Multiphonon decay of excited states of rare earth ions in crystals

Abstract

Although the relaxation of excited electronic states through radiationless multiphonon processes has been well established by experiment, there are several serious problems concerning the current theoretical model in which the electron-phonon interaction is treated as a small perturbation, and the multiphonon transitions are attributed to high order expansion terms of perturbation theory. Here, we approach the problem in the framework of the adiabatic approximation. The rate of the multiphonon process is expressed in the form of the linear response time correlation function which is then evaluated by means of the saddle point approximation. The resulting expression predicts an approximately exponential dependence of the rate on the transition gap and a temperature dependence that agrees quantitatively with experiment.