Secondary bow with ripples in \(^{12}\)C+\(^{12}\)C rainbow scattering

Abstract

We report, for the first time, the emergence of a secondary bow with ripples in \(^{12}\)C+\(^{12}\)C nuclear rainbow scattering. This finding was achieved by studying the experimental angular distributions in \(^{12}\)C+\(^{12}\)C scattering at incident energies \(E_L\) = 240 and 300 MeV, utilizing an extended double-folding model. This model accurately describes all diagonal and off-diagonal coupling potentials derived from the microscopic wave functions for \(^{12}\)C. Although the observed angular distributions of rainbow scattering at large angles (approaching \(90^\circ \)) are complicated by the symmetrization of two identical bosonic nuclei, the Airy minimum, associated with a dynamically generated secondary bow with ripples, is clearly identified at approximately 77\(^\circ \) for 240 MeV in the fall-off region of the primary nuclear rainbow. This finding, along with previous findings in the \(^{16}\)O+\(^{12}\)C and \(^{13}\)C+\(^{12}\)C systems, reinforces the concept of a secondary bow in nuclear rainbow scattering.