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.