Emergence of a secondary rainbow and the dynamical polarization potential for 16O on 12C at 330 MeV

Background: An anomaly in the elastic scattering of O-16 on C-12 around 300 MeV was resolved by including collective excitations of both nuclei, leading to a secondary rainbow. There is little systematic knowledge of the contribution of collective excitations to the interaction between nuclei, particularly in the overlap region of heavy nuclei. Purpose: To study the dynamic polarization potential (DPP) generated by channel coupling that had been validated for a case where scattering is sensitive to the nuclear potential over a wide radial range; to exhibit evidence of the non-locality due to collective coupling; to validate, or otherwise, the representation of DPPs by uniform renormalization of potentials. Methods: S-matrix to potential inversion yields local potentials reproducing the elastic channel S-matrix of coupled channel calculations. Subtracting the elastic channel uncoupled potential yields a local L-independent representation of the DPP. The dependence of the DPP on the nature of the coupled states and other parameters can be studied. Results: Local DPPs were found due to the excitation of C-12 and the combined excitation of O-16 and C-12. The radial forms found were very different from uniform renormalization of the potential. Full coupling led to a 10 percent increase in the volume integral of the real potential. Evidence for the non-locality of the underlying formal DPP and the effect of direct coupling between the collective states is found. Conclusions: The local DPP generating the secondary rainbow is found. DPPs have forms depending on the specific excitations and cannot be represented by a uniform renormalization of the potential. The method is useful for study of the contribution of collective excitations to internuclear potentials, concerning which remarkably little is known in general.