Theory of Vibrational Structure in Optical Spectra of Impurities in Solids. I. Singlets

Abstract

General expressions are derived describing the modifications of the optical spectra of isolated impurities induced by the subclass of interactions with host-lattice phonons which shift the energy eigen-values of the internal impurity state but which do not mix those internal states. The results apply to localized phonon modes as well as to extended modes (whose individual coupling decreases with increasing lattice volume), to anharmonic- as well as harmonic-phonon systems, and to phonon-impurity couplings which need not be linear in the dynamic local strain field. They take the form of ``linked-cluster'' expansions which, in the linear-coupling harmonic-phonon case, terminate after the second term. The relation of these expansions to moment methods is indicated. As a simple application of the linked-cluster expansions, we compute the dependence of the sharp ``no-phonon'' spectral line on impurity mass. We conclude that the no-phonon line should not exhibit isotopic-mass displacements in those impurity sites for which the lattice is inversion symmetric.