Revisiting the Off-Center Impurity Problem: Reorientational Rate by Mathieu Functions

摘要

We revisit the quantum mechanical problem of an off-centered impurity in an alkali halide crystal by means of the Pseudo-Jahn-Teller Effect. We confirm that while an impurity may be displaced off-center by virtue of first- order vibronic mixing, reorientational barriers hindering the rotation of an off-centered impurity around a lattice site arise by third-order mixing. The eigenvalue equation of a hindered rotation in-plane is Mathieu's equation. We use the exact eigenstates and eigenvalues to derive a reorientational rate. The rate is compared with available paraelectric data on a Li impurity in KCl.