Nucleonic superfluidity in neutron stars: 1S 0 neutron pairing in the inner crust

Abstract

This paper begins a renewed attack on the problem of nucleonic superfluids, with a microscopic investigation of 1S 0 neutron pairing in low-density neutron-star matter, i.e. in the inner-crust regime of neutron stars. The superfluid energy gap and condensation energy are calculated in the framework of second-order correlated-basis perturbation theory, thereby incorporating important effects of polarization of the medium on the effective pairing interaction. The energy gap and condensation energy are found to be emphatically suppressed, relative to the results of earlier variational treatments. The calculations are carried out for two “realistic” semiphenomenological nucleonnucleon potentials, based on the Reid and Bethe-Johnson interactions. The dependence of the energy gap on the effective mass is studied, and the implications of proton contamination of neutron matter are addressed briefly. The accuracy of the standard BCS weak-coupling formulae is assessed. The consequences of the strong suppression of 1S 0 neutron superfluidity in the inner-crust region for observational properties of neutron stars (cooling and post-glitch dynamics) are discussed.