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Correlations between the thickness of the neutron skin in finite nuclei andthe nuclear matter symmetry energy are studied in the Skyrme Hartree-Fockmodel. From the most recent analysis of the isospin diffusion data in heavy-ioncollisions based on an isospin- and momentum-dependent transport model within-medium nucleon-nucleon cross sections, a value of $L=88\pm 25$ MeV for theslope of the nuclear symmetry energy at saturation density is extracted, andthis imposes stringent constraints on both the parameters in the Skyrmeeffective 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.Comment: 6 pages, 4 figures, 1 table, revised version, to appear in PR

Nuclear matter symmetry energy and the neutron skin thickness of heavy nuclei