Abstract A new spectrum function is obtained by use of the Compton scattering cross section in the laboratory frame derived earlier. This spectrum function, besides some modifications in the coefficients of the resonant term, contains also a non-resonant term which is inversely proportional to the square of the magnetic field. Based on this spectrum function, the hardening of thermal photons through inverse Compton scattering by relativistic electron beams on the surface of a strongly magnetized neutron star is investigated. Two new features are found. First, there is a maximum scattered photon energy for a given resonant scattering, beyond which resonance disappears. This maximum depends on the electron energy and the magnetic field, but is independent of the incident photon energy. Second, beyond each resonant scattering, there is a high-energy tail, resulting from non-resonant scattering. It is also found that all the tails have a common upper limit which is the highest scattered photon energy for the given incident photon and electron energies. These two new features are absent in the Monte Carlo simulations and therefore, may have physical implications for γ-ray emissions.

Keywords stars: neutron star --- magnetic fields --- scattering --- gamma rays

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