Many theoretical methods, such as the non-relativistic Brueckner approach, relativistic Brueckner approach, variational many body, the relativistic mean field theory, non-relativistic many body theory and the quarkmeson coupling model, have been used to explore the properties of neutron stars. In the present work, we shall study the properties of neutron stars within the framework of Hartree-Fock theory using the extended Skyrme effective interaction[1]. Many theoretical studies indicate that the relation between the single nucleon energy and the relative neutron excess satisfies the parabolic law approximately when δ and density p is not too high, the δ4 and higher-order terms of δ are negligible, we shall show the higher-order terms of symmetry energy are important in studying neutron stars.
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