Threshold singularities of the x-ray Raman scattering in metals

Abstract

We study the theory of x-ray Raman scattering involving the virtual excitation of a deep-core-state hole in a metal. In the intermediate state the conduction electrons experience a transient potential due to the temporary appearance of the core hole; the resulting "final state" interactions determine the singular behavior of the scattering rate near threshold just as they do in x-ray absorption or emission. This is described using a time representation of perturbation theory in the Kjeldysh formalism which permits an exact determination of the power law of the threshold singularities. We discuss the role of lifetime effects and the distinction between scattering and fluorescence. We discuss at length the role of interference between different intermediate localized core hole sites. If we neglect interference effects we can give an expression for the scattering rate which is suitable for computing. We are unable to solve the coupled Dyson equations when interference is included; in that case we give only qualitative results and discuss the interplay of interference and lifetime effects, especially in the fluorescence case where the final-state interactions tend to destroy interference in the long-lifetime limit.