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 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, 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. The formalism employs both the 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. Relatively
compact analytic forms for the cross sections are presented that will prove
useful for astrophysical modelers.Comment: 45 pages, 10 figures, accepted for publication in Phys. Rev.
