  The symmetry energy, the neutron pressure and the asymmetric compressibility
of deformed neutron-rich even-even nuclei are calculated on the examples of Kr
and Sm isotopes within the coherent density fluctuation model using the
symmetry energy as a function of density within the Brueckner energy-density
functional. The correlation between the thickness of the neutron skin and the
characteristics related with the density dependence of the nuclear symmetry
energy is investigated for isotopic chains of these nuclei in the framework of
the self-consistent Skyrme-Hartree-Fock plus BCS method. Results for an
extended chain of Pb isotopes are also presented. A remarkable difference is
found in the trend followed by the different isotopic chains: the studied
correlations reveal a smoother behavior in the Pb case than in the other cases.
We also notice that the neutron skin thickness obtained for $^{208}$Pb with
SLy4 force is found to be in a good agreement with recent data.
