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 $α_ {\text{D}}$ in $^{208}$Pb is sensitive to both the magnitude $E_{\text{sym}}(ρ_{\text{c}})$ and density slope $L(ρ_{\text{c}})$ of the symmetry energy at a subsaturation cross density $ρ_{\text{c}} = 0.11$ fm$^{-3}$. Using the experimental data of $α_ {\text{D}}$ in $^{208}$Pb from RCNP and the recent accurate constraint of $E_{\text{sym}}(ρ_{\text{c}})$ from the binding energy difference of heavy isotope pairs, we extract a value of $L(ρ_{\text{c}}) = 47.3 \pm 7.8$ MeV. The implication of the present constraint of $L(ρ_{\text{c}})$ 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.