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