Proximity Effect of Pair Correlation in the Inner Crust of Neutron Stars with Hartree–Fock–Bogoliubov Theory

Abstract

We study proximity effect of neutron superfluid in the inner crust of neutron stars by solving the Hartree-Fock-Bogoliubov equation in a spherical Wigner-Seitz cell. Numerical analysis shows that the presence of nuclei affects the pair correlation of neutron superfluid in proximity region, which is characterized by the coherence length measured from the edge of the nuclei. Reflecting strong density-dependence of the coherence length, the proximity effect is small in lower layers of the inner crust while it becomes as large as the cell size in upper layers.