was a correlation between neutron skin thickness of nuclei and properties of neutron stars.

For the sake of completeness, the results of the present work, whenever possible are compared with the results obtained with the NL3 parametrization of the NLWM, known to describe finite nuclei properties well.

We perform two different numerical calculations to obtain the $^{208}$Pb properties: a Thomas-Fermi approximation based on the liquid-gas phase transition developed in [@gotas] and a Thomas-Fermi approximation based on a method proposed in [@ring], where a harmonic oscillator basis is used. We restrict ourselves to the Thomas-Fermi approximation because, as we show in the Results section at the end of the paper, for the purpose of obtaining correct surface energy and neutron-skin thickness, it is almost as good as the solution of the Dirac equation.

At this point it is worth mentioning that the scalar-isovector $\delta$ mesons, which play an important role in the isospin channel, could also be incorporated in our work as done in [@gaitanos; @inst04; @inst06] but in order to make the comparisons among different approximations as simple as possible, they will be included in a future work. Finally, as we are interested in nuclei ground state properties, all calculations 