Compiled properties of nucleonic matter and nuclear and neutron star models from nonrelativistic and relativistic interactions

This paper compiles the model parameters and zero-temperature properties of an extensive collection of published theoretical nuclear interactions, including 255 nonrelativistic (Skyrme-like) forces, 270 relativistic mean field (RMF) and point-coupling (RMF-PC) forces, and 13 Gogny-like forces. This forms the most exhaustive tabulation of model parameters to date. The properties of uniform symmetric matter and pure neutron matter at the saturation density are determined. Symmetry properties found from the second-order term of a Taylor expansion in neutron excess are compared with the energy difference of pure neutron and symmetric nuclear matter at the saturation density. Selected liquid-droplet model parameters, including the surface tension and surface symmetry energy, are determined for semi-infinite surfaces. Theoretical liquid droplet model neutron skin thicknesses of the neutron-rich closed-shell nuclei ${}^{48}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$ are compared with published theoretical Hartree-Fock and experimental results. A similar comparison is made between theoretical liquid-droplet and experimental values of dipole polarizabilities. In addition, radii, binding energies, moments of inertia and tidal deformabilities of $1.2{\mathrm{M}}_{\odot }, 1.4{\mathrm{M}}_{\odot }$ and $1.6{\mathrm{M}}_{\odot }$ neutron stars are computed. An extensive correlation analysis of bulk matter, nuclear structure, and low-mass neutron star properties is performed and compared with nuclear experiments and astrophysical observations.

Figure 1

The correlations between the saturation density $n_0$ and the bulk energy per particle $E_0$ (left panel) and the incompressibility $K_0$ (right panel) of symmetric matter at $n_0$ for Skyrme (black filled circles), Gogny (green triangles) and RMF (red pluses) models. Solid and dashed lines indicate $1\sigma$ and $2\sigma$ confidence ellipses for each force type.

Figure 2

Similar to Fig. 1, but for the correlations between the symmetric-matter skewness $Q_0$ with $n_0$ (left panel) and $Q_0$ with $K_0$ (right panel).

Figure 3

Similar to Fig. 1, but for correlations between the parameters $J_2$ and $n_0$ (left panel) and $L_2$ and $n_0$ (right panel).

Figure 4

Similar to Fig. 1 but showing the correlation between $L_2$ and $J_2$.

Figure 5

Similar to Fig. 1, but for correlations between $K_0$ and $L_2$ (left panel) and $K_{N0}$ and $L_2$ (right panel).

Figure 6

Similar to Fig. 1, but for correlations between $Q_0$ and $L_2$ (left panel) and $Q_{N0}$ and $L_2$ (right panel).

Figure 7

Similar to Fig. 1, but for correlations between $K_{\mathrm{sym}}$ and $L_2$ (left panel) $Q_{\mathrm{sym}}$ and $L_2$ (right panel).

Figure 8

Differences between the two methods for determining symmetry energy parameters.

Figure 9

Correlations between the surface tension ${\sigma }_0$ and the saturation density $n_0$ (left panel) and the binding energy $-E_0$ at saturation (right panel) in Skyrme (black) and RMF (red) models. $1\sigma$ and $2\sigma$ confidence ellipses are indicated by solid and dashed lines for each force type.

Figure 10

The left panel is the same as Fig. 9 except for the surface tension ${\sigma }_o$ and the incompressibility at saturation $K_0$. The right panel shows the nearly linear correlations, with standard deviations, between $S_s/J_2$ and the symmetry energy slope $L_2$.

Figure 11

Skyrme and RMF predictions of the neutron skin thicknesses of ${}^{48}\mathrm{Ca}$ (red) and ${}^{208}\mathrm{Pb}$ (black) for the DM, including surface diffuseness corrections, (left panel) and Hartree-Fock calculations (right panel). Linear correlations and one standard deviation are shown as solid and dashed diagonal lines, respectively. The narrow hatched horizontal bands indicate the one standard deviation ranges of the previous averaged experimental results for these nuclei [12]. The dotted black (red) lines indicate the one standard deviation ranges of $r_{np}^{208}$ ($r_{np}^{48}$) from PREX I $+$ II [17] (CREX [18]). The wide black hatched band shows the one standard deviation range of the Large Hadron Collider ${}^{208}\mathrm{Pb}$ neutron skin measurement [19].

Figure 12

Comparison of the neutron skin thicknesses of ${}^{48}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$ calculated from the DM including surface diffuseness corrections with those from the HF method, for selected Skyrme (left panel) and RMF (right panel) models.

Figure 13

Skyrme and RMF predictions of the dipole polarizability of ${}^{48}\mathrm{Ca}$ (left) and ${}^{208}\mathrm{Pb}$ (right) calculated with hydrodynamical model. The dotted black lines in both figures indicate the ranges of the experimental results for these nuclei, Refs. [21, 22], respectively.

Figure 14

Relationship between neutron star parameters and slope of symmetric energy.

Figure 15

(left) $I_{1.4}$ vs $R_{1.4}$. The correlation is given in Eq. (135). (right) $ln{\mathrm{\Lambda }}_{1.4}$ vs $R_{1.4}$. The correlation is given in Eq. (142).

Figure 16

The relation between tidal deformability and moment of inertia for neutron stars with 1.4 solar mass is shown in the upper panel. The line in the upper panel is the Yagi-Yunes (YY) universal relation [29], and the lower panel shows the deviation from it. Equations of state with the largest deviations, which in no case exceed 2%, are indicated.

Figure 17

Correlation matrix for Skyrme forces.

Figure 18

Correlation matrix for RMF forces.