Coupled-reaction-channel study of the C12(α,Be8) reaction and the Be8+Be8 optical potential

Abstract

Background: Given the established $2\ensuremath{\alpha}$ structure of $^{8}\mathrm{Be}$, a realistic model of four interacting $\ensuremath{\alpha}$ clusters must be used to obtain a $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ interaction potential. Such a four-body problem poses a challenge for the determination of the $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ optical potential (OP) that is still unknown due to the lack of the elastic $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ scattering data.Purpose: To probe the complex $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ optical potential in the coupled-reaction-channel (CRC) study of the $\ensuremath{\alpha}$ transfer $^{12}\mathrm{C}(\ensuremath{\alpha},^{8}\mathrm{Be})$ reaction measured at ${E}_{\ensuremath{\alpha}}=65$ MeV and to obtain the spectroscopic information on the $\ensuremath{\alpha}+^{8}\mathrm{Be}$ cluster configuration of $^{12}\mathrm{C}$.Method: The three- and four-body continuum-discretized coupled-channel (CDCC) methods are used to calculate the elastic $\ensuremath{\alpha}+^{8}\mathrm{Be}$ and $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ scattering at the energy around 16 MeV/nucleon, with the breakup effect taken into account explicitly. Based on the elastic cross section predicted by the CDCC calculation, the local equivalent OP's for these systems are deduced for the CRC study of the $^{12}\mathrm{C}(\ensuremath{\alpha},^{8}\mathrm{Be})$ reaction.Results: Using the CDCC-based OP's and $\ensuremath{\alpha}$ spectroscopic factors given by the cluster model calculation, a good CRC description of the $\ensuremath{\alpha}$ transfer data for both the $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ and $^{8}\mathrm{Be}+^{8}\mathrm{Be}_{{2}^{+}}^{*}$ exit channels is obtained without any adjustment of the (complex) potential strength.Conclusion: The $\ensuremath{\alpha}+^{8}\mathrm{Be}$ and $^{8}\mathrm{Be}+^{8}\mathrm{Be}$ interaction potential can be described by the three- and four-body CDCC methods, respectively, starting from a realistic $\ensuremath{\alpha}+\ensuremath{\alpha}$ interaction. The $\ensuremath{\alpha}$ transfer $^{12}\mathrm{C}(\ensuremath{\alpha},^{8}\mathrm{Be})$ reaction should be further investigated not only to probe of the $4\ensuremath{\alpha}$ interaction but also the cluster structure of $^{12}\mathrm{C}$.