Group theoretical selection rules for inelastic neutron scattering with applications to LiNbO3

The one phonon coherent inelastic neutron scattering cross section is analysed in terms of the transformation properties of the phonon polarization vectors. An expression involving characters of point group representations is derived which is zero when the scattering conditions are such that a particular branch of the phonon dispersion curve has zero scattering cross section. This expression is related to Elliott and Thorpe's expression for sums of the scattering over branches with polarization vectors transforming as the same irreducible representation. The selection rules for LiNbO 3 are derived as an example.