Phenomenological Analysis of theC12+C12Reaction

The total ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ low-energy reaction cross section has been reanalyzed. Three phenomena suggest an $\alpha$-particle model for the reaction: (1) the giant resonances, (2) the intermediate-structure resonances, and (3) anomalous branching ratios. The energy dependence of the total cross section over the energy range 2.4 to 9.0 MeV cannot be explained solely by the energy dependence of the penetration of the Coulomb barrier. There is some nuclear structure. The structure can be explained by an optical potential based on the $\alpha$ model leading to absorption under the barrier. It could also be explained with two giant resonances in a Woods-Saxon potential. The intermediate structure is explained as due to special states of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ built of a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ core and three $\alpha$ particles, and so are the anomalous branching ratios.