We show that the neutron skin thickness \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 \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 } of Sn isotopes and \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 \Delta r _ { np } of ^ { 208 } Pb and the core-crust transition density in neutron stars is discussed .