Time-dependent QED approach to x-ray nonlinear Compton scattering

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Motivated by a recent experiment [Fuchs et al., Nat. Phys. 11, 964 (2015)], we theoretically investigate the process of x-ray nonlinear Compton scattering (XNLC). Our approach is based on the time-dependent Schr\"odinger equation for an atomic system subject to an intense x-ray pulse, and explicitly accounts for the spontaneous scattering into a quantized photonic mode. We employ our framework to study multiple nonlinear scattering scenarios. Initially, we consider soft x rays at 5000.16em0exeV photon energy to scatter nonlinearly off a helium target. For this, we find that XNLC is dominated by certain third-order processes rather than the na\"{}vely expected mechanisms pertaining to the lowest order of perturbation theory. Subsequently, we apply our model to XNLC in helium at 4.00.16em0exkeV photon energy and beryllium at 9.70.16em0exkeV. Contrary to the conclusions drawn from the experimental observations, our results suggest a good agreement of the XNLC spectrum with simple, free-electron model predictions. Moreover, our studies reveal striking qualitative similarities of linear and nonlinear Compton scattering cross sections in this regime.