Constraining the density slope of nuclear symmetry energy at subsaturation densities using electric dipole polarizability in ${}^{208}$Pb

Abstract

Nuclear structure observables usually most effectively probe the properties of nuclear matter at subsaturation densities rather than at saturation density. We demonstrate that the electric dipole polarizibility $\hat{I}{\pm }_{\text{D}}$ in ${}^{208}$Pb is sensitive to both the magnitude $E_{\text{sym}}(\ddot{I}{}_{\text{c}})$ and density slope $L(\ddot{I}{}_{\text{c}})$ of the symmetry energy at a subsaturation cross density $\ddot{I}{}_{\text{c}}=0.11$ fm${}^{-3}$. Using the experimental data of $\hat{I}{\pm }_{\text{D}}$ in ${}^{208}$Pb from RCNP and the recent accurate constraint of $E_{\text{sym}}(\ddot{I}{}_{\text{c}})$ from the binding energy difference of heavy isotope pairs, we extract a value of $L(\ddot{I}{}_{\text{c}})=47.3\pm 7.8$ MeV. The implication of the present constraint of $L(\ddot{I}{}_{\text{c}})$ to the symmetry energy at saturation density, the neutron skin thickness of ${}^{208}$Pb and the core-crust transition density in neutron stars is discussed.

7 pages, 3 figures. Significantly expanded to include some details and discussions. Accepted version to appear in PRC