On the superfluid properties of the inner crust of neutron stars

TL;DR

This paper explores the superfluid characteristics of the neutron star inner crust by solving Hartree-Fock-Bogoliubov equations with realistic interactions, revealing the impact of pairing strength and limitations of the Wigner-Seitz approximation.

Contribution

It provides a detailed analysis of neutron pairing and superfluidity in neutron star crusts using realistic forces, highlighting discrepancies with effective interactions and the breakdown of approximations.

Findings

Neutron coherence length depends on pairing strength.

Significant differences between realistic and effective pairing interactions.

Wigner-Seitz approximation fails at high densities.

Abstract

We investigated the superfluid properties of the inner crust of neutron stars, solving the Hartree-Fock-Bogoliubov equations in spherical Wigner-Seitz cells. Using realistic two-body interactions in the pairing channel, we studied in detail the Cooper-pair and the pairing-field spatial properties, together with the effect of the proton clusters on the neutron pairing gap. Calculations with effective pairing interactions are also presented, showing significant discrepancies with the results obtained with realistic pairing forces. At variance with recent studies on finite nuclei, the neutron coherence length is found to depend on the strength of the pairing interaction, even inside the nucleus. We also show that the Wigner-Seitz approximation breaks down in the innermost regions of the inner crust, already at baryonic densities $\rho_b \ge 8 \cdot 10^{+13}$ g $\cdot$ cm$^{-3}$.