it was shown that the difference between the neutron and the proton radii, the neutron skin thickness, is linearly correlated with the pressure of neutron matter at sub-nuclear densities. This is so because the properties of neutron stars are obtained from appropriate EoS whose symmetry energy depends on the density and also controls the size of the neutron skin thickness in heavy and asymmetric nuclei, as $^{208}$ Pb, for instance. It is important to remember that the EoS in neutron stars is also very isospin asymmetric due to the $\beta$- equilibrium constraint.

Hence, isospin asymmetry plays a major role in the understanding of the density dependence of the symmetry energy and the consequences it may arise [@steiner]. In [@hp01; @piek06] it was shown that the models that yield smaller neutron skins in heavy nuclei tend to yield smaller neutron star radii due to a softer EoS.

Neutron stars are believed to have a solid crust formed by nonuniform neutron rich matter in $\beta$-equilibrium above a liquid mantle. In the inner crust nuclei coexist with a gas of neutrons which have dripped out. The properties of this crust as, for instance, its thickness and pressure at the crust-core interface depend a 