Proximity effect of pair correlation in the inner crust of neutron stars

TL;DR

This study investigates how the pair correlation in neutron superfluid within the inner crust of neutron stars is influenced by nuclear clusters, revealing a strong density-dependent proximity effect using advanced theoretical modeling.

Contribution

It introduces a detailed coordinate-space Skyrme-Hartree-Fock-Bogoliubov approach to analyze the proximity effect in neutron star crusts, highlighting its density dependence and spatial extent.

Findings

Proximity effect varies significantly with density.

In middle layers, the effect is localized near nuclear clusters.

In shallow and deep layers, the effect extends throughout the Wigner-Seitz cell.

Abstract

We study proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme-Hartree-Fock-Bogoliubov theory formulated in the coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superfluid, which is confined in a spherical box. Using a density-dependent effective pairing interaction which reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in neutron superfluid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of neutron superfluid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density $5 \times 10^{-4}$ fm$^{-3} < \rho_b < 2\times 10^{-2}$ fm$^{-3}$, the proximity effect is well limited in the vicinity of the nuclear cluster, i.e. in a sufficiently smaller area than the Wigner-Seitz cell. On the contrary, the proximity effect is predicted to extend to the whole volume of the Wigner-Seitz cell in shallow layers of the inner crust with $\rho_b < 2 \times 10^{-4}$ fm$^{-3}$, and in deep layers with $\rho_b > 5 \times 10^{-2}$ fm$^{-3}$.