Limitations on the validity of impulse approximation in Compton scattering

Abstract

The validity of impulse approximation (IA), which is commonly used in the description of Compton scattering of photons from atomic electrons, is discussed with particular attention to the kinematical region in which the photon momentum transfer k is not much larger than the average bound electron momentum a of a given shell. IA can be justified in the Compton peak region of the spectrum if a/k << 1. However, for the doubly differential cross-section of photon-atom scattering (ejected electrons not observed) IA is commonly used, and viewed as adequate, while only requiring that a/k < 1. In addition to a general discussion of the validity of IA (and the relativistic version RIA) for doubly and triply differential cross-sections, in this paper, we are particularly concerned with (1) the asymmetry around the IA peak of the Compton profile and (2) the contribution of the <(p)over right arrow> center dot (A) over right arrow interaction term (neglected in IA) in the peak region for a/k < 1. We argue that the observed asymmetry of the Compton profile is to a large extent just a shift of the IA profile. We find that <(p)over right arrow> center dot (A) over right arrow contribution to the peak region for a/k approximate to 1 is important only for scattering from high Z K-shells