QED Phenomena in an Ultrastrong Magnetic Field. II. Electron-Positron Scattering, $e^\\pm$-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 $e^\\pm$-ion bremsstrahlung. The evaluation of differential and total cross sections simplifies considerably when the magnetic field lies in the range $10^3B_{\\rm Q} \\gg B \\gg B_{\\rm Q}$, where $B_{\\rm Q} \\equiv m^2/e = 4.4\\times 10^{13}$ G. Then, relativistic motion of $e^\\pm$ 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.