Nonsequential two-photon absorption in solid Ge irradiated by an intense x-ray free-electron-laser pulse

We theoretically investigate the formation of highly charged ions in a germanium (Ge) solid driven by intense, ultrashort x-ray pulses and its effect on the cross sections for nonsequential two-photon absorption from the K shell. Our investigation is related to an experiment conducted at the Linac Coherent Light Source, in which K alpha fluorescence was measured to identify nonsequential two-photon ionization. When a solid Ge target is irradiated by an intense x-ray free-electron-laser (XFEL) pulse, it undergoes severe ionization and turns into a plasma state. We employ a Monte Carlo molecular-dynamics approach to simulate the time evolution of Ge plasma formation, and the time-dependent configuration-interaction-singles method for cross-section calculations, taking into account various experimental x-ray beam parameters and Ge charge states created during the plasma formation dynamics. We find that under the given experimental condition at a photon energy of 7200 eV, charged ions are formed quickly (the average charge is approximate to +6 at the peak of the pulse and approximate to +10 at the end of the pulse). The cross sections of Ge for nonsequential two-photon absorption, however, turn out to be insensitive to different charge states, and the average value over all computed data is (2.61 +/- 0.05) x 10-59 cm4 s. Our paper proposes a theoretical framework of photoabsorption cross-section calculations under the influence of plasma formation, when a solid target is employed in XFEL experiments.