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The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs - Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of a direct variational method based on Fermi-like trial functions.

The neutron skin and halo distributions in medium and heavy nuclei are calculated within the extended Thomas - Fermi approximation. Calculations are carried out for the effective Skyrme-like forces using the direct variational method. The analytical expression for the isovector shift of the rms radii Δrnp as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to Δrnp are found to be approximately equal.

The isovector particle densities and surface tension coefficients for the average binding energy in the approximation of a sharp edge proton-neutron asymmetric nucleus are used for analytical calculations of its neutron skin and isovector stiffness coefficients. They are significantly different from the well-known ones for the most Skyrme forces. The energies and energy-weighted sum rules of the isovector giant dipole resonances obtained within the Fermi-liquid drop model are in good agreement with the experimental data.