This paper develops a theory of resonant Raman scattering within the f
ramework of a localized model. Expressions for the scattering amplitud
e and cross section are derived by employing the methods of spherical-
tensor analysis. a simple factorization is obtained for the geometrica
l (angular dependence) and electronic (matrix element) components, whi
ch can therefore be studied independently. Photon polarization effects
are examined. It is shown that, for fast collisions, the integrated i
ntensity is expressible by way of spin and orbital effective operators
, thus allowing for a simple interpretation of the scattering process.
For the 2p-->4f, 3d-->2p resonance in Gd3+, Dy3+, Ho3+ and Er3+, nume
rical calculations of the cross section are discussed. In the case gad
olinium, the agreement between calculations and experiments provides f
urther evidence for the quadrupolar nature of certain spectral feature
s.