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

Abstract

We consider the oneand two-photon e+e− annihilation processes in an ultra-strong magnetic eld, at middly relativistic regime. Such conditions are reached in neutron stars and especially in magnetars, where electrons and positrons ow within the magnetar corona with average momenta of the order of p ∼ m0c, where m0 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 B0 = 4.41×10 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.