We present a theoretical study of the inelastic scattering of vortex electrons by a hydrogen atom. In our study, special emphasis is placed on the effects of the Coulomb interaction between a projectile electron and a target atom. To understand these effects, we construct vortex electron wave functions both from free space and distorted solutions of the Schrödinger equation. These wave functions give rise to the first Born and distorted wave scattering amplitudes, respectively. The derived theory has been employed to investigate the 1s → 2p transition of a hydrogen atom induced by electrons with the kinetic energies in the range from 20 to 100 eV. The results of the calculations have clearly indicated that the Coulomb interaction can significantly affect the phase pattern and probability density of a vortex electron beam as well as the squared transition amplitudes. For the latter, the most pronounced effect was found for the excitation to the |2p m_f=0⟩ sublevel and large scattering angles.

We present a theoretical study of elastic photon scattering by atomic targets. This process is of special interest since various channels from atomic and nuclear physics as well as quantum elctrodynamics (QED) contribute to it. In this work, we focus on Delbr\"uck scattering which proceeds via production of virtual $e^+e^-$ pairs. In particular, we explore whether and how the Delbr\"uck channel can be "seen" in present synchrotron experiments which employ strongly linearly polarized light in the energy range of a few hundred keV. In order to answer this question, detailed calculations have been performed for the scattering of 300 keV and 889.2 keV photons off helium-like tin ions. Based on these calculations, we argue that the Delbr\"uck scattering for the energies below the threshold for $e^+e^-$ pair creation leads to a shift in the angular distribution and the polarization of the scattered photons which can be observed by state-of-the-art solid-state detectors.

We present a theoretical study on the elastic Rayleigh scattering of x-ray photons by closed-shell atoms. Special attention is paid to the transfer of linear polarization from the incident to the outgoing photons. To study this process, we apply the density-matrix formalism combined with the relativistic perturbation theory. This formalism enables us to find general relations between the Stokes parameters of the incident and scattered photons. By using these expressions, we revisit the recent proposal to use Rayleigh scattering for the analysis of the polarization purity of synchrotron radiation. We show that this analysis can be performed without any need for the theoretically calculated scattering amplitudes, if the linear polarization of the scattered light is measured simultaneously at the azimuthal angles ${0}^{\ensuremath{\circ}}$ and ${45}^{\ensuremath{\circ}}$ with respect to the plane of the synchrotron. To illustrate our approach, we present detailed calculations for scattering of 145 keV photons by lead atoms.