Variational Calculation of the Polarizability of an Electron Trapped by a Point Defect

A variational method is used to determine the polarizability of an electron trapped by a positive point defect in an ionic crystal. The model Hamiltonian describing the interaction between the point defect and an electron in an ionic crystal is related to the model introduced by Simpson to calculate the charge distribution and energy levels of trapped electrons in ionic crystals. However, in the problem considered here, an applied electric field is also present, and consequently a somewhat different model is proposed. The polarizabilities are calculated for both the new model and Simpson's original model, and the results are compared with the results of a theoretical calculation by Adamov, Ledovskaya, and Rebane of the polarizability of an $F$ center in alkali halide crystals. In atomic units, the polarizabilities obtained for the new model range from 227 for NaF to 4280 for LiI.