Band structure approach to the resonant x-ray scattering

We study the resonance behaviour of the forbidden 600 and 222 x-ray Bragg peaks in Ge using LDA band structure methods. These Bragg peaks remain forbidden in the resonant dipole scattering approximation even taking into account the non local 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 behaviour, including the phase of the scattering, is a direct measure of this p-d hybridization.and obtain quantitative agreement with experiment. A simple physical picture involving a product of dipole and quadrupolar transition matrix elements explains this behaviour and shows that it should be generally true for cases where the resonating atom is not at an inversion center. This has strong implications for the description of the resonance behavior of x-ray scattering in materials where the resonant atom is not at an inversion center such as V2O3 and in ferro and antiferro electric and piezo electric materials in general.