Equation of state in the inner crust of neutron stars: discusion of the unbound neutron states

TL;DR

This paper investigates the nuclear shell effects in the inner crust of neutron stars, distinguishing between bound and unbound states, and proposes a correction to improve energy calculations in Wigner-Seitz cells.

Contribution

It introduces a method to differentiate genuine shell effects from spurious ones caused by unbound states and proposes a correction to the Hartree-Fock energy calculations.

Findings

Spurious shells significantly affect total energy estimates.

A correction method to the Hartree-Fock energy improves accuracy.

Distinction between bound and unbound state effects clarifies crust modeling.

Abstract

In this paper, we calculate the stable Wigner-Seitz (W-S) cells in the inner crust of neutron stars and we discuss the nuclear shell effects. A distinction is done between the shell effects due to the bound states and those induced by the unbound states, which are shown to be spurious. We then estimate the effects of the spurious shells on the total energy and decompose it into a smooth and a residual part. We propose a correction to the Hartree-Fock binding energy in Wigner-Seitz cell (HF-WS).