  Recent analysis of the isospin diffusion data from heavy-ion collisions based
on an isospin- and momentum-dependent transport model with in-medium
nucleon-nucleon cross sections has led to the extraction of a value of $L=88\pm
25$ MeV for the slope of the nuclear symmetry energy at saturation density.
This imposes stringent constraints on both the parameters in the Skyrme
effective interactions and the neutron skin thickness of heavy nuclei. Among
the 21 sets of Skyrme interactions commonly used in nuclear structure studies,
the 4 sets SIV, SV, G$_\sigma$, and R$_\sigma$ are found to give $L$ values
that are consistent with the extracted one. Further study on the correlations
between the thickness of the neutron skin in finite nuclei and the nuclear
matter symmetry energy in the Skyrme Hartree-Fock approach leads to predicted
thickness of the neutron skin of $0.22\pm 0.04$ fm for $^{208}$Pb, $0.29\pm
0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $^{124}$Sn.
