Quantifying Correlations Between Isovector Observables and the Density Dependence of Nuclear Symmetry Energy away from Saturation Density

According to the Hugenholtz-Van Hove theorem, the nuclear symmetry energy $S(\rho)$ and its slope $L(\rho)$ at arbitrary densities can be decomposed in terms of the density and momentum dependence of the single-nucleon potentials in isospin-asymmetric nuclear matter which are potentially accessible to experiment. We quantify the correlations between several well-known isovector observables and $L(\rho)$ to locate the density range in which each isovector observable is most sensitive to the density dependence of the $S(\rho)$. We then study the correlation coefficients between those isovector observables and all the components of the $L(\rho)$. The neutron skin thickness of $^{208}$Pb is found to be strongly correlated with the $L(\rho)$ 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 $L(\rho)$ over a wide range of supra-saturation 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 $L(\rho)$, it is strongly correlated with the momentum derivative of the first-order symmetry potential, and the density dependence of the second-order symmetry potential.