3-D off-center Li+ rotors in alkali halides: solving for the eigenvalue problem

TL;DR

This paper investigates the quantum eigenstates and eigenvalues of off-center Li+ ions in alkali halides, modeling their complex 3D rotational motion as Mathieu oscillators and including anharmonic vibrational effects.

Contribution

It provides a detailed quantum-mechanical analysis of off-center impurity ion rotations in alkali halides, incorporating Mathieu oscillator models and anharmonic vibrations for the first time.

Findings

Identifies two rotational modes described by Mathieu's equations.

Models the ion's motion as coupled rotations in (x,y) plane and along theta.

Includes anharmonic vibrational mode along z.

Abstract

We are dealing with the long-standing problem of the eigenstates and eigenvalues of 3-D rotators by off-center impurity ions in alkali halides. The ion runs along the brim of a sombrero-like vibronic potential. The quantum-mechanical motion depending on two angular coordinates, we consider the motion along theta at averaged phi, and vice versa. We find the off-center ion performing two rotations: one in (x,y) plane along the azimuth phi and another one along the position angle theta, respectively, which are both described as Mathieu's non-linear oscillators. The motion along z is complemented by an anharmonic vibrational mode.