Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and neutron skin thickness

TL;DR

This paper constrains the symmetry energy parameters at subsaturation density using isotope binding energy differences and neutron skin thickness, providing new insights into nuclear matter and neutron star properties.

Contribution

It establishes a novel method to simultaneously determine symmetry energy and its slope at subsaturation density from experimental data.

Findings

Determined $E_{sym}( ho_c)$ and $L( ho_c)$ with high precision.

Extrapolated to find symmetry energy and slope at saturation density.

Discussed implications for neutron star crust properties.

Abstract

We show that the neutron skin thickness $\Delta r_{np}$ of heavy nuclei is uniquely fixed by the symmetry energy density slope $L({\rho})$ at a subsaturation cross density $\rho_c \approx 0.11$ fm$^{-3}$ rather than at saturation density $\rho_0$, while the binding energy difference $\Delta E$ between a heavy isotope pair is essentially determined by the magnitude of the symmetry energy $E_{\text{sym}}({\rho})$ at the same $\rho_c$. Furthermore, we find a value of $L({\rho_c})$ leads to a negative $E_{\text{sym}}({\rho_{0}})$-$L({\rho_{0}})$ correlation while a value of $E_{\text{sym}}({\rho_{c})}$ leads to a positive one. Using data on $\Delta r_{np}$ of Sn isotopes and $\Delta E$ of a number of heavy isotope pairs, we obtain simultaneously $E_{\text{sym}}({\rho_{c})}=26.65\pm0.20$ MeV and $L({\rho_c})= 46.0\pm4.5$ MeV at 95% confidence level, whose extrapolation gives $E_{\text{sym}}({\rho_{0}})=32.3\pm1.0$ MeV and $L({\rho_{0}})=45.2\pm10.0$ MeV. The implication of these new constraints on the $\Delta r_{np}$ of $^{208}$Pb and the core-crust transition density in neutron stars is discussed.