Scattering delle particelle di materia oscura nelle stelle di neutroni: analisi del rate di cattura per diversi operatori

Neutron stars are the densest objects known in the Universe and provide a unique environment to test fundamental properties of matter under extreme conditions. Therefore, they can offer an important cosmic laboratory to also study the nature of dark matter particles and their interactions. If dark matter particles couple to visible matter, they will scatter off the constituents of stars and the accumulation of dark matter in stars has a range of potentially observable consequences, such as the collapse of neutron stars to black holes or a modification of the rate of neutron star mergers. In this master thesis project I present an improved treatment of dark matter capture, valid for a wide dark matter mass range that properly incorporates many of the important physical effects: gravitational focusing, Pauli blocking and a fully relativistic scattering treatment. The approximations used to derive the expressions are valid when the differential cross section depends on powers of the Mandelstam variable t, but not on the centre of mass energy s. The aim of my project is to evaluate numerically the capture rate, for different operators for the scattering of Dirac dark matter from nuclei. This formalism is applicable to the scattering of dark matter from any neutron star constituents, or to the capture of dark matter in other compact objects.