  We consider the capture of dark matter (DM) in neutron stars via scattering
on hadronic targets, including neutrons, protons and hyperons. We extend
previous analyses by including momentum dependent form factors, which account
for hadronic structure, and incorporating the effect of baryon strong
interactions in the dense neutron star interior, rather than modelling the
baryons as a free Fermi gas. The combination of these effects suppresses the DM
capture rate over a wide mass range, thus increasing the cross section for
which the capture rate saturates the geometric limit. In addition, variation in
the capture rate associated with the choice of neutron star equation of state
is reduced. For proton targets, the use of the interacting baryon approach to
obtain the correct Fermi energy is essential for an accurate evaluation of the
capture rate in the Pauli-blocked regime. For heavy neutron stars, which are
expected to contain exotic matter, we identify cases where DM scattering on
hyperons contributes significantly to the total capture rate. Despite smaller
neutron star capture rates, compared to existing analyses, we find that the
projected DM-nucleon scattering sensitivity greatly exceeds that of nuclear
recoil experiments for a wide DM mass range.
