Nuclear Alpha-Particle Condensates

Abstract

The $\alpha$-particle condensate in nuclei is a novel state described by a product state of $\alpha$'s, all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical $\alpha$-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 $\alpha$ 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 $\alpha$-particle condensate states also exist in heavier $n\alpha$ 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 $4\alpha$ condensate. The calculated small width (34 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 $\alpha$'s, triton's, and neutrons etc. The relationship of $\alpha$-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 $\alpha$ particle condensation in infinite nuclear matter. The strong qualitative difference with the pairing case is pointed out.

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)

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• Signatures of $\alpha$-clustering in ${}^{12}$C and ${}^{13}$C
• Theory for Quartet Condensation in Fermi Systems with Applications to Nuclei and Nuclear Matter
• Clustering effects induced by light nuclei
• Ab initio calculation of the Hoyle state and a new look at clustering in nuclei