Partial g-Sum Rule, a Tool for Interpreting Impurity Ion Spectra

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Abstract
It is shown that one can define signed g∥ for spaces of atomic wavefunctions characterized by the crystal quantum numbers μ and −μ if these spaces are disjoint with respect to the crystal field interaction. In general, the states in these spaces will be pairwise degenerate and will be split by a magnetic field along the axis of symmetry of the crystal. Within a Russell—Saunders approximation, traces of the Zeeman interaction for each q, μ pair in a given JLS multiplet are calculated, where q is related to the q‐fold field of the point group symmetry of the crystal field. The partial g‐sum rule, that these traces are approximately invariant even when substantial term and J mixing are present, is tested by comparing various g sums to theoretical and experimental results reported in the literature. It is shown that the partial g‐sum rule provides a useful tool that can aid in the analysis of spectra without resorting to involved calculations. Examples of such applications are discussed, and tables are given for the partial g sums for each q, μ pair over every J multiplet of the terms in pn, dn, and fn configurations.