Borromean Binding of Three or Four Bosons

Abstract

We estimate the ratio $R=g_3/g_2$ of the critical coupling constants $g_2$ and $g_3$ which are required to achieve binding of 2 or 3 bosons, respectively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give $R\simeq 0.8$. A wide repulsive core pushes this ratio close to R=1. On the other hand, for an attractive well protected by an external repulsive barrier, the ratio approaches the rigorous lower bound $R=2/3$. We also present results for N=4 bosons, sketch the extension to $N>4$, and discuss various consequences.

12 pages, RevTeX, 5 Figures in tex included

References in corpus (5)

• Solution of few-body problems with the stochastic variational method: I. Central forces
• Exploration of resonances by analytic continuation in the coupling constant
• Limits on the Domain of Coupling Constants for Binding N-Body Systems with No Bound Subsystems
• Three-Body Configuration Space Calculations with Hard Core Potentials
• Weakly-Bound Three-Body Systems with No Bound Subsystems

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