Intra and inter-ionic multiphonon transitions in rare earth doped crystals

A theory has been developed for non-radiative multiphonon transitions in ionic crystals doped by RE-impurities. The degeneration of final electronic states has been taken into account in the framework of the first cumulant approximation. An analytical expression has been obtained for the rate of non-resonant energy transfer caused by electrostatic inter-ionic interaction and numerical estimations for Yb → Tm and Yb → Ho transitions in YAlO₃ and YLiF₄ crystals are listed. The intra-center multiphonon non-radiative relaxation has been considered in the case where acoustical modes of lattice vibrations are the promoting ones.