Multiphonon relaxation of excited rare-earth ions in ionic matrices

A theory of multiphonon relaxation for rare-earth ions in ionic crystals and glasses is presented. The theory is based on the static coupling scheme. The electron-vibration coupling is assumed to be linear with respect to the relative ligand rare-earth displacements. The multiphonon transitions are induced by higher-order lattice anharmonicity of the ionic motions. The probability of multiphonon transitions could be related to the IR multiphonon spectrum. A simplified form of the general expression is proposed. The electronic part of the expression obtained has exactly the same form as the corresponding expression in the well-known Judd-Ofelt theory for optical transitions between multiplets of rare-earth ions in solids.