We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV(＜～)L(＜～)82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.
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