Molecular structure of highly excited resonant states in ${}^{24}\mathrm{Mg}$ and the corresponding ${}^8\mathrm{Be}+{}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ decays

Exotic ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$ decays from high-lying resonances in ${}^{24}\mathrm{Mg}$ are analyzed in terms of a cluster model. The calculated quantities agree well with the corresponding experimental data. It is found that the calculated decay widths are very sensitive to the angular momentum carried by the outgoing cluster. It is shown that this property makes cluster decay a powerful tool to determine the spin as well as the molecular structures of the resonances.