Theoretical studies of nonradiative 4f–4f multiphonon transitions in dielectric crystals containing rare earth ions

Detailed calculations have been performed of multiphonon relaxation rates of optical excitations in Nd-doped LiYF4 and Pr-doped CsCdBr3 crystals in the frameworks of the exchange charge model of the crystal fields and rigid ion harmonic models of lattice dynamics. It is shown that the empirical energy gap low emerges from the exponential diminishing of spectral densities of n-phonon correlation functions with the increase of an order n. Calculated transition probabilities for 2-, 3-phonon processes agree with experimental data. However, for energy gaps exceeding the maximum phonon energy more than twice, the existing theory which neglects the lattice anharmonicity brings about underestimated relaxation rates.