Light-ion elastic scattering potentials: Energy and projectile-mass dependence

Volume integrals of the real potentials derived from elastic scattering studies of deuterons, tritons, ${}^3\mathrm{He},$ and $\alpha$ particles have been calculated for data available from the lowest to the highest energy. These volume integrals have been plotted as a function of energy per nucleon for each projectile. By selecting energy regions where there were least ambiguities in the potentials and averaging the volume integrals in 1 MeV bins, the energy dependences were determined. The volume integrals show a logarithmic dependence on the energy per nucleon. The zero crossing of the potentials is at about the same value of $\sim 650\mathrm{MeV}/$nucleon for all projectiles. With increasing projectile mass, the potentials become weaker, possibly due to Pauli blocking effects in the projectile. Neutron-rich projectiles have smaller volume integrals due to the manifestation of the isospin effect. A similar analysis of the imaginary volume integrals shows that they increase from zero at the lowest energies to about $100–150{\mathrm{MeV}\mathrm{}\mathrm{fm}}^3$ around $10\mathrm{MeV}/$nucleon and then remain essentially constant.