This paper develops a theory of resonant Raman scattering within the framework of a localized model. Expressions for the scattering amplitude and cross section are derived by employing the methods of spherical-tensor analysis; a simple factorization is obtained for the geometrical (angular dependence) and electronic (matrix element) components, which can therefore be studied independently. Photon polarization effects are examined. It is shown that, for fast collisions, the integrated intensity 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 ${\mathrm{Gd}}^{3+}$, ${\mathrm{Dy}}^{3+}$, ${\mathrm{Ho}}^{3+}$, and ${\mathrm{Er}}^{3+}$, numerical calculations of the cross section are discussed. In the case gadolinium, the agreement between calculations and experiments provides further evidence for the quadrupolar nature of certain spectral features. © 1996 The American Physical Society.

• Received 12 March 1996

DOI:https://doi.org/10.1103/PhysRevB.54.16010