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

We show that the neutron skin thickness $\mathrm{\Delta }{r}_{np}$ 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 $\mathrm{\Delta }E$ 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 $\Delta r_{np}$ofSnisotopesand$\Delta E$ of a number of heavy isotope pairs, we obtain simultaneously $E_{\text{sym}}({\rho }_c)=26.65\pm 0.20$ MeV and $L({\rho }_c)=46.0\pm 4.5$ MeV at 95% confidence level, whose extrapolation gives $E_{\text{sym}}({\rho }_0)=32.3\pm 1.0$ MeV and $L({\rho }_0)=45.2\pm 10.0$ MeV. The implication of these new constraints on the $\mathrm{\Delta }{r}_{np}$ of ${}^{208}$Pb and the core-crust transition density in neutron stars is discussed.