The α-particle condensate in nuclei is a novel state described by a
product state of α's, all with their c.o.m. in the lowest 0S orbit. We
demonstrate that a typical α-particle condensate is the Hoyle state
(Ex=7.65 MeV, 02+ state in 12C), which plays a crucial role for
the synthesis of 12C in the universe. The influence of antisymmentrization
in the Hoyle state on the bosonic character of the α particle is
discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle
state, therefore, are predominant. It is conjectured that α-particle
condensate states also exist in heavier nα nuclei, like 16O,
20Ne, etc. For instance the 06+ state of 16O at Ex=15.1 MeV
is identified from a theoretical analysis as being a strong candidate of a
4α condensate. The calculated small width (34 keV) of 06+,
consistent with data, lends credit to the existence of heavier Hoyle-analogue
states. In non-self-conjugated nuclei such as 11B and 13C, we discuss
candidates for the product states of clusters, composed of α's,
triton's, and neutrons etc. The relationship of α-particle condensation
in finite nuclei to quartetting in symmetric nuclear matter is investigated
with the help of an in-medium modified four-nucleon equation. A nonlinear order
parameter equation for quartet condensation is derived and solved for α
particle condensation in infinite nuclear matter. The strong qualitative
difference with the pairing case is pointed out.Comment: 71 pages, 41 figures, review article, to be published in "Cluster in
Nuclei (Lecture Notes in Physics) - Vol.2 -", ed. by C. Beck,
(Springer-Verlag, Berlin, 2011