Sub-Coulomb cross sections for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C→α${+}^{20}$Ne, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C→p${+}^{23}$Na, and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C→n ${+}^{23}$Mg are calculated in a semistatistical framework that allows a comparison to experiment in terms of the general energy dependence and magnitude. Intermediate structure previously produced in the generalized doorway model via calculations of the structure factor is not evident in the present approach because of the large energy dependence of the reaction cross sections. The compound nucleus is described in a generalized doorway model where the doorways are obtained by coupling the shape resonances in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$${+}^{12}$C to the single and mutual excitation channels. The transmission coefficients for decay are determined in a modified form of the Hauser-Feshbach method. Agreement is good in terms of energy dependence and magnitude even though the experimental cross sections vary by about 4 orders of magnitude between 3 and 5 MeV c.m.

• Received 14 December 1989

DOI:https://doi.org/10.1103/PhysRevC.42.1768