Binding three or four bosons without bound subsystems - art. no. 032504

We estimate the ratio R=g(3)/g(2) Of the critical coupling constants g(2) a nd g(3) that are required to achieve binding of two or three bosons, respec tively, with a short-range interaction, and examine how this ratio depends on the shape of the potential. Simple monotonous potentials give R similar or equal to 0.8. A wide repulsive core pushes this ratio close to R=1. On t he other hand, for an attractive well protected by an external repulsive ba rrier, the ratio approaches the rigorous lower bound R = 2/3. We also prese nt results for N = 4 bosons, sketch the extension to N>4, and discuss vario us consequences.