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

Abstract

We analyze how the structure of the inner crust is influenced by the pairing correlations. The inner crust matter, formed by nuclear clusters immersed in a superfluid neutron gas and ultrarelativistic 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--Hartree-Fock-Bogoliubov (HFB) calculations with zero-range density-dependent pairing forces of various intensities. The most important effect of pairing is to smooth the dependence of Hartree-Fock (HF) energy on proton number. For some cells pairing can change significantly the proton number of the HF configurations. However, these changes are not so relevant because the energy difference between the absolute HFB minima and the energies corresponding to HF minima is very small. In the high-density cells, well-defined absolute minima are not found since the binding energies decrease continuously for small proton numbers. We show that the structure of these cells can be eventually determined by taking into account the underestimation of the binding energy due to the discretization of the energy spectrum of the nonlocalized neutrons induced by the boundary conditions at the border of the cells.