  Nucleon density distributions and nucleus-nucleus interaction potentials for
the reactions $^{16}$O+$^{40}$Ca, $^{16}$O+$^{56}$Fe and $^{16}$O+$^{90}$Zr
have been calculated in the framework of the modified Thomas-Fermi method and
considering all terms up to the second order in $\hbar$ in the quasi-classical
expansion of the kinetic energy. Skyrme forces dependent on the nucleon density
are used as the nucleon-nucleon interaction. A parametrization of the
nucleus-nucleus interaction potential, which well describes the potential value
calculated within the modified Thomas-Fermi approach with density-dependent
Skyrme forces, is found. On the basis of the obtained potentials, the
cross-sections of elastic scattering are calculated in a good agreement with
experimental data.
