Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The relationship between perturbation theory and direct calculations of
  rare-earth transition intensities   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.

31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom