Properties of dense, asymmetric nuclear matter in Dirac-Brueckner-Hartree-Fock approach

Within the Dirac-Brueckner-Hartree-Fock approach, using the Bonn potentials, we investigate the properties of dense, asymmetric nuclear matter and apply it to neutron stars. In the actual calculations of the nucleon self-energies and the energy density of matter, we study in detail the validity of an angle-averaged approximation and an averaging of the total momentum squared of interacting two-nucleons in nuclear matter. For practical use, we provide convenient parametrizations for the equation of state for symmetric nuclear matter and pure neutron matter. We also parametrize the nucleon self-energies in terms of polynomials of nucleon momenta. Those parametrizations can accurately reproduce the numerical results up to high densities.

Figure 1

Binding energy per particle in symmetric nuclear matter and pure neutron matter as a function of the total baryon density, $n_B$. Results for Bonn potentials A, B, and C are shown. Solid (dashed) curves are for symmetric nuclear (pure neutron) matter. Inset: Magnifcation of the shaded rectangular region around $n_B^0$. Also see the text and Table for details.

Figure 2

Three components of the self-energies at $\underline{k}=k_F$ in symmetric nuclear matter. The Bonn A potential is used. The dashed curve represents the two-dimensional calculation ($\Sigma 2d$); the solid curve, the one-dimensional one ($\Sigma 1d$). The two results are very close to each other.

Figure 3

Binding energy per particle for nuclear matter as a function of the total baryon density, $n_B$. Bonn A potential and self-energies, $\Sigma 1d$, are used in the calculation. We present the full result, $E3d$, as well as the approximated ones, $E1d$ and $E2d$. Solid and dashed curves represent the results for pure neutron matter (n.m.) and symmetric nuclear matter (s.n.m.), respectively. From top to bottom, curves represent the results of $E3d$, $E2d$, and $E1d$, respectively.

Figure 4

Neutron-star mass versus radius in three approximations. The Bonn A potential is used. From top to bottom, curves are the results of $E3d$, $E2d$, and $E1d$. Filled circles on the curves represent maximum-mass stars. Also see Table .

Figure 5

EoS for nuclear matter as a function of the total baryon density, $n_B$. DBHF results are represented by filled (red) circles; parametrization results, by solid (green) curves.

Figure 6

Neutron-star mass versus radius with or without the parabolic interpolation. The upper (green) curve represents the result by $\Sigma 1d-E3d$ (without interpolation); the lower (pink) curve, the result by the interpolation between Eqs. (21) and (22).