Theory of the Absorption and Emission of theFCenter in Alkali-Halide Crystals

Abstract

The absorption and emission processes of the $F$ center and their relationship to each other are treated using a model which contains many of the features of an exact treatment. The calculations are based on a formulation in which the total energy of the crystal in the ground and excited states is expressed as a function of the variational parameters in the $F$-center wave functions and of the displacements of the neighboring ions. The $F$ electron is treated quantum-mechanically, but classical ionic crystal theory is used for all other terms in the total energy. A modified method of steepest descents is used to minimize the total energy. The electronic structure of the outer shells of the first nearest neighbor ions is taken into account in detail in the expression for the energy of the $F$-center electron. Simple, one-parameter, vacancy-centered wave functions are used to describe the $F$ electron. A large Stokes shift is obtained in all crystals. The distortions are small in the ground state but, in the relaxed excited state, they are of the order of 10% of the nearest-neighbor distance and have a pronounced asymmetry.