Boundary Conditions of Wigner-Seitz Cell in Inner Crust of Neutron Stars with Relativistic Mean Field Approach

Abstract

The microscopic structure of the Wigner–Seitz (W-S) cell in the inner crust of neutron stars is investigated with the relativistic mean field (RMF) approach. The W-S cell is composed of a cluster of neutrons and protons localized in a region around the centre and surrounded by a neutron gas of approximately uniform density. In order to generate the density of the W-S cell, appropriate boundary conditions in the calculation of the single-particle wavefunctions are necessary. We emphasize on the choice of the boundary conditions in the RMF approach. Three kinds of boundary conditions are suggested. The properties of the W-S cell with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree–Fock–Bogoliubov (HFB) models are compared. It is found that the neutron gas densities of the W-S cell in the RMF model is higher than those obtained in the HFB model.