Electron-Positron Annihilation in Ultra-Strong Magnetic Fields. Comparison of One- and Two-Photon Annihilation at Middly Relativistic Regime

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 p~$m_0c$, 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.