K-shell Compton scattering at high photon energy

Abstract

We examine very high energy Compton scattering on bound electrons, comparing cross sections obtained using relativistic impulse approximation RIA to the extreme relativistic ER limit of the exact Coulomb EC results for the 1s electron. For this purpose, in the case of an initial bound s state, we establish analytic expressions, valid within RIA, for the triply differential cross section TDCS, corresponding to the detection of photons and electrons in coincidence, and for the ER limit of TDCS and of photon double-differential cross section DDCS. We find that the RIA-ER expression for DDCS is the product of a simple factor, depending only on the ratio of initial and final photon frequencies, and a function of a single kinematic variable. Since the same structure is displayed by the EC-ER cross section, we present a compact representation of the ER results, in which the main differences between RIA-ER and EC-ER are displayed as a shift of the peak position of the frequency distribution and an asymmetry about that position. The comparison shows to what extent RIA, which becomes exact for vanishing nuclear charge Z, remains a good approximation for low and medium values of Z in the peak region of high-energy Compton scattering.