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We treat three-dimensional bosonic clusters wih up to N=40 atoms, interactingadditively through two-body Van der Waals potentials, in the near-thresholdregime. Our study inludes super-borromean systems with N atoms for which allsubsystems are unbound. We determine the energetics and structural propertiesas the expectation value of the interparticle distance as a function of thecoupling strength. It has been shown that the coupling strength g*(N), forwhich the N-body systems becomes unbound, is bounded by the coupling constantg*(N-1) for which the next smaller system with N-1 atoms becomes unbound, i.e.,g*(N) >= (N-1)/Ng*(N-1). By fitting our numerically determined ground stateenergies to a simple functional form with three fitting parameters, wedetermine the relationship between g*(N) and g*(N-1). Our trimer and tetramerenergies fall on the so-called Tjon line, which has been studied in nuclearphysics. We confirm the existence of generalized Tjon lines for largerclusters. Signatures of the universal behavior of weakly-boundthree-dimensional clusters can possibly be observed in ultracold Bose gases.Comment: 12 pages, 12 figure

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