A projection operator method based on the Feshbach doorway approach is developed for low-energy heavy-ion scattering. Applications to ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ are made with doorways taken as quasibound or virtual states of the reduced mass coupled to $2^{+}$ and $3^{-}$ vibrations. For ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ the elastic differential cross section at 90° c.m. is calculated. For ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ we calculate the ratio of the differential cross section to the Rutherford cross section at a range of angles between 90° and 160° c.m. In both cases the calculations agree well with experiment by producing both the gross and intermediate molecular structure. The conditions under which intermediate structure can be expected are discussed.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ elastic scattering, $E=10-30\mathrm{}$ MeV c.m., ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ elastic scattering, $E=18-26\mathrm{}$ MeV c.m., projection operator intermediate structure theory, calculated $\sigma \left(90\mathrm{}°\right)$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and $\frac{\sigma }{{\sigma }_{\mathrm{Ruth}}}$ (90°-160°, increments of 10°) for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.

• Received 7 January 1980

DOI:https://doi.org/10.1103/PhysRevC.22.1145