Theory of the Dynamical Jahn-Teller Effect

A theory is given of dynamical effects arising from configurational instability of the Jahn-Teller type due to electronic degeneracy in solid-state impurities or in molecules. The model assumes a bilinear interaction coupling one pair of degenerate electronic states to $n$ pairs of degenerate normal coordinates of lattice vibration in a system possessing a threefold symmetry axis. It is shown that in the strong-coupling approximation two modes of collective motion may be distinguished. In the first mode, the collective energy is small, the collective motion is stabilized by elastic restoring forces, and one angular collective coordinate is separable. In the second mode of collective motion, the collective energy is large, the motion is stabilized by pseudocentrifugal forces, and an additional, pseudoradial collective coordinate is approximately separable. Approximate formulas are given for the energy levels and widths of the second mode. It is suggested that these levels might be observable in solids with appropriate impurities or in molecules.