Dependence of photon-atom scattering on energy resolution and target angular momentum

Abstract

We consider a more correct treatment of photon scattering from randomly oriented atoms, going beyond the level of description used in currently available results. We focus on cross sections which include an elastic scattering component. The most sophisticated results available to describe high-energy elastic scattering are relativistic coherent elastic S-matrix calculations within independent-particle approximation, which, however, perform an averaging over magnetic substates at the level of the amplitude (averaged-amplitude approach), exact only for fully filled subshells. The present S-matrix calculations also do not consider incoherent elastic scattering (in which an electron makes a transition to a different magnetic substate in the same subshell), which can occur when there are partially filled subshells. A more proper treatment of these situations involves an averaging over the cross sections for all possible orientations of the target. Here we consider the total elastic scattering (both coherent and incoherent), and we also include the unresolved contributions of inelastic (Raman and Compton) scattering. In particular we consider inelastic Raman scattering between relativistic subshells that are nearly energy degenerate, which may not be resolved, given finite experimental resolution, and which may be degenerate in nonrelativistic theory (e.g., Coulombic ${2p}_{1/2}$ and ${2p}_{3/2}$ subshells). Thus, for example, the nonrelativistic result for elastic scattering (coherent and incoherent) from excited hydrogen in the $2p$ state corresponds to the result obtained by summing relativistic elastic scattering (coherent and incoherent) together with the relativistic inelastic scattering for transitions between the ${2p}_{1/2}$ and ${2p}_{3/2}$ subshells. The averaged-amplitude approach does poorly in this case. However, results for scattering from ground-state boron indicate that the averaged-amplitude approach generally works well for many-electron ground-state atoms, due to the large coherent contribution from electrons in fully filled subshells.