Relativistic mean field model based on realistic nuclear forces

In order to predict properties of asymmetric nuclear matter, we construct a relativistic mean field (RMF) model consisting of one-meson exchange (OME) terms and point coupling (PC) terms. In order to determine the density dependent parameters of this model, we use properties of isospin symmetric nuclear matter in combination with the information on nucleon-nucleon scattering data, which are given in the form of the density dependent G-matrix derived from Brueckner calculations based on the Tamagaki potential. We show that the medium- and long-range components of this G-matrix can be described reasonably well by our effective OME interaction. In order to take into account the short-range part of the nucleon-nucleon interaction, which cannot be described well in this manner, a point coupling term is added. Its analytical form is taken from a model based on chiral perturbation theory. It contains only one additional parameter, which does not depend on the density. It is, together with the parameters of the OME potentials adjusted to the equation of state of symmetric nuclear matter. We apply this model for the investigation of asymmetric nuclear matter and find that the results for the symmetry energy as well as for the equation of state of pure neutron matter are in good agreement with either experimental data or with presently adopted theoretical predictions. In order to test the model at higher density, we use its equation of state for an investigation of properties of neutron stars.

Figure 1

G-matrix potentials in the ${}^1\mathrm{O}$, ${}^3\mathrm{O}$, and ${}^1\mathrm{E}$ channels. Dashed, solid, and dashed-dotted lines represent the potentials at the density, $k_f=1.0$ fm${}^{-1},k_f=1.4$ fm${}^{-1}$, and $k_f=1.8$ fm${}^{-1}$, respectively.

Figure 2

G-matrix potential in the ${}^3\mathrm{E}$ channel. In the left (right) figure, the tensor interaction is excluded (included). Dashed, solid, and dashed-dotted lines represent the potentials at the density, $k_f=1.0$ fm${}^{-1},k_f=1.4$ fm${}^{-1}$, and $k_f=1.8$ fm${}^{-1}$, respectively. In the left figure they are on top of each other.

Figure 3

G-matrix potentials as a function of the relative distance $r$. Dashed, solid, and dashed-dotted lines represent the potentials at the density, $k_f=1.0$ fm${}^{-1},k_f=1.4$ fm${}^{-1}$, and $k_f=1.8$ fm${}^{-1}$, respectively.

Figure 4

One meson exchange Hartree diagram (left) and Fock diagram (right). Solid and dashed lines represent a nucleon and each meson ($\sigma ,\delta ,\pi ,\omega ,\rho$), respectively.

Figure 5

Density dependence of each meson mass. From the left to the right and from the top to the bottom, the pictures represent the density dependence of $m_{\sigma },m_{\delta },m_{\omega }$, and $m_{\rho }$, respectively.

Figure 6

Density dependence of each meson-nucleon coupling. From left to right and from top to bottom, the pictures represent the density dependence of $g_{\sigma },g_{\delta },g_{\omega }$, and $g_{\rho }$, respectively.

Figure 7

G-matrix potentials and OME potentials at the density $k_f=$1.4 fm${}^{-1}$. From left to right and from top to bottom, the pictures represent the potential of each channel, ${\mathcal{V}}_0,{\mathcal{V}}_{\sigma },{\mathcal{V}}_{\tau },{\mathcal{V}}_{\sigma \tau },{\mathcal{V}}_{\mathrm{LS}}$, and ${\mathcal{V}}_T$, respectively. The solid line represents OME potentials and dotted line represents G-matrix potentials (Akaishi potential).

Figure 8

Energy per particle for isospin-symmetric nuclear matter. Results of the present model (solid line) are compared with those of the G-matrix potentials (dashed line) and those of the GT2-interaction Refs. [29, 30] (dashed-dotted line).

Figure 9

Symmetry energy of the present model (solid line) compared with results of the G-matrix potentials (dashed line) and with those of the density dependent RMF parameter set DD-ME1 of Ref. [14] (dashed-double-dotted line).

Figure 10

Energy per particle of pure neutron matter for the present model (solid line), the many-body calculation of Freedman and Phandharipande [23] (dotted line), the density dependent RMF model DD-ME1 of Ref. [14] (dashed-double-dotted line), the modified Gogny interaction of Refs. [29, 30] (dashed-dotted line), the pure G-matrix potential (dashed line with + signs), and the G-matrix containing in addition contributions form three-body forces (dashed line with × signs, explained in the text), respectively.

Figure 11

Energy per particle of nuclear matter as a function of the density for various values of the asymmetry indicated by the $Z/N$ ratio.

Figure 12

Neutron star mass is drawn as a function of the central density (left) and the radius (right) of a neutron star.

Figure 13

Equation of state of $\mathrm{npe}\mu$ neutron star matter.