Comprehensive analysis of large $\alpha$ yields observed in $^{6}$Li induced reactions

Background: Large $\alpha$ yields have been reported over the years in reactions with $^{6}$Li and $^{7}$Li projectiles. Previous theoretical analyses have shown that the elastic breakup (EBU) mechanism (i.e., projectile breakup leaving the target in its ground state) is able to account only for a small fraction of the total $\alpha$ inclusive breakup cross sections, pointing toward the dominance of non-elastic breakup (NEB) mechanisms. Purpose: We aim to provide a systematic study of the $\alpha$ inclusive cross sections observed in nuclear reactions induced by $^{6}$Li projectiles. In addition to estimating the total $\alpha$ singles cross sections, it is our goal to evaluate angular and energy distributions of these $\alpha$ particles and compare with experimental data, when available. Method: We compute separately the EBU and NEB components of the inclusive breakup cross sections. For the former, we use the continuum-discretized coupled-channels (CDCC) method, which treats this mechanism to all orders. For the NEB part, we employ the the model proposed in the eighties by Ichimura, Austern and Vincent [Phys. Rev. C32, 432 (1982)], within the DWBA approximation. Results: Overall, the sum of the computed EBU and NEB cross sections is found to reproduce very well the measured singles cross sections. In all cases analyzed, we find that the inclusive breakup cross section is largely dominated by the NEB component. Conclusions: The presented method provides a global and systematic description of inclusive breakup reactions induced by $^{6}$Li projectiles. It provides also a natural explanation of the previously observed underestimation of the measured $\alpha$ yields by CDCC calculations. The method used here can be extended to other weakly-bound projectiles, including halo nuclei.