Inner Crust Of Neutron Stars In A Relativistic Mean Field Approach

In recent years, the properties of the inner crust of neutron stars have been investigated more and more with an increasing interest, especially the microscopic structure and the superfluid properties. According to the standard model, the inner crust is consist of a lattice of Wigner-Seitz(W-S) cells, i.e. neutron-rich nuclei immersed in a sea of dilute, inhomogeneous neutron gas.The first investigation of microscopic properties of the inner crust matter was investigated by Negele and Vauterin[4]. They applied Hartree-Fock approximation to 11 representative densities of the inner crust matter, obtained the structure for each density by searching the lowest binding energy andβ-stable of the W-S cells. The possibility of superfluidity in the inner crust was suggested long time ago, before the first neutron star was observed. The first experimental fact pointing to the nuclear superfluidity in the neutron stars was the large relaxation times which follow the sudden period changes (so called "glitches") of the neutron star rotation. Furthermore, the superfluidity of the inner crust has important consequences on the cooling of neutron stars. Recently Sandulescu et al investigated the inner curst superfluidity by introducing a Hartree-Fock-Bogoliubov (HFB) model with density dependantδpairing interaction[6]. Late, a energy functional method with the pairing correlation of protons and neutrons was introduced by Baldo et al[10]. They calculated all the possible cells and obtained an optimal structure at each density. In fact, the results of these two investigations are more or less similar.All of the above investigations were done within non-relativistic framework by employing rather simple pairing interactions. We know that relativistic models are as important as non-relativistic models in the investigations of nuclear matter and finite nuclei. In recent years, relativistic mean field model(RMF) has been very successful in the description of ground state properties of finite nuclei. Therefore, it becomes very interesting to investigate the inner crust properties in relativistic models. Due to the importance of superfluidity in the inner crust, it is necessary to employ a more reasonable pairing interaction.In our work, we shall apply the RMF model and BCS pairing correlation with the finite range Gogny force, to investigate the structure of the Wigner-Seitz cells. The densities of the W-S cells are chosen as same as those by Negele and Vauterin. To simulate the homogeneous neutron gas in the W-S cells, we have to impose proper boundary conditions in the RMF model. De to the 2-component Dirac spinors in the relativistic approaches, a proper choice of the boundary condition becomes more complicated, which is one of main tasks in our work.The investigation of the superfluidity in the inner crust matter is another most important task of our work. The finite range Gogny force, which has been proved to be very successful in the description of pairing correlation in finite nuclei, is employed to investigate the pairing correlation in the W-S cells. The W-S cells obtained by Negele and Vauterin contain 40 or 50 protons, except for the one at the highest density. We will choose some typical cells(such as ¹⁸⁰⁰Sn, ⁹⁵⁰Sn, ¹⁵⁰⁰Zr, ⁵⁰⁰Zr), to calculate the pairing fields of neutrons, and compare with the results obtained by the zero range 5 force in the HFB model.Our calculations show that the lattice structure of the W-S cells, where neutron-rich nuclei immersed in a sea of dilute, inhomogeneous neutron gas can be well described in the RMF-BCS model. With the pairing correlations in the RMF-BCS model the neutron gas density distribution is flatter than that in the RMF model. The neutron gas densities in the RMF-BCS model are much higher than those in non-relativistic HFB model.