  Considering four known pulsars J1906+0746, J1933-6211, J2043+1711 and the
Vela pulsar, we study the scenario of dark matter (DM) capture in neutron stars
(NSs). For the purpose we choose four well-known relativistic mean field models
to obtain the radius corresponding to the observed mass of these pulsars and
consequently the scattering cross-section of DM with the different particles of
the $\beta$ stable NS matter. The estimated DM-electron scattering
cross-section in this work is stringent compared to the current direct
detection experimental probe. We then compute the lower limit on the halo
velocity of DM for the four pulsars from the knowledge of the upper limit on
effective temperature of the individual pulsars. We also extend our work to
calculate the value of the effective temperature with the different models
using the fitted values of the halo velocity of DM of the four pulsars with
respect to their distances from the galactic center. Our findings are
consistent with the analysis of the observed data.
