We consider a magnetized neutron star with accretion from a companion star or a surrounding gas cloud as a possible source of gamma rays with energies between 100 MeV and 105-107 GeV. The flow of the accreting plasma is terminated by a shock at the Alfvén surface. Such a shock is the site for the acceleration of particles up to energies of ~106 -108 GeV; gamma photons are produced in the inelastic p-p collisions between shock-accelerated particles and accreting matter. The model is applied to old neutron stars, both isolated and in binary systems. The gamma-ray flux above 100 MeV is not easily detectable, but we propose that gamma rays with very high energy could be used by Cerenkov experiments as a possible signature of isolated, old neutron stars in dense clouds in our Galaxy.
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