title: Calculation of single-beam two-photon absorption rate of lanthanides: effective operator method and perturbative expansion.
abstract: Perturbative contributions to single-beam two-photon transition rates may be divided into two types. The first, involving low-energy intermediate states, require a high-order perturbation treatment, or an exact diagonalization. The other, involving high-energy intermediate states, only require a low-order perturbation treatment. We show how to partition the effective transition operator into two terms, corresponding to these two types, in such a way that a many-body perturbation expansion may be generated that obeys the linked cluster theorem and has a simple diagrammatic representation.
authors.affiliation: Institute of Applied Physics and College of Electronic Engineering, Chongqing University of Post and Telecommunications, Chongqing 400065, China.
authors.forename: Chang-Kui
authors.initials: CK
authors.lastname: Duan
authors.forename: Gang
authors.initials: G
authors.lastname: Ruan
authors.forename: Michael F
authors.initials: MF
authors.lastname: Reid