  Correlations between the thickness of the neutron skin in finite nuclei and
the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock
model. From the most recent analysis of the isospin diffusion data in heavy-ion
collisions based on an isospin- and momentum-dependent transport model with
in-medium nucleon-nucleon cross sections, a value of $L=88\pm 25$ MeV for the
slope of the nuclear symmetry energy at saturation density is extracted, and
this imposes stringent constraints on both the parameters in the Skyrme
effective interactions and the neutron skin thickness of heavy nuclei.
Predicted thickness of the neutron skin is $0.22\pm 0.04$ fm for $% ^{208}$Pb,
$0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $% ^{124}$Sn.
