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We develop {it ab initio} relativistic QED theory for elastic electron scattering on hydrogen-like highly charged ions for impact energies where, in addition to direct (Coulomb) scattering, the process can also proceed via formation and consequent Auger decay of autoionizing states of the corresponding helium-like ions. Even so the primary goal of the theory is to treat electron scattering on highly charged ions, a comparison with experiment shows that it can also be applied for relatively light ions covering thus a very broad range of the scattering systems. Using the theory we performed calculations for elastic electron scattering on B$^{4+}$, Ca$^{19+}$, Fe$^{25+}$, Kr$^{35+}$, and Xe$^{53+}$. The theory was also generalized for collisions of hydrogen-like highly charged ions with atoms considering the latter as a source of (quasi-) free electrons.
The polarization properties of the elastic electron scattering on H-like ions are investigated within the framework of the relativistic QED theory. The polarization properties are determined by a combination of relativistic effects and spin exchange
Two--photon decay of hydrogen--like ions is studied within the framework of second--order perturbation theory, based on relativistic Diracs equation. Special attention is paid to the effects arising from the summation over the negative--energy (inter
Theoretical predictions for elastic neutrino-electron scattering have no hadronic or nuclear uncertainties at leading order making this process an important tool for normalizing neutrino flux. However, the process is subject to large radiative correc
QED corrections to the $g$ factor of Li-like and B-like ions in a wide range of nuclear charges are presented. Many-electron contributions as well as radiative effects on the one-loop level are calculated. Contributions resulting from the interelectr
Calculations of various corrections to the g factor of Li-like ions are presented, which result in a significant improvement of the theoretical accuracy in the region Z = 6-92. The configuration-interaction Dirac-Fock method is employed for the evalu