Calculation of single-beam two-photon absorption transition rate of rare-earth ions using effective operator and diagrammatic representation

Abstract

Effective operators needed in single-beam two-photon transition calculations have been represented with modified Goldstone diagrams similar to the type suggested by Duan et al. [C.-K. Duan, G. Ruan, M.F. Reid, J. Chem. Phys. 121 (2004) 5071]. The rules to evaluate these diagrams are different from those for effective Hamiltonian and one-photon transition operators. It is verified that the perturbation terms considered contain only connected diagrams and the evaluation rules are simplified and given explicitly.