A projection operator method is presented for the calculation of low energy heavy ion inelastic scattering cross sections. The theory treats both gross and intermediate structure and is applied to the case of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+ ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→ ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($2^{+}$)+ ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(g.s.), where particle-vibration doorways of both $2^{+}$ and $3^{-}$ origin are included. The results are in reasonable agreement with experiment. A discussion of the possible effects of doorways of $0_2^{+}$ origin is given.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+ ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$→ ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($2^{+}$)+ ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(g.s.), $E=10-30\mathrm{}$ MeV c.m., projection operator intermediate structure theory, calculated ${\sigma }_{\mathrm{total}}$.

• Received 27 May 1981

DOI:https://doi.org/10.1103/PhysRevC.25.833