Spin-dependent Compton scattering from bound electrons: Quasirelativistic case

We have calculated the Compton cross section for scattering of circularly polarized light [mc2(Z)2 <mc2] from a bound atomic polarized electron. In this analysis the differential cross section includes corrections of order mc2 and pmc, where p is the electron momentum. This gives expressions for the cross section which require additional profile functions beyond the usual J(pz). The calculation is performed by the expansion of the quantum electrodynamic Hamiltonian to the appropriate order by means of a generalized Foldy-Wouthuysen transformation. In general, the profile functions are no longer a function only of the electron momentum component pz in the direction of the momentum transfer, but now they also depend on the scattering angle. This latter dependence varies with the magnetic quantum number. We discuss the case of electron polarization perpendicular to the plane of scattering and show that for this case a single simple profile function suffices.