  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.
