Nuclear effects on superfluid neutron star matter

In the inner crust of a neutron star, the superfluid neutron liquid shares a fraction of the volume with neutron-rich nuclei and thus cannot be considered as uniform. We find that quasi-resonant states, due to elastic scattering with the effective nuclear potential wells, can enhance the neutron density of states at the Fermi surface for some values of the energy of the incident neutron. This may locally change the pairing energy gap of the superfluid neutrons up to a factor of three to four. We then discuss the smoother change of the neutron effective matrix element induced by the presence of the nuclei considering the case in which the superfluid coherence length is larger than the nuclear sizes. The results show that the value of the pairing gap as calculated for infinite systems is not directly the one that should be expected to exist in the crust of a neutron star and we work out an approximate formula for the gap taking into account both effects. The sudden change of the neutronic superfluid gap in localized crust shells due to the nuclear quasi-resonant states can have consequences for theories of the rotational and thermal evolution of neutron stars while the smooth, continuous variation of the effective matrix element can have implications for the cooling of the star.