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

Calculations are made of the Compton scattering cross section in a very strong magnetic field, such as encountered in pulsars, for arbitrary photon and electron energies. The effect of the vacuum polarization in the weak-field limit is included as well as the plasma polarizability. Radiative transitions between any pair of Landau levels are included as well as 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.