  Correlated basis function perturbation theory and the formalism of cluster
expansions have been recently employed to obtain an effective interaction from
a state-of-the-art nuclear Hamiltonian. We report the results of a study of the
superfluid gap in pure neutron matter, associated with formation of Cooper
pairs in the $^1S_0$ sector. 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 realistic microscopic model. Our results
show that the superfluid transition occurs at densities corresponding to the
neutron star inner crust, and that inclusion of three-nucleon interactions
leads to a sizable reduction of the energy gap at the Fermi surface.
