Spin-dependent Compton scattering from bound electrons: Quasirelativistic case

Abstract

We have calculated the Compton cross section for scattering of circularly polarized light [$m{c}^2{\left(Z\alpha \right)}^2\ll \hslash \omega <m{c}^2$] from a bound atomic polarized electron. In this analysis the differential cross section includes corrections of order $\frac{\hslash \omega }{m{c}^2}$ and $\frac{p}{\mathrm{mc}}$, where $p$ is the electron momentum. This gives expressions for the cross section which require additional profile functions beyond the usual $J\left(p_z^{\prime }\right)$. 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 $p_z^{\prime }$ in the direction of the momentum transfer, but now they also depend on the scattering angle $\theta$. 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.