Abstract
A general theory of second-order vibronic reduction factors for degenerate electronic states of impurity systems is presented. The analysis is based entirely on symmetry arguments. It is shown that it is necessary to evaluate only the sums of overlaps (in reduced matrix form) between the appropriate oscillator ground state and the symmetry-adapted oscillator excited states to obtain expressions for the second-order reduction factors. These expressions are derived for perturbations of the same and mixed symmetries labelled by their symmetry properties and cover orbital doublet and triplet states. In addition, the analysis allows for coupling to vibrations of all symmetries. The results are illustrated by the example of spin-orbit coupling as the perturbation acting within an orbital triplet system and between the ground vibronic states and those of an inversion level if present. The specific case of a T(X)e system is considered in detail using projection operator techniques. The expressions obtained are compared with the results reported originally by Ham (1990) and exact agreement is found. This serves to illustrate how the method can be applied to other more complicated systems.
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