Resonant Light Scattering and Luminescence in Weakly Coupled Localized Electron-Phonon System

Abstract

The spectrum of resonance Raman scattering is calculated for a system consisting of a localized electron and the lattice vibrations coupled weakly through quadratic interaction. Dynamics of relaxation process in the resonantly excited intermediate state is treated by means of the resolvent expansion method. The structures of successive terms in the expansion are analysed so as to clarify how the multiple phonon scatterings in the intermediate state breed the luminescence character of the spectrum. The whole spectrum consists of a term representing Rayleigh scattering, a term having both characters of Raman scattering and luminescence and terms representing luminescence, corresponding to zero-, one- and multi-step phonon scatterings, respectively. The relation to the phenomenological and stochastic-theoretical treatments of the same problem is discussed. Temperature-dependence of the line shape is calculated numerically for typical cases.