A Method for Solving Combined Spin-Orbit and Jahn-Teller Coupling and Application to⁴T₂of KMgF₃: V²⁺

Abstract

A method for solving the problem of combined spin-orbit and Jahn-Teller coupling is introduced in the case of an electronic triplet state coupled to a vibration of e mode in cubic symmetry. In this approach a simple recursion relation systematically provides basis functions which are very useful in reducing the size of the Hamiltonian matrix to be diagonalized numerically. As an example of application, the level splitting and optical intensity of the zero-phonon line have been calculated for 4 A 2 → 4 T 2 transition of V 2+ ion in KMgF 3 , and good agreement with experiment has been found.