  A sub-solar mass primordial black hole (PBH) passing through a neutron star,
can lose enough energy through interactions with the dense stellar medium to
become gravitationally bound to the star. Once captured, the PBH would sink to
the core of the neutron star, and completely consume it from the inside. In
this paper, we improve previous energy-loss calculations by considering a
realistic solution for the neutron star interior, and refine the treatment of
the interaction dynamics and collapse likelihood. We then consider the effect
of a sub-solar PBH population on neutron stars near the Galactic center. We
find that it is not possible to explain the lack of observed pulsars near the
galactic center through dynamical capture of PBHs, as the velocity dispersion
is too high. We then show that future observations of old neutron stars close
to Sgr A* could set stringent constraints on the PBHs abundance. These cannot
however be extended in the currently unconstrained asteroid-mass range, since
PBHs of smaller mass would lose less energy in their interaction with the
neutron star and end up in orbits that are too loosely bound and likely to be
disrupted by other stars in the Galactic center.
