Alpha-Particle Condensation in Nuclear Systems
  The onset of quartetting, i.e. alpha-particle condensation, in symmetric nuclear matter is studied with the help of an in-medium modified four nucleon equation. It is found that at very low density quartetting wins over pairing, because of the strong binding of the alpha-particles. The critical temperature can reach values up to around 6 MeV. Also the disappearance of alpha-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 0_2^+ of 12C, is identified as an "alpha-particle condensate" state. It is conjectured that such states also exist in heavier n alpha-nuclei, like 16O, 20Ne, etc. For instance the 6-th 0^+ state of 16O at 15.1 MeV is identified from a theoretical analysis as being a strong candidate for an alpha condensate state. Exploratory calculations are performed for the density dependence of the alpha condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density. Possible quartet condensation in other systems is discussed briefly 
Y. Funaki, T. Yamada, H. Horiuchi, G. R\"opke, P. Schuck and A.   Tohsaki