Energy and structural properties of $N$-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

摘要

The low-energy spectrum of $N$-boson clusters with pairwise zero-rangeinteractions is believed to be governed by a three-body parameter. We study theground state of $N$-boson clusters with infinite two-body $s$-wave scatteringlength by performing {\em{ab initio}} Monte Carlo simulations. To preventThomas collapse, different finite-range three-body regulators are used. Theenergy and structural properties for the three-body Hamiltonian with two-bodyzero-range interactions and three-body regulator are in much better agreementwith the "ideal zero-range Efimov theory" results than those for Hamiltonianwith two-body finite-range interactions. For larger clusters we find that theground state energy and structural properties of the Hamiltonian with two-bodyzero-range interactions and finite-range three-body regulators are notuniversally determined by the three-body parameter, i.e., dependences on thespecific form of the three-body regulator are observed. For comparison, weconsider Hamiltonian with two-body van der Waals interactions and no three-bodyregulator. For the interactions considered, the ground state energy of the$N$-body clusters is---if scaled by the three-body ground state energy---fairlyuniversal, i.e., the dependence on the short-range details of the two-body vander Waals potentials is small. Our results are compared with the literature.