Theoretical description of the spectroscopic properties of rare earth ions in crystals

Abstract

In this article the present state of knowledge of the theory of one- and two-photon processes observed in rare earth ions in crystals is presented. The conclusions are based on the results of ab initio calculations performed for various ions across the lanthanide series. The model applied for the calculations is based on the Rayleigh–Schrödinger perturbation theory, and the amplitude of a certain electric dipole transition is expressed in terms of effective operators. The radial integrals of the effective operators are defined by the perturbed functions that contain the perturbing influence of single excitations from the 4f shell to all one-electron states of a given symmetry, discrete and continuum. In this approach the interactions between the 4f N and the excited configurations via the crystal field potential, the electron correlation operator and the spin–orbit interaction operator are discussed; it is believed that the presented theory contains the most important physical mechanisms responsible for the f↔f electric dipole transitions. Two alternative formulations of the theory of one-photon electric dipole transitions are presented. Consequently, the transition amplitude is defined within the standard theory based on the length formula and within a new approach which is based on the velocity form of the electric dipole radiation operator.