Scattering operators for E1-E2 x-ray resonant diffraction

Resonant x-ray diffraction in noncentrosymmetric crystals is studied by considering E1-E2 processes in the fast-collision approximation. The scattering amplitude is expressed in terms of polar and magnetoelectric operators of the valence states, which are involved in the resonance. Near-edge Bragg peaks from ferroelectric, antiferroelectric, and magnetoelectric structures are predicted.