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

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.