Uniform perturbation approach of the theory of one- and two-photon f⇆f transitions

A consistent theoretical background of published approaches, uniform for one- and two-photon electric dipole transitions in rare earth ions in crystals, is presented. Due to the special electronic structure of trivalent rare earth ions, the theoretical description of their spectroscopic properties is based on perturbation theory. In particular, Rayleigh-Schridinger perturbation theory is applied, and the perturbing expansion of the wave functions is limited to second-order corrections. In the discussion of various models of f <-> f transitions special attention is directed to the detailed definition of the Hamiltonian and to partitioning of the space. The general expressions for various kinds of contributions to the transition amplitude are presented, including the perturbing influence of the crystal field potential, electron correlation effects and spin-orbit interaction. (C) 1998 Elsevier Science B.V. All rights reserved.