Compton scattering in strong magnetic fields

The relativistic cross section for Compton scattering by electrons in strong magnetic fields is derived. The results confirm and extend earlier work which has treated only transitions to the lowest or first excited Landau levels. For the teragauss field strengths expected in neutron star magnetospheres, the relative rates for excited state transitions are found to be significant, especially for incident photon energies several times the cyclotron frequency. Since these transitions must result in the rapid emission of one or more cyclotron photons as well as the Compton-scattered photon, the scattering process actually becomes a photon 'splitting' mechanism which acts to soften hard photon spectra, and also provides a specific mechanism for populating higher Landau levels in the electron distribution function. The results should be significant for models of gamma-ray bursters and pulsating X-ray sources.