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Our present understanding of the structure of the Hoyle state in $^{12}$C and other near-threshold states in $alpha$-conjugate nuclei is reviewed in the framework of the $alpha$-condensate model. The $^{12}$C Hoyle state, in particular, is a candidate for $alpha$-condensation, due to its large radius and $alpha$-cluster structure. The predicted features of nuclear $alpha$-particle condensates are reviewed along with a discussion of their experimental indicators, with a focus on precision break-up measurements. Two experiments are discussed in detail, firstly concerning the break-up of $^{12}$C and then the decays of heavier nuclei. With more theoretical input, and increasingly complex detector setups, precision break-up measurements can, in principle, provide insight into the structures of states in $alpha$-conjugate nuclei. However, the commonly-held belief that the decay of a condensate state will result in $N$ $alpha$-particles is challenged. We further conclude that unambiguously characterising excited states built on $alpha$-condensates is difficult, despite improvements in detector technology.
Method: To examine signatures of this alpha-condensation, a compound nucleus reaction using 160, 280, and 400 MeV 16O beams impinging on a carbon target was used to investigate the 12C(16O,7a) reaction. This permits a search for near-threshold states
In the context of the search for triples of relativistic $alpha$-particles in the Hoyle state, the analysis of available data on the dissociation of the nuclei ${}^{12}$C, ${}^{16}$O and ${}^{22}$Ne in the nuclear emulsion was carried out. The Hoyle
The fragmentation of quasi-projectiles from the nuclear reaction $^{40}Ca$ + $^{12}C$ at 25 MeV/nucleon was used to produce excited states candidates to $alpha$-particle condensation. The experiment was performed at LNS-Catania using the CHIMERA mult
The fragmentation of quasi-projectiles from the nuclear reaction $^{40}$Ca+$^{12}$C at 25 MeV/nucleon was used to produce excited states candidates to $alpha$-particle condensation. Complete kinematic characterization of individual decay events, made
The critical behavior for the light nuclei with A$sim 36$ has been investigated experimentally by the NIMROD multi-detectors. The wide variety of observables indicate the critical point has been reached in the disassembly of hot nuclei at an excitation energy of 5.6$pm$0.5 MeV/u.