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 ${g}_{*}^{(N\ensuremath{-}1)}$, for which the next smaller system with $N\ensuremath{-}1$ atoms becomes unbound, i.e., ${g}_{*}^{(N)}\ensuremath{\geqslant}(N\ensuremath{-}1){g}_{*}^{(N\ensuremath{-}1)}∕N$. 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 ${g}_{*}^{(N\ensuremath{-}1)}$. 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.
A correlated two-body basis function is used to describe the three-dimensional bosonic clusters interacting via two-body van der Waals potential. We calculate the ground state and the zero orbital angular momentum excited states for Rb(N) clusters with up to N = 40. We solve the many-particle Schrödinger equation by potential harmonics expansion method, which keeps all possible two-body correlations in the calculation and determines the lowest effective many-body potential. We study energetics and structural properties for such diffuse clusters both at dimer and tuned scattering length. The motivation of the present study is to investigate the possibility of formation of N-body clusters interacting through the van der Waals interaction. We also compare the system with the well studied He, Ne, and Ar clusters. We also calculate correlation properties and observe the generalised Tjon line for large cluster. We test the validity of the shape-independent potential in the calculation of the ground state energy of such diffuse cluster. These are the first such calculations reported for Rb clusters.