The ground-state properties of magic nuclei have been studied by means of the Gogny force within the Hartree-Fock Scheme using the Slater approximation for the exchange part. A similar analysis has been carried out within the semiclassical framework by considering the extended Thomas-Fermi approach for the kinetic energy density. Comparisons with the complete Hartree-Fock results are made. The ion-ion potential for two colliding nuclei has been obtained in the energy density functional and the double-folded model approaches by using self-consistent semiclassical densities calculated with the Gogny force. These potentials have been applied in the study of ⁴⁰Ca-⁴⁰Ca elastic scattering.