Abstract
The process of inelastic nonresonant two x-ray free-electron laser (XFEL) photon Compton scattering by a free atom is theoretically investigated. The object of the study is the He atom. We obtain the absolute values and the shape of the double differential scattering cross section. The quantum effect of creation of ``hot'' scattered photons with maximum energy $2\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}{I}_{1s}$ is predicted ($\ensuremath{\hbar}\ensuremath{\omega}$ is the energy of the incident XFEL photon on the atom, and ${I}_{1s}$ is the energy of the ionization threshold of an atomic $1{s}^{2}$ shell).
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