Effects of α -cluster potentials for the O 16 + O 16 fusion reaction and S factor

A joint analysis of the elastic-scattering angular distributions and fusion cross sections together with the $S$ factor for the $^{16}\mathrm{O}+^{16}\mathrm{O}$ system near and below the Coulomb barrier is reported. To describe these observables within the framework of the optical model, a comparative study of microscopic $\ensuremath{\alpha}$-$\ensuremath{\alpha}$ double-folding clusters and phenomenological shallow potentials with surface-transparent imaginary parts is performed. Although the phenomenological Woods-Saxon type of shallow real potentials is unable to provide a consistent explanation of these data, the $\ensuremath{\alpha}$-$\ensuremath{\alpha}$ double-folding cluster potential obtained by considering the $\ensuremath{\alpha}$-cluster structure of $^{16}\mathrm{O}$ provides a considerable improvement. The $\ensuremath{\alpha}$-$\ensuremath{\alpha}$ double-folding cluster potential also reproduces the normalized resonant energy states of $^{32}\mathrm{S}$ for the $N=24$ cluster band.