Threshold behavior of bosonic two-dimensional few-body systems

Bosonic two-dimensional self-bound clusters consisting of $N$ atoms interacting through additive van der Waals potentials become unbound at a critical mass m*(N); m*(N) has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy E(N) of the N-atom system varies exponentially as the atomic mass approaches m*. This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass m*, and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio E(N+1)/E(N) near threshold.