  As first shown by Shvartsman (1970), a neutron star accreting close to the
Eddington limit must acquire a positive charge in order for electrons and
protons to move at the same speed. The resulting electrostatic field may
contribute to accelerating positrons produced near the star surface in
conjunction with the radiative force. We reconsider the balance between energy
gains and losses, including inverse Compton (IC), bremsstrahlung and
non--radiative scatterings. It is found that, even accounting for IC losses
only, the maximum positron energy never exceeds $\approx 400$ keV. The
electrostatic field alone may produce energies $\approx 50$ keV at most. We
also show that Coulomb collisions and annihilation with accreting electrons
severely limit the number of positrons that escape to infinity.
