Multiphonon relaxation of the electronic excitation energy of rare-earth ions in laser crystals

The paper discusses both the linear and nonlinear mechanisms of multiphonon relaxation (MR) transitions in trivalent rare-earth (RE) ions in crystals. In the first well-known case, the linear terms of electron-phonon interaction (EPI) with respect to vibronic coordinates are responsible for MR transitions. In the last case, the nonlinear part of EPI induces the multiphonon relaxation. The expression for total rate of the MR transition due to both mechanisms taken into account was obtained.