A nuclear projection model that produces generalized doorways in the sub-Coulomb region is used to calculate the modified structure factor S̃(E) in ${}_{}{}^{12}{}_{}{}^{}$C${+}^{12}$C down to about 3 MeV c.m. The formation of a compound nucleus is enhanced at energies near those of the generalized doorways which are obtained by coupling the shape resonances to the single and mutual excitation channels of the deformed ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ nuclei. The agreement between theory and experiment for S̃(E) in terms of magnitude and intermediate structure is dependent on the spreading width to complicated states as manifested in the energy averaging interval. The agreement in magnitude is striking in that the cross-section values are as small as ${10}^{\mathrm{-}3}$ mb at 3 MeV c.m. At low energies the nonresonant part of ${\sigma }_{\mathrm{comp}}$ is dominant, and the monotonic increase in S̃(E) with decreasing energy can be attributed to absorption under the barrier. Extrapolation of S̃(E) to the astrophysical energy of 1.7 MeV c.m. without a soft core suggests that the resonances will not introduce any dramatic structure. The presence of any prominent structure in this region may point to the need for a repulsive core in the nuclear potential.

• Received 17 October 1988

DOI:https://doi.org/10.1103/PhysRevC.39.897