Quantifying correlations between isovector observables and the density dependence of the nuclear symmetry energy away from saturation density

According to the Hugenholtz-Van Hove theorem, the nuclear symmetry energy $S\left(\rho \right)$ and its slope $L\left(\rho \right)$ at arbitrary densities can be decomposed in terms of the density and momentum dependence of the single-nucleon potentials in isospin-asymmetric nuclear matter. We quantify the correlations between several well-known isovector observables and $L\left(\rho \right)$ to locate the density range in which each isovector observable is most sensitive to the density dependence of the $S\left(\rho \right)$. We then study the correlation coefficients between those isovector observables and all the components of the $L\left(\rho \right)$. The neutron skin thickness of ${}^{208}\mathrm{Pb}$ is found to be strongly correlated with the $L\left(\rho \right)$ at a subsaturation density of $\rho =0.59{\rho }_0$ through the density dependence of the first-order symmetry potential. Neutron star radii are found to be strongly correlated with the $L\left(\rho \right)$ over a wide range of suprasaturation densities mainly through both the density and momentum dependence of the first-order symmetry potential. Finally, we find that although the crust-core transition pressure has a complex correlation with the $L\left(\rho \right)$, it is strongly correlated with the momentum derivative of the first-order symmetry potential and the density dependence of the second-order symmetry potential.

Figure 1

Binding energy per nucleon in SNM (a) and the symmetry energy (b) as a function of baryon density $\rho /{\rho }_0$ for SLy4 and NRAPR Skyrme EDFs.

Figure 2

Density dependence of the $L\left(\rho \right)$ and its decomposition for SLy4 and NRAPR Skyrme EDFs.

Figure 3

Correlation coefficients between the $L\left(\rho \right)$ and the neutron skin thicknesses of ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$ calculated using SLy4 and NRAPR Skyrme EDFs.

Figure 4

Correlation coefficients between various terms in the $L\left(\rho \right)$ and the neutron skin thicknesses of ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$ calculated using SLy4 and NRAPR Skyrme EDFs.

Figure 5

Correlation coefficients between $L\left(\rho \right)$ and the $1.0M_{\odot }$, $1.4M_{\odot }$, and $1.8M_{\odot }$ neutron star radii as a function of the baryon density calculated using SLy4 and NRAPR Skyrme EDFs.

Figure 6

Correlation coefficients between various terms in the $L\left(\rho \right)$ as a function of the baryon density and canonical $1.4M_{\odot }$ neutron star radii are calculated using SLy4 and NRAPR Skyrme EDFs.

Figure 7

Correlation coefficients between various terms in the $L\left(\rho \right)$ and the crust-core transition pressure are calculated using SLy4 and NRAPR models.