The spline analyses on the secondary rainbow pattern in the elastic scattering of 16O+12C at 300MeV and 330MeV

In the elastic scattering angular distributions of nuclei, the secondary rainbow manifests itself as an extra maximum (accompanied with a minimum as well) in the darkside of the primary rainbow. This phenomenon was first observed in the elastic scattering of [Formula: see text]O+[Formula: see text]C at around 300[Formula: see text]MeV. It is believed to be generated by the coupling to the first 2[Formula: see text] excitation of [Formula: see text]C and influenced by the couplings to other inelastic scattering channels. In this work, the optical potentials with a spline real part were utilized in the optical model analyses of the elastic scattering data of [Formula: see text]O+[Formula: see text]C at 300[Formula: see text]MeV and 330[Formula: see text]MeV. The spline real potentials were obtained by performing the data fitting starting from the phenomenological Woods–Saxon form and the double folding one, respectively. Through this approach, the secondary rainbow patterns of the two systems were reproduced well. The obtained spline real potentials exhibit an evident additional refraction (a potential pocket) at around [Formula: see text][Formula: see text]fm and show a preference to the shallow central depth. The semiclassical analyses were performed to learn the physical meaning of these obtained optical potentials. According to the nearside/farside decomposition, this secondary rainbow pattern was shown as the result of the farside scattering. In the deflection functions, a new minimum appears apart from the primary rainbow one, of which the former was proved to be related to the secondary rainbow maximum in the angular distribution. The potential pocket around [Formula: see text][Formula: see text]fm in the real potential was found responsible for the generation of the secondary rainbow pattern. However, the additional refraction caused by this potential pocket might not be associated with the Airy pattern. The present physical picture of the nuclear primary/secondary rainbow pattern is a two-refraction process originating from the non-monotonic repulsive-attractive real potential. Hence, the secondary rainbow pattern in the angular distribution corresponds to a complicated interference of the farside trajectories which distorts the original Airy oscillation pattern. Besides, for the phenomenological analysis of this pattern, a potential ambiguity was also found in the undulations of the real potential.