One- and two-photon Compton scattering in strong magnetic fields

We calculate the Compton scattering cross section in a very strong magnetic field (B∼${10}^{12}$ G), such as encountered in pulsars, for arbitrary photon and electron energies. We include the effect of the vacuum polarization in the weak-field limit (B≪$m^2$ $c^3$/ħe), as well as the plasma polarizability. We include explicitly radiative transitions between any pair of Landau levels, and include also two-photon scattering. The latter process, due to the presence of the cyclotron resonance, becomes comparable to nonresonant one-photon scattering when excited final states are allowed, and acts as a source of photons which is more important than bremsstrahlung at low plasma densities. The treatment is based on the relativistic S matrix, and the cross sections are averaged over a relativistic Maxwellian electron distribution. The results are compared with previous nonrelativistic calculations, and it is found that even for temperatures as low as 10 keV there are significant effects that are peculiar to the relativistic treatment.