Nuclear Rainbow of Core-Symmetric Systems

The nearside-farside (NF) decomposition method developed originally by Fuller for elastic scattering of a nonidentical nucleus-nucleus system was generalized to study the nuclear rainbow pattern in a symmetric or core-symmetric dinuclear system. It has been shown that the projectile-target identity of an identical system implies a symmetric interchange of the nearside and farside components of elastic scattering amplitude around $\theta_{\mathrm{c.m.}}=90^\circ$. A similar interchange appears also in a nonidentical core-symmetric system due to elastic transfer of cluster or nucleon between two identical cores. The analysis of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$, and ${}^{13}\mathrm{C}+{}^{12}\mathrm{C}$ systems shows how the generalized NF decomposition method reveals the nuclear rainbow pattern in these systems, which can be helpful in probing the real optical potential and nuclear clustering.