Phenomenological Analysis of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ Reaction

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.

Astrophysical reaction rates were calculated for a number of possible optical potentials. The giant resonances affect the extrapolation to the energies of astrophysical interest and lead to an uncertainty of a factor of 3 to 10 in the astrophysical reaction rate at $T_9\simeq 0.6$, where $T_9\equiv {10}^{-9\mathrm{}}T$°K.