Systematic differences between beyond K-shell Compton profiles obtained from QED based S-Matrix doubly differential cross sections and those obtained from electron momentum distribution functions.

In this study comparisons are made between Compton profiles (CP) obtained from  full Compton photon scattering S-Matrix doubly differential cross section (DDCS) spectra and those obtained from an electron distribution function (ρ) via J(p_z)=∫_pz ρ(p)pdp, where J represents the CP and p_z denotes the component of the bound state electron momentum along the scattering vector. Good agreement between K-shell CP obtained via the two theories resulted for all atoms tested ranging from very light to the heaviest atoms. However it was found that systematic differences between CP from the two theories occurred for beyond K-shell CP, but only around where p_z≈0. For ns (n>1) subshell CP, those obtained via S-Matrix had a 6-8% lower magnitude at p_z=0  than for those obtained via ρ. Further all np subshell CP generated via ρ were flat on top while those obtained via S-Matrix DDCS had sharp maxima that were about 10-12% greater in magnitude at p_z=0, but were in good agreement on either side of the peak. nd and nf CP generated by the two theories were also found to differ around p_z ≈0 but were in agreement in the tail regions. The present results suggests that there are significant QED factors that contribute to beyond K-shell CPs not accounted for in CP obtained via ρ.