Final-state interactions in theC12(16O,12C12C)α andO16(16O,12C16O)α reactions

The population of excited states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ has been investigated through the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ${(}^{16}$O${,}^{12}$ ${\mathrm{C}}^{12}$C)α and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ ${(}^{16}$O${,}^{12}$ ${\mathrm{C}}^{16}$O)α, at beam energies of 80.5 and 99 MeV. The heavy-ion fragments from the breakup of the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ nuclei were detected in coincidence, permitting a study of both the reaction kinematics and the spins of the fissioning states. These measurements indicate a series of states in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ between 25 and 32 MeV with spins ranging from J=10 to 14 ħ. Evidence was also found for the breakup of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ into ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ from states between 27 and 29 MeV.