Abstract
A variational treatment is applied to the multimode Jahn-Teller effect of an impurity ion in a crystal. The case treated is an electronic doublet. For vibronic coupling to modes in a sufficiently narrow frequency range a single-effective-frequency description is shown to be adequate for the ground state of the system. For coupling to modes whose frequencies are very different (e.g., acoustic- and optical-phonon modes) a two-effective-frequency description is preferred. Expressions are derived for the best (in the variational sense) frequencies and coupling strengths of the effective modes. A solution is given for the linear-coupling problem between an electronic doublet and two vibrational doublets, in the limit of strong coupling. The reduction factors for external perturbations and the coupling to strain are evaluated.
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