Asymmetry and the shift of the Compton profile

Abstract

We show that the conventionally defined asymmetry of the Compton profile (CP) is, to a large extent, simply a shift of CP. Compton scattering is widely used in studying the electron momentum distribution (EMD) of complex systems. Extraction of information about the EMD is based on an impulse approximation (IA) description of the process. In IA the scattering from bound electrons is described as scattering from the EMD of free electrons. Most often the angular and energy distributions of scattered photons (doubly differential cross sections (DDCS)) is measured and presented in terms of CP, which is just the DDCS normalized by a kinematical factor. The deviations of measured CP from the IA results are conventionally described as an asymmetry of CP about the IA peak position. IA predicts CP to be symmetric. We have examined the discrepancy between IA predictions (and the corresponding relativistic version of IA, RIA) and more rigorous approaches ( A 2 and S-matrix), using independent particle approximations for the description of the bound state of electrons. In the nonrelativistic region (in which many measurements of CP are performed) we find that the conventional asymmetry can largely be understood as the shift of the peak position. The true asymmetry with respect to the shifted peak position is in fact much smaller. RIA has similar properties to IA, except that for atoms with high nuclear charge the p ⇒ · A ⇒ interaction may modify the shift and limit the utility of description as a shift.