We investigate the influence of a strong magnetic field on various properties of neutron stars with quark-hadron phase transition. The one-gluon exchange contribution in a magnetic field is calculated in a relativistic Dirac-Hartree-Fock approach. In a magnetic field of 5 × 10 18 G in the center of the star, the overall equation of state is softer in comparison to the field-free case resulting in the reduction of maximum mass of the neutron star.PACS numbers: 26.60.+c, 21.65.+f, 12.39.Ba, 97.60.Jd The matter density in the core of a neutron star could exceed up to a few times the nuclear matter saturation density. At such high density, it is expected that the quark degrees of freedom would be manifested. In fact, quark matter composed of comparable proportions of up, down and strange quarks has been conjectured [1,2] to be the true ground state of QCD at finite baryon density. Therefore, at such high baryon density, a transition from nuclear matter to a stable quark matter is a possibility. Several authors [3][4][5][6] have studied the effect of this phase transition on neutron star properties.The presence of strong magnetic fields in neutron stars might have interesting astrophysical implications. Large magnetic field B m ∼ 10 14 G has been estimated at the surface of neutron stars [7]. On the other hand, in the core, the field may have been amplified considerably due to flux conservation from the original weak field of the progenitor during its core collapse. In fact, field as large as ∼ 10 18 G in the core is predicted [8] using scalar virial theorem which is based on Newtonian gravity. At such high matter density, the effect of general relativity is significant and this gives rise to a very strong gravitational force [9] on the star. Consequently, the value of B m is expected to be further increased above 10 18 G. Because of highly conducting core, such a high field is frozen in [10] and may not manifest at the surface. The energy of a charged particle changes significantly in the quantum limit if the magnetic field is comparable to or above a critical value B (c) m [11], and the quantum effects are most pronounced when the particle moves in the lowest Landau level. The interaction of charged particles with strongly quantizing fields has been shown to modify the gross properties of matter on the surface [8,12] as well as in the core of neutron stars [13,14].Theoretical studies of Fock (exchange) term, relevant to the star surface/crust, in intense magnetic field have been carried out using the simple . In this Letter, we investigate the composition and structure of neutron stars with quark-hadron phase transition under the influence of strong magnetic fields in the Dirac-Hartree-Fock (DHF) approach within a mean-field approximation. This method is rather general, so it should be of correspondingly broad interest.We describe the calculation of the Fock term in presence of a magnetic field in a general formalism within the σ-ω model [14,16]. In a uniform magnetic field B m along z-axis, the Lagrangian is gi...
