Empirical evidence of an energy dependence of the radial shape of the real part of the optical potential

From a compilation of the real parts of phenomenological optical-model potentials which yield very good fits to the differential cross sections, it is concluded that in the cases of protons and neutrons on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and of protons on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ the radial shape of the potential varies rapidly with energy for bombarding energies smaller than 20 MeV. The potential half-depth radius decreases with increasing energy, while the surface diffuseness tends to increase with energy. This empirical energy dependence is stronger than the one calculated in the framework of a theoretical nuclear matter approach.