Scattering tensors and Clebsch-Gordan coefficients in crystals

Abstract

This paper is concerned with the relationship between the scattering tensors for the Raman (inelastic) scattering of light by phonons, or other excitations in a crystal, and the crystal-space-group Clebsch-Gordan coefficients. It is proven that the elements of the first-order scattering tensors are a prescribed linear combination of Clebsch-Gordan coefficients; the elements of the second-order scattering tensors are a prescribed bilinear combination of Clebsch-Gordan coefficients.