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