Compton scattering of photons by inner-shell electrons

Abstract

We have developed an exact second-order S-matrix code for the relativistic numerical calculation of cross sections for Compton scattering of photons by bound electrons within the independent-particle approximation. We find good agreement with less exact treatments in regions where such theories are valid, recovering the impulse approximation and the soft-photon infrared divergence. We do not find agreement with an earlier calculation of Whittingham. We compare with recent scattering experiments in the regime Za(ha)i)~~EB, where we find that the impulse approximation is not adequate.PACS numbers: 32.80.CyWe have developed a code for calculating cross sections for Compton scattering of photons by bound electrons [1]. There has been considerable recent interest [2][3][4][5] in measuring the inelastic (Compton) scattering cross sections on bound atomic electrons, in circumstances in which the composite structure of the initial atomic state modifies the scattering from free particles. Accurate theoretical cross sections for Compton scattering by bound inner-shell electrons are needed as basic data with which experiments may be compared, to provide insight into the nature of the response of the composite system and to separate this process from others of experimental concern. Inelastic scattering from bound inner-shell electrons is important in astrophysical and laser plasmas where ions have only a few electrons remaining and in condensed-matter studies where an accurate knowledge of inner-shell electron Compton profiles permits their separation and so an accurate determination of the properties of valence electrons. The Compton scattering process is one of the few low-order photon-bound-electron interactions that has resisted a reasonably exact treatment. An accurate calculation of Compton scattering requires the evaluation of thousands of slowly converging integrals. Some of the spectra that we present here required several hours of time on a Cray Y-MP supercomputer; such calculations have only recently become feasible. Our approach is exact within the framework of the independent-particle approximation to second-order relativistic external-field quantum electrodynamics. Our calculations use spherically symmetric atomic potentials, both screened (self-consistent) and point Coulombic. We present comparisons with simpler, more approximate calculations, and with experiment. Differences from the widely used simpler approaches are often substantial.The difficulty of performing such calculations of Compton scattering in the past has led to various more approximate theoretical treatments of the process. In the nonrelativistic domain, the interaction Hamiltonian for the electron-photon system is [6] H mt = j e 2 A 2 -ep-A.In this regime, two common approximations are used. One approach that is most widely used is based on the first term (A 2 ) in the nonrelativistic Hamiltonian [7-9]. The other is based on the second or p* A term in the non-relativistic Hamiltonian [10]. The precise criterion of validity of these approaches ...

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