Nonlinear Compton scattering from bound electrons

A recent experiment by Fuchs et al.\footnote{\textbf{Nat. Phys.} 11, 964 (2015)} of non-linear Compton scattering revealed an anomalous frequency shift of high-intensity X-rays by electrons in solid beryllium. This frequency shift was at least 800 eV to the red of the values predicted by analytical free-electron models for the same process. Here, we describe a theoretical method for simulating non-linear Compton scattering from bound electrons in a local spherical potential to explore the role of binding energy in the frequency shift of scattered Xrays.\footnote{\textbf{Phys. Rev. A} 101, 013409 (2020)} The calculations do not reveal an additional redshift in the scattered Xrays beyond the nonlinear Compton shift predicted by the free-electron model. Two alternate causes for the anomalous redshift consisting of electron-electron correlation effects and a case of linear Compton scattering from a photoionized electron followed by electron recapture are examined and ruled out.