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We employ a variational method, in the framework of the Thomas-Fermiapproximation, to study the effect of the symmetry energy on the neutron skinthickness and the symmetry energy coefficients of various neutron rich nuclei.We concentrate our interest on $^{208}$Pb, $^{124}$Sn, $^{90}$Zr, and$^{48}$Ca, although the method can be applied in the totality of medium andheavy neutron rich nuclei. Our approach has the advantage that the isospinasymmetry function $\alpha(r)$, which is the key quantity to calculateisovector properties of various nuclei, is directly related with the symmetryenergy as a consequence of the variational principle. Moreover, the Coulombinteraction is included in a self-consistent way and its effects can beseparated easily from the nucleon-nucleon interaction. We confirm, bothqualitatively and quantitatively, the strong dependence of the symmetry energyon the various isovector properties for the relevant nuclei, using possibleconstraints between the slope and the value of the symmetry energy at thesaturation density.

Symmetry energy effects on isovector properties of neutron rich nuclei with a Thomas-Fermi approach