Perturbation Calculations ofF-Center Wave Functions with Point Ion and Pseudopotentials

Abstract

The Hartree-Fock scheme and pseudopotential theory are used to derive a simplified wave equation for the calculation of $F$-center wave functions in a static lattice. The ions neighboring the vacancy are either represented by point charges or, for one to fourteen shells, by a localized pseudopotential of the form given by Austin and Heine. In both cases the potential is expanded in terms of Kubic harmonics about the center of the vacancy. The spherically symmetric part of the potential leads to a radial Schrödinger equation, which is solved numerically in integral equation form to give $1s$, $2p$, $3d$, $4f$, and $2s$ bound states. The first nonspherical terms in the potential is applied as a perturbation by means of a technique suggested by Dalgarno. Optical-absorption energies, oscillator strengths, and hyperfine interaction constants are computed for NaCl, KCl, and NaF and are compared with experiment and the previous theory of Gourary and Adrian. The results show that the charge distribution of the $F$ electron is concentrated too strongly at the nearest neighbor positive ions when the first nonspherical term is included in the point-ion potential. Since the pseudopotential for a positive ion has a partly repulsive core, the results obtained by including the pseudopotential are in better agreement with experiment.