Pairing gaps in nucleonic superfluids

Abstract

Singlet S-wave nucleonic superfluids are studied within a microscopic many-body theory that incorporates explicit spatial correlations due to strong short-range repulsive forces as well as the momentum-space pairing correlations of BCS theory. The theory is formulated within the method of correlated basis functions (CBF). Within this scheme, there results a nonlinear problem for the superfluid energy gap that is identical in form to the gap problem of conventional BCS theory. However, the input single-particle energies and pairing matrix elements are dressed by the short-range spatial correlations and accordingly incorporate an important class of medium corrections. The effective pairing force of the theory is finite even if the bare two-nucleon potential contains an infinitely hard core; both the pairing matrix elements and single-particle energies are to be constructed from normal-state CBF matrix elements and may be evaluated by cluster-expansion techniques. The theory is explicated and applied at a variational level that is equivalent to the leading order of a CBF superstate perturbation theory. New results are presented for the 1s 0 pairing gap Δ k F in pure neutron matter at densities relevant to the inner crust of a neutron star, based on a simplified version of the Reid soft-core interaction and spin-dependent spatial correlations optimized in the correlated normal state. Careful consideration is given to the treatment of the gap equation at large intermediate-state momenta, correcting quantitative defects of earlier calculations. The variational gap function evaluated at the Fermi surface, Δ F, which serves as a critical input to models of the cooling and internal dynamics of neutron stars, is found to be larger than predicted in earlier work. Estimates of the suppression of the gap due to polarization processes (and other particle-particle and hole-hole irreducible medium effects of higher order within CBF superstate perturbation theory) yield values for Δ k F that are generally compatible with results from the semi-empirical polarization-potential approach, except at higher densities where the gap is closing. Updated solutions of the gap problem at the variational-CBF level are also given for 1S 0 proton pairing in the quantum fluid interior of a neutron star and for 1S 0 like-nucleon pairing in symmetrical nuclear matter at densities typical of the nuclear surface.