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Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei

Expressing explicitly the parameters of the standard Skyrme interaction in terms of the macroscopic properties of asymmetric nuclear matter, we show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. We find that existing data on neutron skin thickness $Δr_{np}$ of Sn isotopes give an important constraint on the symmetry energy $E_{sym}({ρ_{0}})$ and its density slope $L$ at saturation density ${ρ_{0}}$. Combining these constraints with those from recent analyses of isospin diffusion and double neutron/proton ratio in heavy-ion collisions at intermediate energies leads to a more stringent limit on $L$ approximately independent of $E_{sym}({ρ_{0}})$. The implication of these new constraints on the $Δr_{np}$ of $^{208}$Pb as well as the core-crust transition density and pressure in neutron stars is discussed.