Role of neutron pairing with density-gradient dependence in the semi-microscopic treatment of the inner crust of neutron stars

TL;DR

This study employs an advanced semi-microscopic approach to model the inner crust of neutron stars, emphasizing the role of density-gradient dependent neutron pairing, and compares results with previous models.

Contribution

It introduces a new pairing functional with density-gradient dependence, improving the realism of neutron superfluid modeling in neutron-star crusts.

Findings

Proton number Z remains constant at 40 across densities.

The new functional yields an equation of state similar to previous models.

Neutron clusters are impermeable to superfluid, affecting superfluid dynamics.

Abstract

Using the fourth-order extended Thomas-Fermi method with Strutinsky-integral shell and pairing corrections, we calculate the inner crust of neutron stars with the BSk31 functional, whose pairing has two terms: i) a term that is fitted to the results of microscopic calculations on homogeneous nuclear matter (accounting for both medium polarization and self-energy effects) that are more realistic than those of our earlier functionals; ii) an empirical term that is dependent on the density gradient, which permits an excellent fit to nuclear masses. Both proton and neutron pairing are taken into account, the former in the BCS theory and the latter in the local density approximation. We found that the equilibrium value of the proton number $Z$ remains 40 over the entire density range considered, whether or not neutron pairing is included. The new equation of state and the composition are very similar to those of our previously preferred functional, BSk24. However, the predicted neutron pairing fields are quite different. In particular, clusters are found to be impermeable to the neutron superfluid. The implications for the neutron superfluid dynamics are briefly discussed. Since the new pairing is more realistic, the functional BSk31 is better suited for investigating neutron superfluidity in neutron-star crusts.