Band structure approach to resonant X-ray scattering

We study the resonance behavior of the forbidden 600 and 222 x-ray Bragg peaks in Ge. These peaks remain forbidden in the resonant dipole scattering approximation, even taking into account the nonlocal nature of the band states. However, they become allowed at resonance if the eigenstates of the unoccupied conduction band involve a hybridization of p-like and d-like atomic states. We show that the energy dependence of the resonant behavior, including the phase of the scattering, is a direct measure of this p-d hybridization and obtain quantitative agreement with experiment. We discuss the implications of this to other materials like V2O3 in which the resonating atom is not at a center of inversion symmetry.