Theory and Simulations of Time-Resolved X-Ray Scattering

Recent advances in the preparation of intense and ultrafast hard X-ray pulses permit the observation of dynamical changes in atoms and molecules in real time via non-resonant scattering. The analysis and interpretation of these experiments, however, require a sound and elaborate theoretical framework as well as advanced numerical simulations. In this doctoral thesis, the quantum electrodynamical description of time-resolved non-resonant X-ray scattering by atoms and molecules in non-stationary states is reviewed. A unified and coherent rederivation is presented. Different contributions to the scattering signal are identified and discussed. Particular attention is paid to inelastic scattering and to scattering related to electronic coherences. A general analytic solution to one-electron scattering matrix elements of the hydrogen atom is derived. These solutions allow a computationally efficient and mathematically exact evaluation of the X-ray scattering signal of the atom in any non-stationary state. Based on the developed framework, the time-resolved X-ray scattering signals of two systems are simulated. First, the analytic solutions are applied to an electronic wave packet of the hydrogen atom. Previously published results that involved numerical integration are reproduced. It is shown that the time-dependence of the scattering signal stems solely from the contributions related to the electronic coherence, whereas the elastic and inelastic signals are independent of time. The effect of the pulse duration on the X-ray scattering signal is revised and explained differently than in the published work. It is shown that the existence of an optimum pulse duration at which the scattering signal displays the strongest time-dependence is entirely due to a restriction on the range of photon energies that are accepted by the detector. Second, the scattering signal of the hydrogen molecule subsequent to UV excitation from its X¹Σ⁺_g ground state to its B¹Σ⁺_u excited state is simulated. To the best of the author’s knowledge, this is the first full simulation of two-dimensional time-resolved X-ray scattering patterns of a molecule. All contributions to the scattering signal are evaluated. The separability of the contribution related to the electronic coherence from the total scattering signal is discussed.