We discuss the issue on dark matter capture by neutron stars, in particular the process of dark matter thermalization, by which the scattering cross section and the mass of dark matter can be constrained. At first, we evaluate the thermalization time of self-interacting dark matter and find the effect of the self-interaction is small compared with that of the interaction with nucleons. Then we generalize the thermalization time by introducing a set of new parameters. We show how the cross section is affected by those new parameters. It turns out that the cross section gets very sensitive to and strongly constrained by one of the new parameters.
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