| According to quark theory, when several times of normal nuclear matter density is achieved, quarks may deconfine from baryons in neutron stars. This process is so called deconfinement phase transition. The problem whether the mixed phase of hadrons and quarks exits in the deconfinement phase transition confused people for decades. In early works, people thought that this process is a first order phase transition with one conserved quantity which means that the phase transition from normal nuclear matter to quark matter is a sudden one and the hadronic matter can not coexist with quark matter. However, in 1992, Glendenning pointed out that since there are two independent conserved quantities - baryon charge and electric charge,neutron star matter requires only global rather than local neutrality. So quark matter and nuclear matter may co-exist in this first order phase transition. Results show that the normal quark matter in neutron star will soften the equation of state (EOS), thus reduce the maximum mass of the star. Quarks with Fermi energy have to form BCS pair because of the attractive interaction among quarks. Consequently the color superconductive phase and color-flavor-locked (CFL) phase should exist in neutron star. The free energy decrease along with the increase of the energy gapΔ. It also results in the harden of the EOS and consequently the increase of the maximum mass and radius of the star. In this paper, we show a simple way in which the hadron-quark phase (including normal and CFL quark phase) transition can be studied. The characteristics of strange star and hybrid star are showed qualitatively. Our results are identical with the observation.
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