Density dependence of proton fraction in neutron stars

Within the framework of Skyrme-Hartree-Fock theory based on the extended Skyrme effective interaction, the proton fraction in beta -stable neutron stars was investigated for the charge neutrality condition. The density dependence of symmetry energy strength coefficient was studied with different potential parameters, and the behavior of proton fraction in neutron stars at high density for these potential parameters was obtained. The calculated results show that the proton fraction disappears at high density for potential parameters SII, SIII and SKM, which implies that the pure neutron matter may exist in the interior of neutron stars. It is also found that adding muons in neutron stars will increase the proton fraction.