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

TL;DR

This paper investigates the energetics and structures of three-dimensional bosonic clusters with up to 40 atoms near the unbinding threshold, revealing universal behaviors and bounds on coupling strengths.

Contribution

It provides the first detailed analysis of large bosonic clusters near threshold, including super-borromean systems, and establishes bounds and relationships for their unbinding coupling constants.

Findings

Bound on unbinding coupling strength g*(N) for N-body systems.

Ground state energies follow the Tjon line, indicating universal correlations.

Universal behavior signatures could be observed in ultracold Bose gases.

Abstract

We treat three-dimensional bosonic clusters wih up to N=40 atoms, interacting additively through two-body Van der Waals potentials, in the near-threshold regime. Our study inludes super-borromean systems with N atoms for which all subsystems are unbound. We determine the energetics and structural properties 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 systems 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)/Ng*(N-1). 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.