Bound-state Compton scattering of linearly polarized photons

We present a theoretical study of Compton scattering of X- and $\gamma$-rays by a $K$-shell electron. Special attention is paid to the double-differential cross section and polarization of the scattered photons for linearly polarized incident photons. To investigate these observables, we employ the scattering matrix (S-matrix) approach based on relativistic Green's functions. The S-matrix results are moreover compared with predictions of the free-electron and impulse approximations, allowing us to assess the role of electron binding effects. Detailed calculations are carried out for hydrogen-like Ne$^{9+}$ and Pb$^{81+}$ targets over a wide range of incident photon energies and scattering angles. The calculations reveal kinematic regimes in which the impulse approximation agrees reasonably well with the S-matrix results. We also explore the polarization of scattered photons for slightly depolarized incident radiation, including the highly sensitive case of scattering at $90^\circ$.