Symmetry energy: from nuclear matter to finite nuclei

We suggest a particular procedure of derivation of the beta-stability line and isotopic symmetry energy. The behavior of the symmetry energy coefficient $b(A,N-Z)$ is analyzed. We redefine the surface tension coefficient and the surface symmetry energy for an asymmetric nuclear Fermi-liquid drop with a finite diffuse layer. Following Gibbs-Tolman concept, we introduce the equimolar radius at which the surface tension is applied. The relation of the nuclear macroscopic characteristics like surface and symmetry energies, Tolman length, etc. to the bulk properties of nuclear matter is considered. The surface-to-volume symmetry energy ratio for several Skyrme-force parametrizations is obtained.