Effective operators for p admixtures into the f shell for the rare-earth elpasolites

Abstract

A two-electron effective operator V 2 is constructed to reproduce, to lowest order of perturbation theory, the effect of p-electron admixtures in configurations of f electrons occurring in rare-earth ions located at octahedral sites in elpasolite crystals. These admixtures can arise from excitations of the type f → p as well as p → f, the latter including electron transfer from neighbouring ligands to the central rare-earth ion. The effective operator is decomposed into nine orthogonal components . For octahedral symmetry their strengths are specified by coefficients that depend on just two parameters. The insensitivity of the crystal splitting of of to some , as found by McCaw and Denning, is related to exceptionally small values of the corresponding reduced matrix elements of . The discrepancies that these authors have found in fitting their experimental data for other levels to the standard one-electron crystal-field Hamiltonian V 1 are examined. The effective operator V 2 is found to reproduce the general trends of these discrepancies provided allowance is made for transitions of the type f ← f ′ which are implicit in the spin-correlated crystal-field model.