Abstract. Elastic scattering of α-particle 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 nucleusnucleus 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 ρ 0 . For the calculation of the nucleus-nucleus OP in the doublefolding 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 ≈ 230 − 260 MeV. Our folding analysis of numerous rainbow systems has shown that the elastic α-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 quasielastic scattering reactions have also been discussed. Some evidences for the refractive effect in the elastic scattering of unstable nuclei are presented and perspectives for the future studies are discussed.

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The reaction mechanism of heavy-ion charge-exchange scattering at low and intermediate incident energies is studied theoretically. Contributions of direct charge exchange due to central and tensor isovector interactions and of charge exchange via sequential proton and neutron transfer are taken into account in one-step and two-step exact-finite-range distorted-wave Born-approximation calculations. The nuclear structure of the intermediate and final states is described within the shell model. Calculations for ' C(' C, ' N) "B indicate that direct charge exchange is safely dominant for incident energies F/A~100 MeV. PACS numbers: 25.70.Cd, 24. 50.+gCharge-exchange scattering has become a very useful new application of heavy-ion physics aiming at spectroscopic studies of both proton-neutron (p, n) and neutron-proton (n, p) type transitions in nuclei. However, the interpretation of such data is complicated because the final channels can be populated by the two distinct reaction mechanisms of direct and transfer charge exchange. In the direct process the final states are excited

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