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 ^ { 3 } B _ { Q } \gg B \gg B _ { Q } , where B _ { 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 .