the Skyrme interaction.

There have already been some efforts in order to compare nuclear matter and finite nuclei properties obtained both with relativistic and non-relativistic models [@bao-li; @ring97] but there is no clear or obvious explanations for the differences. At very low densities both, the relativistic and the non-relativistic approaches predict a non-homogeneous phase commonly named [*pasta phase*]{}, formed by a competition between the long-range Coulomb repulsion and the short-range nuclear attraction [@pasta].

Based on the above arguments, it is very important that an accurate experimental measurement of the neutron skin thickness is achieved. This depends on a precise measurement of both the charge and the neutron radius. The charge radius is already known within a precision of one percent for most stable nuclei, using the well-known single-arm and non-polarized elastic electron scattering technique as well as the spectroscopy of muonic atoms [@vries] . For the neutron radius, our present knowledge has an uncertainty of about 0.2 fm [@horo]. However, using polarized electron beams it is possible to obtain the neutron distribution in nuclei in a fairly model independent way, as first discussed in [@Don] and, as a consequence, to obtain the desired neutron radius. In fact, the Parity Radius 