Uniquenucleus6optical potentials from elastic scattering of 210 MeVLi6ions bySi28,Ca40,Zr90, andPb208

Differential cross sections for the elastic scattering of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ions have been measured at a bombarding energy of 210 MeV. Angular distributions for ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ (3.6°–45.9°), ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ (4.6°–43.5°), and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ (4.0°–43.6°) extend sufficiently into the rainbow region to enable the extraction of unique ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ potentials. For the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ target (3.1°–36.0°), Coulomb scattering dominates with only a slight evidence of nuclear diffraction at the largest angles. The data were analyzed in terms of a six-parameter phenomenological optical-model potential with Woods-Saxon form factors. The unique potentials obtained show a weak target-mass dependence, which allowed the prediction of ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ potential parameters. Using the present results and lower energy analyses, an energy dependence for the ${}_{}{}^6{}_{}{}^{}\mathrm{nucleus}$ potentials was derived. For all targets, the volume integral per nucleon pair of the real potential seems to satisfy a logarithmic energy dependence of the form ${\mathit{J}}_{\mathit{R}}$/6A=${\mathit{J}}_{\mathit{R}}^0$/6A-β ln ${\mathit{E}}_{\mathrm{lab}}$ with $J_R^0$/6A=830±30 MeV ${\mathrm{fm}}^3$ and β=105±5 MeV ${\mathrm{fm}}^3$. This result is consistent with elastic scattering of other light ions. By truncating the angular distributions for the lighter targets up to the rainbow angle, several discrete potentials, corresponding to the different families found at lower energies, were obtained.