Effects of the symmetry energy on the isovector properties of neutron-rich nuclei within a Thomas-Fermi approach

We employ a variational method, in the framework of the Thomas-Fermi approximation, to study the effect of the symmetry energy on the neutron skin thickness and the symmetry energy coefficients of various neutron-rich nuclei. We concentrate our interest on Pb-208, Sn-124, Zr-90, and Ca-48, although the method can be applied in the totality of medium and heavy neutron-rich nuclei. Our approach has the advantage that the isospin asymmetry function alpha(r), which is the key quantity for calculating isovector properties of various nuclei, is directly related to the symmetry energy as a consequence of the variational principle. Moreover, the Coulomb interaction is included in a self-consistent way and its effects can be separated easily from the nucleon-nucleon interaction. We confirm, both qualitatively and quantitatively, the strong dependence of the symmetry energy on the various isovector properties for the relevant nuclei, using possible constraints between the slope and the value of the symmetry energy at the saturation density.