Binary reaction decays from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Mg</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>24</mml:mn></mml:mrow></mml:mmultiscripts><mml:mrow><mml:mo>+</mml:mo></mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

Charged-particle and $\ensuremath{\gamma}$ decays in $^{24}\mathrm{Mg}{}^{*}$ are investigated for excitation energies where quasimolecular resonances appear in $^{12}\mathrm{C}+^{12}\mathrm{C}$ collisions. Various theoretical predictions for the occurrence of superdeformed and hyperdeformed bands associated with resonance structures with low spin are discussed within the measured $^{24}\mathrm{Mg}{}^{*}$ excitation energy region. The inverse kinematics reaction $^{24}\mathrm{Mg}+^{12}\mathrm{C}$ is studied at ${E}_{\mathrm{lab}}(^{24}\mathrm{Mg})=130$ MeV, an energy that enables the population of $^{24}\mathrm{Mg}$ states decaying into $^{12}\mathrm{C}+^{12}\mathrm{C}$ resonant breakup states. Exclusive data were collected with the Binary Reaction Spectrometer in coincidence with Euroball IV installed at the Vivitron tandem facility at Strasbourg. Specific structures with large deformation were selectively populated in binary reactions, and their associated $\ensuremath{\gamma}$ decays studied. Coincident events associated with inelastic and $\ensuremath{\alpha}$-transfer channels have been selected by choosing the excitation energy or the entry point via the two-body $Q$ values. The analysis of the binary reaction channels is presented with a particular emphasis on $^{24}\mathrm{Mg}\text{\ensuremath{-}}\ensuremath{\gamma}$, $^{20}\mathrm{Ne}\text{\ensuremath{-}}\ensuremath{\gamma}$, and $^{16}\mathrm{O}$-$\ensuremath{\gamma}$ coincidences. New information (spin and branching ratios) is deduced on high-energy states in $^{24}\mathrm{Mg}$ and $^{16}\mathrm{O}$, respectively.

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