In the framework of the first Born approximation, we present a semirelativistic theoretical study of the inelastic excitation (1s_{1/2} → 2s_{1/2}) of hydrogen atom by electronic impact. The incident and scattered electrons are described by a free Dirac spinor and the hydrogen atom target is described by the Darwin wave function. Relativistic and spin effects are examined in the relativistic regime. A detailed study has been devoted to the nonrelativistic regime as well as the moderate relativistic regime. Some aspects of this dependence as well as the dynamic behavior of the differential cross-section in the relativistic regime have been addressed.
compared to experiment. Recent corrections from radiative recoil of order α(Zα)^{5}m^{2}/M and pure recoil of order (Zα)^{6}m^{2}/M are reviewed. Contributions of order α^{2}(Zα)^{5}m have been calculated from certain classes of diagrams. These are described while other as yet uncalculated terms are mentioned. The largest error in the theory is the uncertain measured value of the proton electromagnetic radius.
We consider the one- and two-photon e^+e^- annihilation processes in an ultra-strong magnetic field, at middly relativistic regime. Such conditions are reached in neutron stars and especially in magnetars, where electrons and positrons flow within the magnetar corona with average momenta of the order of pım m_0c, where m_0 - electron mass, c - light speed. We pay special attention to the ratio of the total annihilation rates of both processes. The well-known result is that in the limit p → 0 and for magnetic induction above the critical Schwinger value B_0=4.41× 10^9 T, one-photon annihilation dominates over the two-photon process. Results presented in this article verify the current knowledge about this ratio in magnetars; the calculations indicate that for particles moving with middly relativistic momenta both processes can be equally important.
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