Nuclear rainbow scattering and nucleus-nucleus potential

Elastic scattering of alpha-particles and some tightly bound light nuclei has shown the pattern of rainbow scattering at medium energies, which is due to the refraction of the incident wave by a strongly attractive nucleus-nucleus potential. This review gives an introduction to the physics of the nuclear rainbow based essentially on the optical model description of the elastic scattering. Since the realistic nucleus-nucleus optical potential (OP) is the key to explore this interesting process, an overview of the main methods used to determine the nucleus-nucleus OP is presented. Given the fact that the absorption in a rainbow system is much weaker than that usually observed in elastic heavy- ion scattering, the observed rainbow patterns were shown to be linked directly to the density overlap of the two nuclei penetrating each other in the elastic channel, with a total density reaching up to twice the nuclear matter saturation density rho(0). For the calculation of the nucleus-nucleus OP in the double-folding model, a realistic density dependence has been introduced into the effective M3Y interaction which is based originally on the G-matrix elements of the Reid and Paris nucleon-nucleon (NN) potentials. Most of the elastic rainbow scattering data were found to be best described by a deep real OP like the folded potential given by this density-dependent M3Y interaction. Within the Hartree-Fock formalism, the same NN interaction gives consistently a soft equation of state of cold nuclear matter which has an incompressibility constant K approximate to 230-260 MeV. Our folding analysis of numerous rainbow systems has shown that the elastic alpha-nucleus and nucleus-nucleus refractive rainbow scattering is indeed a very helpful experiment for the determination of the realistic K value. The refractive rainbow-like structures observed in other quasi-elastic scattering reactions have also been discussed. Some evidences for the refractive effect in the elastic scattering of unstable nuclei are presented and perspectives for future studies are discussed.