The extreme conditions in Neutron Stars make them ideal test facilities for fundamental interactions.
A Neutron Star can capture Dark Matter via scattering. As a result of the scattering, Dark Matter kinetic energy is transferred to the star.
An observational consequence of this can be the warming of old neutron stars to near-infrared temperatures.
Different approximations or simplifications have been applied to previous analyses of the capture process.
In this article, we summarise a significantly improved treatment of Dark Matter capture, which properly accounts for all relevant physical effects over a wide range of Dark Matter masses.
Among them are gravitational focusing, a fully relativistic scattering treatment, Pauli blocking, neutron star opacity and multiple scattering effects.
This paper cites general expressions that allow the capture rate to be computed numerically, and simplified expressions for particular types of interactions or mass regimes, which greatly increase the efficiency of computation.
As a result of our method, we are able to model the scattering of Dark Matter from any neutron star constituent as well as the capture of Dark Matter in other compact objects.
Our results are applied to scattering of Dark Matter from neutrons, protons, leptons and exotic baryons.
For leptonic targets, we find that a relativistic description is essential. In our analysis of the capture of Dark Matter in Neutron Stars, we include two important effects that are generally ignored by most studies.
Because the scattering of Dark Matter with nucleons in the star exhibits large momentum transfers, the nucleon structure must be considered via momentum-dependent hadronic form factors.
Moreover, because of the extreme densities of matter inside Neutron Stars, we should consider nucleon interactions instead of assuming all nucleons are a perfect Fermi gas.
Taking into account these effects results in a decrease of up to three orders of magnitude in the dark matter capture rate.

The potential Neutron Star sensitivity to DM-lepton scattering cross sections is much greater than electron-recoil experiments, particularly in the sub-GeV regime, with a sensitivity to sub-MeV DM well beyond the reach of future terrestrial experiments.
We also present results for DM-Baryon scatterings in Neutron Stars, where the sensitivity is expected to exceed that of current DD experiments for spin-dependent cases across the entire mass range, and for spin-independent cases across the high and low mass ranges.