  Dark matter (DM) may be captured around a neutron star (NS) through
DM-nucleon interactions. We observe that the enhancement of such capturing is
particularly significant when the DM velocity and/or momentum transfer depend
on the DM-nucleon scattering cross-section. This could potentially lead to the
formation of a black hole within the typical lifetime of the NS. As the black
hole expands through the accretion of matter from the NS, it ultimately results
in the collapse of the host. Utilizing the existing pulsar data J0437-4715 and
J2124-3858, we derive the stringent constraints on the DM-nucleon scattering
cross-section across a broad range of DM masses.
