Superfluid Gap in Neutron Matter from a Microscopic Effective Interaction

Correlated Basis Function (CBF) perturbation theory and the formalism of cluster expansions have been recently employed to obtain an effective interaction from a nuclear Hamiltonian strongly constrained by phenomenology. We report the results of a study of the superfluid gap in pure neutron matter, associated with the formation of Cooper pairs in the ${}^1{S}_0$ channel. The calculations have been carried out using an improved version of the CBF effective interaction, in which three-nucleon forces are taken into account using a microscopic model. Our results show that a non-vanishing superfluid gap develops at densities in the range $2 \times 10^{-4} \lesssim \rho/\rho_0 \lesssim 0.1 $,where$\rho_0 = 2.8 \times 10^{14}$gcm$^{-3}$ is the equilibrium density of isospin-symmetric nuclear matter, corresponding mainly to the neutron star inner crust.