P. Froelich et W. Weyrich, ON THE RELATIVISTIC CORRECTIONS TO THE CROSS-SECTION FOR INELASTIC-SCATTERING OF PHOTONS ON ATOMIC ELECTRONS, Zeitschrift fur Physik. D, Atoms, molecules and clusters, 38(3), 1996, pp. 185-190
The relativistic cross-section for inelastic photon scattering on boun
d electrons is reconsidered, and lowest-order corrections to the sudde
n-impulse approximation are derived. These corrections stem from inclu
ding the presence of the external (Coulombic) field in the electron pr
opagator that propagates the intermediate states of the scattering pro
cess. We find that these corrections are of the order Za with respect
to the result obtained within the impulse approximation, and are an or
der of magnitude larger than the corrections obtained previously by in
clusion of the binding effects in the initial state only.