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

TL;DR

This paper investigates how various isovector observables relate to the density dependence of nuclear symmetry energy across different densities, revealing specific correlations that can inform experimental and theoretical studies of nuclear matter and neutron stars.

Contribution

It provides a detailed analysis of correlations between isovector observables and the density dependence of symmetry energy, identifying key density ranges and potential experimental probes.

Findings

Neutron skin thickness correlates strongly with $L( ho)$ at 0.59 $ ho_0$.

Neutron star radii are strongly correlated with $L( ho)$ over a wide density range.

Crust-core transition pressure correlates with the momentum derivative of the symmetry potential.

Abstract

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.