Improved accuracy of Compton profiles obtained from the Compton peak region of full spectrum S-Matrix photon scattering doubly differential cross sections.

A full  Compton photon scattering doubly differential cross section (DDCS) spectrum consists of a Compton peak, an infrared rise and resonances, the later occurring beyond the K-shell. The S-matrix code of Bergstrom et. al. provides such spectra for all atomic subshells. A nonrelativistic expression DDCS=KJ where K is a kinematic factor and J is the Compton profile (CP) is often used to obtain CP from a DDCS spectrum. However this expression is not valid for high photon energies and for the inner and middle shells of moderate to heavy atoms. Here one must use an expression based on the relativistic impulse approximation (RIA). In order to obtain a CP from a DDCS spectrum such an expression must be further approximated so that it is in a DDCS=KJ form.  Unfortunately such an expression to be called RKJ becomes progressively less valid with increasing ejected electron binding energy E_b increasing orbital angular momentum quantum number (l) and increasing photon scattering angle θ. In the present work it is demonstrated that a corrected RKJ expression can yield an accurate CP from the Compton peak region of a full DDCS spectrum even for the inner and middle shells of heavy atoms where the RKJ error is greatest.