Direct Two-Nucleon Pickup in (d, α) Reactions

Angular distributions for the ($d, \alpha$) reactions on ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ targets have been measured in the 10-12-MeV incident-deuteron energy range. The ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}(d, \alpha ){}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ measurements have been repeated at a deuteron energy of 33.7 MeV. The experimental angular distributions for the first three $\alpha$ groups in each reaction have been fitted and analyzed using a zero-range distorted-wave Born-approximation two-particle pickup calculation. Nuclear-structure factors were computed from shell-model wave functions and tested against the experimental results. The shapes of the angular distributions and the relative magnitudes of the experimental cross sections are both found to be successfully predicted by the theory. The ground-state reactions have also been analyzed using a simple cluster-transfer approximation, and the results are compared with the more exact analysis. The cluster-transfer approximation is shown to predict correctly the dominant $L$, $J$ values contributing to the ($d, \alpha$) reactions, but cannot give absolute cross sections.