Energetics and structural properties of three-dimensional bosonic clusters near threshold

We treat three-dimensional bosonic clusters with up to N=40 atoms, interacting additively through two-body van der Waals potentials, in the near-threshold regime. Our study includes super-borromean systems with N atoms for which all subsystems are unbound. We determine the energetics and structural properties such as the expectation value of the interparticle distance as a function of the coupling strength. It has been shown that the coupling strength g(*)((N)), for which the N-body system becomes unbound, is bounded by the coupling constant g(*)((N-1)), for which the next smaller system with N-1 atoms becomes unbound, i.e., g(*)((N))>=(N-1)g(*)((N-1))/N. By fitting our numerically determined ground-state energies to a simple functional form with three fitting parameters, we determine the relationship between g(*)((N)) and g(*)((N-1)). Our trimer and tetramer energies fall on the so-called Tjon line, which has been studied in nuclear physics. We confirm the existence of generalized Tjon lines for larger clusters. Signatures of the universal behavior of weakly bound three-dimensional clusters can possibly be observed in ultracold Bose gases.