The astrophysical observations of neutron stars, like the cooling rate and the pulsar frequency glitches, are explained using the phenomena of superfluidity of the neutrons present in them. The pairing of nucleons depends on the nature of the interaction used. When the conventional NN interactions based on phenomenological models are used for nuclear many-body calculations, the results turn out to be model-dependent. In the last few decades, the ideas from Effective Field Theory and Renormalization Group techniques have been used to decouple the low energy degrees of freedom from the high energy physics and develop low momentum interactions. These low momentum interactions are better suited for studying the nuclear many-body problems. We propose to study the superfluid properties of neutron stars, modelled as pure neutron matter, using these RG-based low momentum interactions as inputs at densities relevant to the neutron star.

In this talk we compute the energy per particle for pure neutron matter, including pairing, via the Hartree-Fock-Bogoliubov perturbation theory. We compare our results against many-body perturbation theory and study its dependence on the renormalization scale in order to assess the scale of the missing many-body/medium corrections.