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 Schrödinger 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 $500\text{eV}$ 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 naïvely expected mechanisms pertaining to the lowest order of perturbation theory. Subsequently, we apply our model to XNLC in helium at $4.0\text{keV}$ photon energy and beryllium at $9.7\text{keV}$. 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.

• Received 13 September 2017
• Revised 21 May 2018

DOI:https://doi.org/10.1103/PhysRevA.99.022120