The angular distributions of cross sections for the reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${(}^3$He${,}^4$He${)}^{12}$C leading to ground state and first excited 4.44 MeV, $2^{+}$ state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured at sub-Coulomb energies of ${\mathit{E}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$=1.20 and 1.05 MeV. The angular distributions are asymmetric with respect to 90° and anisotropies are also found to be much larger than those expected from compound nuclear processes. Analyses of the data, with assumptions of direct transfer processes, by exact finite range distorted wave Born approximation calculations show the presence of interference of two modes of direct transfer mechanisms of neutron transfer and ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ cluster transfer from the target ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ to the projectile ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. These direct transfer calculations are in good agreement with the angular distributions and yield the value of the ratio of three nucleon spectroscopic strengths of first excited state to ground state of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ in good agreement with the value predicted from structure calculations.

• Received 11 May 1989

DOI:https://doi.org/10.1103/PhysRevC.42.1036