We have calculated the scattering cross section for a third-order process in which a hard x ray incident on an atomic system is absorbed with the emission of two lower-energy x rays. This process is resonant when one of the two lower-energy x rays has an energy equal to the K-shell binding energy. We calculated the resonant term in the scattering with a one-electron model using shielded hydrogenic wave functions. This work was motivated by a recent coincidence inelastic x-ray scattering experiment on copper which claimed to show by such scattering. We find that even at resonance the third-order scattering process is too weak by 3 orders of magnitude to account for the spectral feature which was attributed to it.

• Received 22 October 1986

DOI:https://doi.org/10.1103/PhysRevA.35.3128