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Nuclear Alpha-Particle Condensates

  • T. Yamada
  • Y. Funaki
  • H. Horiuchi
  • G. Röpke
  • P. Schuck
  • A. Tohsaki
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 848)

Abstract

The \(\alpha\)-particle condensate in nuclei is a novel state described by a product state of \(\alpha\hbox{'s},\) all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical \(\alpha\)-particle condensate is the Hoyle state \((E_{x}=7.65\,\hbox{MeV},\;0^+_2\) state in \(^{12}\hbox{C}),\) which plays a crucial role for the synthesis of \(^{12}\hbox{C}\) 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 \(^{16}\hbox{O},\;^{20}\hbox{Ne},\) etc. For instance the \(0^+_6\) state of \(^{16}\hbox{O}\) at \(E_{x}=15.1\,\hbox{MeV}\) is identified from a theoretical analysis as being a strong candidate of a \(4\alpha\) 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 \(^{11} \hbox{B}\) and \(^{13} \hbox{C},\) we discuss candidates for the product states of clusters, composed of \(\alpha\hbox{'s},\) 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.

Keywords

Wave Function Nuclear Matter Occupation Probability Particle Condensation Condensate Fraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors would like to thanks to B. Borderie, M. Freer, Y. Hatanaka, K. Ikeda, M. Itoh, T. Kawabata, K. Kat\(\bar{\hbox{o}}\), W. von Oertzen, M. F. Rivet, T. Sogo, and T. Wakasa for useful discussions and comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg  2012

Authors and Affiliations

  • T. Yamada
    • 1
  • Y. Funaki
    • 2
  • H. Horiuchi
    • 3
    • 4
  • G. Röpke
    • 5
  • P. Schuck
    • 6
    • 7
    • 8
  • A. Tohsaki
    • 3
  1. 1.Laboratory of PhysicsKanto Gakuin UniversityYokohamaJapan
  2. 2.Nishina Center for Accelerator-based ScienceThe Institute of Physical and Chemical Research (RIKEN)WakoJapan
  3. 3.Research Center for Nuclear Physics (RCNP)Osaka University IbarakiOsakaJapan
  4. 4.International Institute for Advanced StudiesKyotoJapan
  5. 5.Institut für PhysikUniversität RostockRostockGermany
  6. 6.Institut de Physique NucléaireCNRSOrsayFrance
  7. 7.Université Paris-SudOrsayFrance
  8. 8.Labratoire de Physique et Modélisation des Milieux Condensés, CNRS etUniversité Joseph FourierGrenoble Cedex 9France

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