X-ray spectra from magnetar candidates. II Resonant cross sections for electron-photon scattering in the relativistic regime

Recent models of spectral formation in magnetars called renewed attention on electron-photon scattering in the presence of ultra-strong magnetic fields. Investigations presented so far mainly focussed on mildly relativistic particles and magnetic scattering was treated in the non-relativistic (Thomson) limit. This allows for consistent spectral calculations up to a few tens of keVs, but becomes inadequate in modelling the hard tails (<200 keV) detected by INTEGRAL from magnetar sources. In this paper, the second in a series devoted to model the X-/soft gamma-ray persistent spectrum of magnetar candidates, we present explicit, relatively simple expressions for the magnetic Compton cross-section at resonance which account for Landau-Raman scattering up to the second Landau level. No assumption is made on the magnetic field strength. We find that sensible departures from the Thomson regime can bealready present at B ~5E12 G. The form of the magnetic cross section we derived can be easily implemented in Monte Carlo transfer codes and a direct application to magnetar spectral calculations will be presented in a forthcoming study.