The cluster structure of the inner crust of neutron stars in the Hartree-Fock-Bogoliubov approach

TL;DR

This paper investigates how pairing correlations affect the structure of the neutron star inner crust using Hartree-Fock-Bogoliubov calculations within the Wigner-Seitz approximation, revealing smaller proton numbers and boundary condition issues.

Contribution

It introduces a detailed HFB analysis of the inner crust structure considering pairing effects, highlighting limitations of the Wigner-Seitz approximation.

Findings

Wigner-Seitz cells have fewer protons than previously estimated.

Small proton number configurations lack a well-defined energy minimum.

Boundary conditions lead to underestimation of binding energies.

Abstract

We analyse how the structure of the inner curst is influenced by the pairing correlations. The inner-crust matter, formed by nuclear clusters immersed in a superfluid neutron gas and ultra-relativistic electrons, is treated in the Wigner-Seitz approximation. The properties of the Wigner-Seitz cells, i.e., their neutron to proton ratio and their radius at a given baryonic density, are obtained from the energy minimization at beta equilibrium. To obtain the binding energy of baryonic matter we perform Skyrme-HFB calculations with zero-range density-dependent pairing forces of various intensities. We find that the Wigner-Seitz cells have much smaller numbers of protons compared to previous calculations. For the dense cells the binding energy of the configurations with small proton numbers do not converge to a well-defined minimum value which precludes the determination of their structure. We show that for these cells there is a significant underestimation of the binding energy due to the boundary conditions at the border of the cells imposed through the Wigner-Seitz approximation.