<p>This dissertation discusses the theoretical methods for quantum scattering in the context of x-ray scattering from electrons and classical scattering in the context of collisions between Rydberg atoms.</p> <p><br></p> <p>A method for describing non-relativistic x-ray scattering from bound electrons is presented. The approach described incorporates the full spatial dependence of the incident x-ray field and is non-perturbative in the incident x-ray field. The x-ray scattering probability obtained by numerical solution for the case of free-electrons is bench-marked with well known analytical free-electron results.</p> <p><br></p> <p>A recent investigation by Fuchs \emph{et al.} [Nat. Phys. 11, 964 (2015)] revealed an anomalous frequency shift of at least 800 eV in non-linear Compton scattering of high-intensity x-rays by electrons in solid beryllium. The x-ray scattering approach described is used to explore the role of binding energy, band structure, electron-electron correlation and a semi-Compton channel in the frequency shift of scattered x-rays for different scattered angles. The results of the calculation do not exhibit an additional redshift for the scattered x-rays beyond the non-linear Compton shift predicted by the free-electron model. </p> <p><br></p> <p>The interference between Compton scattering and nonlinear Compton scattering from a two-color field in the x-ray regime is theoretically analyzed for bound electrons. A discussion of the underlying phase shifts and the dependence of the interference effect on the polarizations of the incident and outgoing fields are presented. </p> <p><br></p> <p>The problem of using x-ray scattering to image the dynamics of an electron in a bound system is examined. Previous work on imaging electronic wave-packet dynamics with x-ray scattering revealed that the scattering patterns deviate substantially from the notion of instantaneous momentum density of the wave packet. Here we show that the scattering patterns can provide clear insights into the electronic wave packet dynamics if the final state of the scattered electron and the scattered photon momentum are determined simultaneously. The scattering probability is shown to be proportional to the modulus square of the Fourier transform of the instantaneous electronic spatial wave function weighted by the final state of the electron.</p> <p><br></p> <p>Collisional ionization between Rydberg atoms is examined. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. The case of exchange ionization is examined and its dependence on the magnitude of angular momentum of the electrons is discussed.</p> <p><br></p>

The newly emerging technology of X-ray free-electron lasers (XFELs) has the potential to revolutionise molecular imaging. XFELs generate very intense X-ray pulses and predictions suggest that they may be used for structure determination to atomic resolution even for single molecules. XFELs produce femtosecond pulses that outrun processes of radiation damage and permit the study of structures at room temperature and of structural dynamics. While the first demonstrations of flash X-ray diffractive imaging (FXI) on biological particles were encouraging, they also revealed technical challenges. In this work we demonstrated how some of these challenges can be overcome. We exemplified, with heterogeneous cell organelles, how tens of thousands of FXI diffraction patterns can be collected, sorted, and analysed in an automatic data processing pipeline. We improved  image resolution and reduced problems with missing data. We validated, described, and deposited the experimental data in the Coherent X-ray Imaging Data Bank. We demonstrated that aerosol injection can be used to collect FXI data at high hit ratios and with low background. We reduced problems with non-volatile sample contaminants by decreasing aerosol droplet sizes from ~1000 nm to ~150 nm. We achieved this by adapting an electrospray aerosoliser to the Uppsala sample injector. Mie scattering imaging was used as a diagnostic tool to measure positions, sizes, and velocities of individual injected particles. XFEL experiments generate large amounts of data at high rates. Preparation, execution, and data analysis of these experiments benefits from specialised software. In this work we present new open-source software tools that facilitates prediction, online-monitoring, display, and pre-processing of XFEL diffraction data. We hope that this work is a valuable contribution in the quest of transitioning FXI from its first experimental demonstration into a technique that fulfills its potentials.

Investigations of soft matter using ultrashort high intensity pulses have been made possible through the advent of X-ray free-electrons lasers. The last decade has seen the development of a new type of protein crystallography where femtosecond dynamics can be studied, and single particle imaging with atomic resolution is on the horizon. The pulses are so intense that any sample quickly turns into a plasma. This thesis studies the ultrafast transition from soft matter to warm dense matter, and the implications for structural determination of proteins.                    We use non-thermal plasma simulations to predict ultrafast structural and electron dynamics. Changes in atomic form factors due to the electronic state, and displacement as a function of temperature, are used to predict Bragg signal intensity in protein nanocrystals. The damage processes started by the pulse will gate the diffracted signal within the pulse duration, suggesting that long pulses are useful to study protein structure. This illustrates diffraction-before-destruction in crystallography. The effect from a varying temporal photon distribution within a pulse is also investigated. A well-defined initial front determines the quality of the diffracted signal. At lower intensities, the temporal shape of the X-ray pulse will affect the overall signal strength; at high intensities the signal level will be strongly dependent on the resolution. Water is routinely used to deliver biological samples into the X-ray beam. Structural dynamics in water exposed to intense X-rays were investigated with simulations and experiments. Using pulses of different duration, we found that non-thermal heating will affect the water structure on a time scale longer than 25 fs but shorter than 75 fs. Modeling suggests that a loss of long-range coordination of the solvation shells accounts for the observed decrease in scattering signal. The feasibility of using X-ray emission from plasma as an indicator for hits in serial diffraction experiments is studied. Specific line emission from sulfur at high X-ray energies is suitable for distinguishing spectral features from proteins, compared to emission from delivery liquids. We find that plasma emission continues long after the femtosecond pulse has ended, suggesting that spectrum-during-destruction could reveal information complementary to diffraction.