The population and decay of excited states in ${}^{24}\mathrm{Mg}$ has been investigated through the ${}^{12}{\mathrm{C}(}^{16}{\mathrm{O},}^{12}{\mathrm{C}}^{12}\mathrm{C})\alpha$ and ${}^{12}{\mathrm{C}(}^{16}{\mathrm{O},}^8{\mathrm{Be}}^{16}\mathrm{O})\mathrm{\alpha }$ reactions, at beam energies of 75, 85, and 115 MeV. The fragments from the breakup of the ${}^{24}\mathrm{Mg}$ nucleus were detected in coincidence, permitting a study of both the excitation energies and the spins of the fissioning states. These measurements indicate a series of states in ${}^{24}\mathrm{Mg}$ between 20 and 40 MeV with spins ranging from $J=4\mathrm{}$ to 14 $ħ$. The results are discussed in the context of the ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ quasimolecular scattering resonances and other ${}^{24}\mathrm{Mg}$ breakup reactions.

• Received 10 October 1997

DOI:https://doi.org/10.1103/PhysRevC.57.1277