QED Phenomena in an Ultrastrong Magnetic Field. II. Electron–Positron Scattering, e ± –Ion Scattering, and Relativistic Bremsstrahlung

Abstract

This paper continues the approach of Kostenko & Thompson to calculating quantum electrodynamic processes in the ultrastrong magnetic field near some neutron stars, such as magnetars or merging binary neutron stars. Here we consider electron–positron scattering, the Coulomb scattering of electrons and positrons off ions, and relativistic e ± –ion bremsstrahlung. The evaluation of differential and total cross sections simplifies considerably when the magnetic field lies in the range 10 3 B Q ≫ B ≫ B Q , where B Q ≡ m 2 / e  = 4.4 × 10 13 G. Then, relativistic motion of e ± is possible even when restricted to the lowest Landau state. Accurate results for differential and total cross sections are obtained by truncating the sum over intermediate-state Landau levels and otherwise disregarding terms inversely proportional to the magnetic field, which are complicated enough to have inhibited previous attempts to calculate magnetic electron–positron scattering and relativistic bremsstrahlung. A quantitative account is made of the effects of Debye screening.