Simulation of nonlinear Compton scattering from bound electrons

Recent investigations by Fuchs et al. [Matthias Fuchs, Mariano Trigo, Jian Chen, Shambhu Ghimire, Sharon Shwartz, Michael Kozina, Mason Jiang, Thomas Henighan, Crystal Bray, Georges Ndabashimiye et al., Anomalous nonlinear X-ray Compton scattering, Nat. Phys. 11, 964 (2015)] revealed an anomalous frequency shift in nonlinear Compton scattering 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. In this paper, we describe a method for simulating nonlinear Compton scattering. The method is applied to the case of bound electrons in a local, spherical potential to explore the role of binding energy in the frequency shift of scattered x rays for different scattered angles. The results of the calculation do not exhibit an additional redshift for the scattered x rays beyond the nonlinear Compton shift predicted by the free-electron model. However, they do reveal a small blueshift relative to the free-electron prediction for nonlinear Compton scattering. The effect of electron-electron correlation effects is calculated and determined to be unlikely to be the source of the redshift. The case of linear Compton scattering from a photoionized electron followed by electron recapture is examined as a possible source of the redshift and ruled out.