Unbound states of $^{10}$C nuclei produced as quasi-projectiles in $^{12}$C+$^{24}$Mg collisions at E/A = 53 and 95 MeV are studied with the Indra detector array. Multi-particle correlation function analyses provide experimental evidence of sequential de-excitation mechanisms through the production of intermediate $^{9}$B, $^{6}$Be and $^{8}$Be unbound nuclei. The relative contributions of different decay sequences to the total decay width of the explored states is estimated semi-quantitatively. The obtained results show that heavy-ion collisions can be used as a tool to access spectroscopic information about exotic nuclei.
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