Couplings For Two-Electrons Configurations

Magnetic and spectroscopic properties of free atoms depend on the interplay of the interactions Hi and H2, since they determine the magnetic moment and the energy spectrum of the atom. Models of this interplay (coupling models) are assumed for lanthanide and d-transition elements. We shall examine in a simple way possible couplings, and point out the difficult case of actinide atoms. 

In first-order perturbation theory (and restricted for simplicity, to two-electron configurations) the Eq. (9) is simplified if it is possible to neglect one of the two terms Hi or H2 as a perturbing term (this is of course possible if the two differ greatly in magnitude). Three cases may therefore be distinguished (couplings)  

In this case, the energy matrices are diagonal only in J and Mj and are independent of Mj. Consequently, it is impossible to define a coupling in the configurations under discussion. The lack of a definite coupling is referred to as intermediate coupling. 

If the atom or ion is situated in an environment of different atoms or ions, as, for instance, ions in a soUd, the surrounding hgands exert on it a further interaction, which is called the crystal field interaction Hcp and enters Eq. (9). One has to compare Hcf with Hi and H2, in order to decide whether it is or not a small perturbative term. In actinide solids, it is usually found that Hcf is of the same order of magnitude as Hi and H2, so that intermediate coupling schemes are necessary which include Hcf as well. (For a more exhaustive treatment of couplings in actinides, see Chap. D.) 

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