# QED Phenomena in an Ultrastrong Magnetic Field. II. Electron-Positron Scattering, $e^\pm$-Ion Scattering, and Relativistic Bremsstrahlung

## TL;DR

This paper calculates quantum electrodynamic processes such as electron-positron scattering and bremsstrahlung in ultrastrong magnetic fields near neutron stars, providing simplified and accurate cross sections relevant for astrophysical phenomena.

## Contribution

It introduces a simplified method for calculating QED processes in ultrastrong magnetic fields, accounting for Landau level truncation and Debye screening effects.

## Key findings

- Accurate differential and total cross sections for electron-positron scattering.
- Simplified calculations valid in magnetic fields $10^3B_Q \,\gg\, B \gg B_Q$.
- Quantitative analysis of Debye screening effects.

## 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.