Abstract
The possibility that a four component Fermi gas with attractive interaction can form a quartet condensate at low density is pointed out. It is discussed that for quartets only the Bose-Einstein Condensatio (BEC) phase exists and that the analogue to the weak coupling long coherence BCS phase of pairing is absent. Precurser phenomena in finite nuclei are presented. For instance, the present understanding of the structure of the Hoyle state in 12C being the gateway for Carbon production in the universe is reviewed. It is pointed out that a crucial test of any theory is the good reproduction of the experimental results for the inelastic form factor from ground to the Hoyle state. The performances of the so-called THSR wavwe function are outlined confirming the α particle condensation hypothesis proposed 15 years back in [1].
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