A previously derived projection operator method is applied to the calculation of the cross section for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\mathrm{O}}_2^{+}$) + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(g.s.) with a breathing mode model being used to describe the ${\mathrm{O}}_2^{+}$ (7.68 MeV) state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The relationship to processes leading to alpha particle channels is discussed. The cross section for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ($3^{-}$) + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(g.s.) is also calculated and possible correlations with inelastic scattering to the ${\mathrm{O}}_2^{+}$ and $2^{+}$ states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ are discussed. The results for both ${\mathrm{O}}_2^{+}$ and $3^{-}$ inelastic scattering are in reasonable agreement with experiment.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${\mathrm{O}}_2^{+}$) + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(g.s.) and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($3^{-}$) + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(g.s.), $E=10-30\mathrm{}$ MeV c.m., projection operator intermediate theory, calculated $\sigma$ (angle integrated ${\theta }_{\mathrm{lab}}=15\mathrm{}° \mathrm{to} 25°$).

• Received 29 June 1981

DOI:https://doi.org/10.1103/PhysRevC.25.1058