$α$-cluster decay from $^{24}$Mg resonances produced in $^{12}$C($^{16}$O,$^{24}$Mg)$α$ reaction
A transfer reaction and cluster-decay experiment, $^{12}$C($^{16}$O,$^{24}$Mg$\rightarrow$$α$+$^{20}$Ne)$α$, was performed at a beam energy of 96 MeV. Both recoil and decay $α$ particles were detected in coincidence, allowing us to deduce the energy-momentum of a $^{20}$Ne fragment. A number of resonant states of $^{24}$Mg were reconstructed up to an excitation energy of approximately 30 MeV. Owing to the experimentally achieved excellent resolutions of the $Q$-value and excitation-energy spectra, the relative decay widths for each resonant state in $^{24}$Mg to various final states of $^{20}$Ne were extracted, alone with the total decay width. The obtained results provide good testing ground for theoretical descriptions of the multiple clustering configurations in $^{24}$Mg.