The quantum electrodynamical (QED) process of Compton scattering in strong magnetic fields is commonly invoked in atmospheric and inner magnetospheric models of x-ray and soft gamma-ray emission in high-field pulsars and magnetars. A major influence of the field is to introduce resonances at the cyclotron frequency and its harmonics, where the incoming photon accesses thresholds for the creation of virtual electrons or positrons in intermediate states with excited Landau levels. At these resonances, the effective cross section typically exceeds the classical Thomson value by over 2 orders of magnitude. Near and above the quantum critical magnetic field of 44.13 TeraGauss, relativistic corrections must be incorporated when computing this cross section. This profound enhancement underpins the anticipation that resonant Compton scattering is a very efficient process in the environs of highly magnetized neutron stars. This paper presents formalism for the QED magnetic Compton differential cross section valid for both subcritical and supercritical fields, yet restricted to scattered photons that are below pair creation threshold. Calculations are developed for the particular case of photons initially propagating along the field, and in the limit of zero vacuum dispersion, mathematically simple specializations that are germane to interactions involving relativistic electrons frequently found in neutron star magnetospheres. This exposition of relativistic, quantum, magnetic Compton cross sections treats electron spin dependence fully, since this is a critical feature for describing the finite decay lifetimes of the intermediate states. Such lifetimes are introduced to truncate the resonant cyclotronic divergences via standard Lorentz profiles. The formalism employs both the traditional Johnson and Lippmann (JL) wave functions and the Sokolov and Ternov (ST) electron eigenfunctions of the magnetic Dirac equation. The ST states are formally correct for self-consistently treating spin-dependent effects that are so important in the resonances. It is found that the values of the polarization-dependent differential cross section depend significantly on the choice of ST or JL eigenstates when in the fundamental resonance but not outside of it, a characteristic that is naturally expected. Relatively compact analytic forms for the cross sections are presented that will prove useful for astrophysical modelers.

• Received 8 July 2013

DOI:https://doi.org/10.1103/PhysRevD.90.043014