Neutron stars within a relativistic central variational method

The properties of neutron stars are investigated within the relativistic central variational method by using a realistic nucleon-nucleon ($NN$) interaction. The strong repulsion of realistic $NN$ interactions at short distances is treated by a Jastrow central correlation function, whose form is completely determined through minimization of the total energy of the nuclear many-body system. The relativistic Hartree-Fock wave functions are chosen as the trial wave function. In this framework, the equation of state of the neutron star matter in $\beta$ equilibrium is obtained self-consistently. We further determine the properties of neutron stars via the Tolman-Oppenheimer-Volkoff equation using Bonn A, B, and C potentials. The maximum masses of neutron stars with these realistic potentials are around $2.18M_{\odot }$ and their corresponding radii are around 11 km. These results are in accordance with the calculations of the relativistic Brueckner-Hartree-Fock theory with the same potentials. Furthermore, we also find that the splitting of proton-neutron effective masses will be reversed at high density in the neutron star matter, which are caused by the contribution of short-range correlation on kinetic energy.

Figure 1

The energy per nucleon as a function of density (a) and the pressure as a function of energy density (b) of neutron star matter with Bonn A, Bonn B, and Bonn C potentials.

Figure 2

The central correlation on kinetic energy for neutron star matter with Bonn A, Bonn B, and Bonn C potentials.

Figure 3

The variational parameter $c_4$ as a function of density for neutron star matter with Bonn A, Bonn B, and Bonn C potentials.

Figure 4

The mass-radius relations (a) and mass-density relations (b) of neutron stars with Bonn A, Bonn B, and Bonn C potentials.

Figure 5

The particle fractions in neutron stars with Bonn A, Bonn B, and Bonn C potentials.

Figure 6

The proton fraction in neutron stars with Bonn A, Bonn B, and Bonn C potentials.

Figure 7

The effective proton and neutron masses in neutron stars with Bonn A, Bonn B, and Bonn C potentials.

Figure 8

The kinetic and potential contributions on the nucleon effective masses in neutron stars with Bonn A potential.