Resonant scattering tensors in spherical and cubic symmetries

The angular and polarization dependence of resonant scattering of X-rays by spherical atoms, and atoms with the symmetry of one of the cubic point groups, is described by formulae derived from an expansion in tensors of order up to four. At this level of approximation, the scattering can be anisotropic for any crystallographic symmetry. The change of scattering amplitude with Bragg angle is different for different polarization states, even for spherical atoms. The polarization dependence of this scattering offers a new method for estimating this theta dependence.