systematically larger, what results in a thicker neutron skin. This is correlated with the fact that the surface energy is lower within the nucleation calculation than within the harmonic oscillator method. Within the same numerical prescription, the neutron skin thickness is smaller with the TW model than with the NL3. As the coupling strength $\Lambda_v$ increases in the NL$\omega\rho$ model, the results move from the original NL3 to the TW results for all quantities, except the proton radius, which oscillates a little. We have also included the results obtained with the HS parametrization [@hs] because we have used this parametrization in order to compare the TF and the Dirac results for the cross sections, as discussed in the following. As this parametrization is known not to give as good results as the other parametrizations of the NLWM for finite nuclei, we do not comment on the results it provides. Notice that the experimental radius for the protons is obtained from the charge radius $R_c$ and it is given by $R_p=\sqrt{R_c^2 -0.64}$ in fm [@ring]. Our results can be compared with experimental and other theoretical results found in the literature. The proton radius, which is known to better than 0.001 fm 