A. Leonov, D. Ksenzov, A. Benediktovitch, I. Feranchuk, U. Pietsch
Time evolution of the electron density and the resulting time dependence of X-ray diffraction peak intensity in a crystal irradiated by the highly intense femtosecond pulses of an XFEL is investigated theoretically on the basis of rate equations. In the fs time range the atomic positions are frozen and the main source of variation is the electronic excitation and Auger recombination of bound electrons induced by the X-ray beam. In contrast to the case of isolated molecules and clusters unbound electrons play an essential role in the time evolution of electron density. Therefore additional terms such as electron-impact ionization, electron-electron scattering and three-body recombination have been implemented to the rate equations. The kinetics of the electron gas in the medium is described by the Boltzmann equation that is included in the system of rate equations. An effective algorithm for the numerical solution of rate equations is achieved considering analytical expressions for the cross sections of all electron configurations in ions derived within the framework of effective charge approximation. Using this approach we evaluate the time dependence of inner shell population and electronic kinetic energy during the time of XFEL pulse propagation through the crystal for photon energies of 3 and 8 keV and pulse width of 40 fs at flux of 10^12 ph/pulse. The time evolution of the atomic scattering factor and its fluctuation is numerically analyzed for the case of a Silicon crystal. As a result, we find a decrease of bound electron density during the pulse propagation. The amount of unbound electrons is higher for photon energy closer to the K-edge. As a consequence, the atomic form factor and subsequently the X-ray diffraction intensity alters during the propagation of XFEL pulse through the crystal.
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http://arxiv.org/abs/1302.4848
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