Nuclear alpha-particle condensates: Definitions, occurrence conditions, and consequences

Abstract

There has been a recent flurry of interest in the possibility of condensates of $\alpha$-particles in nuclei. In this letter we discuss occurrence conditions for such states. Using the quantality condition of Mottelson we show that condensates are only marginally expected in $\alpha$-particle states. We proceed to demonstrate that few-body nuclear condensates are ill-defined, and emphasize the conflict between $\alpha$-localization and $\alpha$-condensate formation. We also explore the connection between Ikeda diagrams, linear chains, and Tonks-Girardeau gases. Our findings show that no new information is contained in the approximations of nuclear states as $\alpha$-cluster condensates. Furthermore, condensates of more than three $\alpha$-particles are very unlikely to exist due to couplings to other degrees of freedom.

5 pages, revtex4 format. Final published version with date of submission, revision, and publication

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• Comparing and contrasting nuclei and cold atomic gases
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• Analytic Harmonic Approach to the N-body problem
• Nuclear Alpha-Particle Condensates
• Number-parity effect for confined fermions in one dimension
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• How bosonic is a pair of fermions?
• Two-boson composites
• Relative and center-of-mass motion in the attractive Bose-Hubbard model