  The full relaxed-density potential between spherical nuclei is considered as
a sum of the macroscopic and shell-correction contributions. The macroscopic
part of the potential is related to a nucleus-nucleus potential obtained in the
framework of the extended Thomas-Fermi approach with the Skyrme and Coulomb
forces and the relaxed-density ansatz for evaluation of proton and neutron
densities of interacting nuclei. A simple prescription for the shell-correction
part of the total potential is discussed. The parameters of the
shell-correction and macroscopic parts of the relaxed-density potential are
found by fitting the empirical barrier heights of the 89 nucleus-nucleus
systems as well as macroscopic potentials evaluated for 1485 nucleus-nucleus
systems at 12 distances around touching points.
