Abstract
The proton fraction in β-stable neutron stars is investigatedwithin the framework of the Skyrme-Hartree-Fock theory using the extendedSkyrme effective interaction for the first time. The calculated results showthat the proton fraction disappears at high density, which implies that thepure neutron matter may exist in the interior of neutron stars. Theincompressibility of the nuclear equation-of-state is shown to be moreimportant to determine the proton fraction. Meanwhile, it is indicated thatthe addition of muons in neutron stars will change the proton fraction. Itis also found that the higher-order terms of the nuclear symmetry energyhave obvious effects on the proton fraction and the parabolic law of thenuclear symmetry energy is not enough to determine the proton fraction. PACS: 97. 60. Jd, 26. 60. +c
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