Ham factors and energy levels in multimode Jahn-Teller systems

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Abstract
A method of calculating the energy levels and Ham factors of a Jahn-Teller system interacting with many modes of vibration is described. The multimode effect in the ground states is dealt with by first doing a transformation to concentrate most of the Jahn-Teller interaction into an effective cluster Hamiltonian, and then allowing for the remainder by introducing one extra phonon mode at a time. Calculations are done using a numerical perturbation theory: energies are calculated by the Lanczos method of diagonalising large sparse matrices, and the small changes in energy resulting from the introduction of small interactions are used to deduce perturbation parameters. This method is applied to E*( Sigma i epsilon i), with the inclusion of a quadratic Jahn-Teller coupling or warping term. Experimental results on Ni3+:Al2O3 are discussed as an example.

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