The recent observations of soft gamma-ray repeaters and anomalous X-ray pulsars furnish data for greater evidence of the existence of a class of neutron stars with surface magnetic fields exceeding the critical field of 4.4 ten thousand billion Gauss. This research effort seeks to understand the role of strong-field, quantum electrodynamic (QED) processes such as Compton scattering, pair production, photon splitting, and cyclotron and synchrotron radiation in the magnetospheres of neutron stars. In this study, an acceleration model of electrons and positrons will be developed to provide a self-consistent description of the input parameters to a Monte Carlo cascade model that simulates the emission of X-rays and gamma rays from the magnetosphere. The main effort will be to study the role of relativistic Compton scattering as it operates with other QED processes, to develop approximate expressions of the exact QED scattering cross section and incorporate them in a full acceleration-cascade model. Previous studies have assumed that Compton scattering can be adequately described by the non-relativistic Compton scattering cross section (Thomson limit) below resonance and at the resonance, or the Klein-Nishina cross section for scattering above the resonance. Consequently, these studies have not included the effects of the strong magnetic fields. Since these processes are highly dependent upon the polarization of the interacting photons, polarized differential rates for each QED process will be investigated. Pulse profiles as well as phase dependent spectra of the soft gamma-ray repeaters, anomalous X-ray pulsars, the high field gamma-ray pulsars, PSR 1509-58 and PSR 0656+14, along with the Crab, Vela and Geminga pulsars will be simulated and compared with those observed by the Compton Gamma-Ray Observatory (CGRO), the Rossi X-ray Timing Explorer (RXTE) and the Advanced Satellite for Cosmology and Astrophysics (ASCA). The calculated thermal X-ray emission from polar cap heating by pair-created positrons returning to the surface will be compared with the observations of Roentgen Satellite (ROSAT) and upcoming measurements from the Chandra X-ray Observatory that is scheduled to be launched in 1999. The study of the strong field effects on the inverse Compton scattering process will provide insight into the particle-photon interactions associated with a variety of pulsar phenomena, including burst spectra of soft gamma-ray repeaters and the transport of thermal radiation through neutron star atmospheres.
