Model Hamiltonian for Paraelectric Impurities in Alkali Halides

Abstract

Certain dipolar impurities in alkali halides, such as O${\mathrm{H}}^{\ensuremath{-}}$ in KCl, are free to reorient themselves among the six $〈100〉$ directions of the crystal. A one-parameter model Hamiltonian is introduced to describe the properties of such an impurity in the presence of electric and strain fields. Wave functions and energy levels are calculated for fields along the [100], [110], and [111] directions. The susceptibility is calculated for frequencies much smaller or much larger than ${{\ensuremath{\tau}}_{1}}^{\ensuremath{-}1}$, the rate of relaxation to the lattice. Resonance transitions between different energy levels are described and the matrix elements for such transitions are tabulated for several orientations of dc and rf electric fields. A simple theory of line broadening due to inhomogeneous strains is presented and compard with experimental results.