Compton scattering from bound electrons is studied within external field quantum electrodynamics and the independent-particle approximation (IPA), but without making use of any additional approximations, such as the impulse or incoherent-scattering factor approximations. Our calculations of the doubly differential cross section for scattering of unpolarized and polarized photons from bound atomic electrons as a function of scattered photon energy and angle are based on a numerical evaluation of the second-order S matrix in self-consistent screened atomic potentials. Such calculations permit the simultaneous discussion of all regions of the Compton spectrum for scattering from any atomic subshell. We present a systematic theoretical investigation of this process for atomic inner subshells at energies where binding effects in these subshells are important. We also discuss the efficient evaluation of the total atom scattering cross section in these cases. For individual subshells, we discuss the applicability of widely used approximate methods with regard to the spectral features they describe. For the K shell, we compare with earlier attempts at calculations within the relativistic S-matrix framework. We also discuss the cross section singly differential in scattered photon angle, emphasizing the contribution of terms neglected when making the incoherent-scattering factor approximation, as well as implications for total cross sections and for attenuation coefficients. Finally we discuss several recent experiments, including the efforts to find the infrared rise for soft photons.

• Received 25 January 1993

DOI:https://doi.org/10.1103/PhysRevA.48.1134