The relationship between perturbation theory and direct calculations of rare-earth transition intensities

TL;DR

This paper demonstrates the equivalence of three methods for calculating transition line strengths in rare-earth ions, highlighting the complex interplay of spin-orbit and correlation effects in two-photon transitions.

Contribution

It shows the equivalence of different computational methods for transition intensities, clarifying their relationship and the underlying physics in rare-earth ions.

Findings

Three methods yield equivalent transition line strengths.

Spin-orbit and correlation effects significantly influence two-photon transitions.

Simplified calculations reveal the interplay between different physical contributions.

Abstract

We use a simplified calculation to demonstrate the equivalence between three different methods for calculating transition line strengths [B.R. Judd and D. R. Pooler, J. Phys. C 15 (1982) 591; G. W. Burdick and M. F. Reid, Phys. Rev. Lett. 70 (1993) 2491; G. W. Burdick, H. J. Kooy, and M. F. Reid, J. Phys.: Condens. Matter 5 (1993) L323]. These calculations demonstrate the complex interplay between spin-orbit and correlation contributions to two-photon transitions in rare-earth ions.