Phonon Sidebands, Multiphonon Relaxation of Excited States, and Phonon-Assisted Energy Transfer between Ions in Solids

A unified treatment is given in the adiabatic approximation for phonon sideband intensities, multiphonon relaxation transition probabilities, and phonon-assisted energy-transfer probabilities. The intensity distribution of phonon sidebands is determined by coupling constants of the vibrational modes with electrons or holes and a criterion for the appearance of discrete sidebands is given. Transition probabilities of multiphonon relaxation processes among various excited levels of an ion are shown to depend exponentially on the energy gap between these levels, in agreement with recent experimental results. A similar dependence is derived for the energy-transfer probabilities between two ions on the energy mismatch between excitation energies of these ions.