Evidence for the existence of the lowest $N=24\mathrm{}$ and $N=28\mathrm{}$ cluster bands with the ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ cluster structure in ${}^{32}\mathrm{S}$ is shown from the viewpoint of unified description of bound and scattering states of the ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ system. The ${}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ cluster band structure, the gross structure of the $90°$ excitation function ${\mathrm{for}}^{16}\mathrm{O}{+}^{16}\mathrm{O}$ elastic scattering, and the Airy minima are understood in a unified way. The existence of the unobserved $N=26\mathrm{}$ higher nodal band is predicted.

• Received 18 March 2002

DOI:https://doi.org/10.1103/PhysRevC.66.021301