Multiphonon relaxation of the energy of electronic excitation in optical crystals doped with rare-earth ions

A review of the theory of multiphonon relaxation is presented. The theoretical analysis of the rare-earth doped oxides and fluorides multiphonon relaxation rates regularities was done considering both the Coulomb interaction between race-earth ion and the Ligands and the corrections to the Coulomb interaction resulting from the spatial distribution of the ligand electronic charge, the energy of exchange interactions, and the contributions from the charge transfer states.