Rayleigh scattering of two x-ray photons by an atom

Abstract

The process of elastic (Rayleigh) scattering of two x-ray free-electron laser (XFEL) photons by a free He atom is theoretically investigated. We obtain the absolute values and the forms of the triple differential scattering cross section. The main theoretical result is the highest probability of creation of scattered photons with energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\cong}\ensuremath{\hbar}\ensuremath{\omega}\ifmmode\pm\else\textpm\fi{}{I}_{1s}$ $(\ensuremath{\hbar}\ensuremath{\omega}$ is the energy of the incident XFEL photon, ${I}_{1s}$ is the energy of the ionization threshold of the $1{s}^{2}$ atomic shell). The probability of creation cooled $(l{\ensuremath{\omega}}_{\ensuremath{-}})$ and hot $(g{\ensuremath{\omega}}_{+})$ photons is smaller by many orders of magnitude, and is identically zero when the formal (nonphysical) energy of one of the scattered photons is $2\ensuremath{\hbar}\ensuremath{\omega}$.