Probing the cluster structure of $^6$Li with the nuclear reaction $^6$Li + $^{12}$C at 68 MeV

Abstract

This work presents a combined experimental and theoretical investigation of the nuclear reaction $^{6}$Li + $^{12}$C at a laboratory energy of 68 MeV. The reaction products are identified via the standard $\Delta$E-E technique. Angular distributions are constructed for the elastic, inelastic, and deuteron transfer channels by detecting emitted particles -- $^{6}$Li and $\alpha$. Elastic and inelastic scattering of $^{6}$Li on $^{12}$C are analyzed using both the Optical Model and Coupled channels approaches, with the interaction described by a double-folding potential. This potential is calculated based on the three-body wave function of $^{6}$Li. Pronounced coupled-channel effects are observed, which modify the potential and allow accurate reproduction of the experimental cross sections. The resulting polarized potentials provide a more precise description of the initial-state interaction for further reaction modelling. The deuteron transfer channel, $^{12}$C($^{6}$Li, $\alpha$)$^{14}$N, is studied using the Coupled Reaction Channels method. The coupling between the transfer and elastic channels is implemented using the three-body wave function of $^{6}$Li. As an alternative, a regular wave function constructed with a phenomenological Woods-Saxon potential is also employed. Comparison between the calculated differential cross sections and experimental data reveals a more complex and nuanced reaction mechanism, which supports the cluster structure of $^{6}$Li.