Shapes of Absorption and Emission Lines of Impurities in Solids

Abstract

Existing treatments of band shapes in solids, for the simplest impurity centers, predict Gaussian shape functions. These treatments assume for simplicity that the electronic matrix element is independent of the nuclear wave functions, and that the energy width of the band is negligible compared with the energy of the mid-point of the band. We estimate here the expected magnitude of the effect of correcting these assumptions in typical cases, and find that the emission or absorption band may deviate from a Gaussian by twenty percent or more on the wings.