  The effective-surface approximation is extended taking into account
derivatives of the symmetry-energy density per particle with respect to the
mean particle density. The isoscalar and isovector particle densities in this
extended effective-surface approximation are derived. The improved expressions
of the surface symmetry energy, in particular, its surface tension coefficients
in the sharp-edged proton-neutron asymmetric nuclei take into account important
gradient terms of the energy density functional. For most Skyrme forces the
surface symmetry-energy constants and the corresponding neutron skins and
isovector stiffnesses are calculated as functions of the Swiatecki derivative
of the nongradient term of the symmetry-energy density per particle with
respect to the isoscalar density. Using the analytical isovector surface-energy
constants in the framework of the Fermi-liquid droplet model we find energies
and sum rules of the isovector giant-dipole resonance structure in a reasonable
agreement with the experimental data, and they are compared with other
theoretical approaches.
