Revisiting the Off-Center Impurity Problem: Reorientational Rates of Hindered Rotators

摘要

The off-center displacements of impurity ions in polar crystals are regarded as hPseudo-Jahn—Teller effect. They are shown to arise from first-order vibronic mixing, while third-order mixing creates barriers for reorientating an off-center impurity. The rotational equation in two dimensions is Mathieu 's equation, with known eigenstates and eigenvalues. Rotational bands are found, allowing for reorientational transitions. Intraband transition probabilities in terms of Mathieu's eigenfunctions and eigenvalues are derived and compared with those based on harmonic-oscillator eigenstates and eigenenergi es. We check the reorientational rates derived by both means against paraelectric resonance data.