurations of opposite parity, for example d states, or charge transfer. These f-f transitions become parity-allowed in two-photon absorptions that are g g and u u. These even-parity transitions are forbidden for one photon but not for two photons, and vice versa for g u transitions [46],... 

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