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 the 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 .