High energy gamma rays from old accreting neutron stars

We consider a magnetized neutron star with accretion from a companion star or a gas cloud around it, as a possible source of gamma rays with energy between $100$ $MeV$ and $10^{14}-10^{16}~eV$. The flow of the accreting plasma is terminated by a shock at the Alfv\'en surface. Such a shock is the site for the acceleration of particles up to energies of $\sim 10^{15}-10^{17}~eV$; gamma photons are produced in the inelastic $pp$ collisions between shock-accelerated particles and accreting matter. The model is applied to old neutron stars both isolated or 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 Cherenkov experiments as a possible signature of isolated old neutron stars in dense clouds in our galaxy.