  Semiclassical expansions derived in the framework of the Extended
Thomas-Fermi approach for the kinetic energy density tau(r) and the spin-orbit
density J(r) as functions of the local density rho(r) are used to determine the
central nuclear potentials V_n(r) and V_p(r) of the neutron and proton
distribution for effective interactions of the Skyrme type. We demonstrate that
the convergence of the resulting semiclassical expansions for these potentials
is fast and that they reproduce quite accurately the corresponding Hartree-Fock
average fields.
