Nuclear Alpha-Particle Condensates

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 (E_x=7.65 MeV,0^+_2 state in ^{12}C), which plays a crucial role for the synthesis of ^{12}C 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 ^{16}O,^{20}Ne, etc. For instance the 0^+_6 state of ^{16}O at E_x=15.1 MeV is identified from a theoretical analysis as being a strong candidate of a 4α condensate. The calculated small width (140 keV) of 0^+_6, consistent with data, lends credit to the existence of heavier Hoyle-analogue states. In non-self-conjugated nuclei such as ^{11} B and ^{13} C, 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.