Universality of Brunnian ($N$-body Borromean) four and five-body systems

TL;DR

This paper investigates the universal properties of weakly bound four and five-body bosonic systems, analyzing their energies, sizes, and spatial distributions to understand their universal or non-universal nature.

Contribution

It provides detailed calculations of energies and radii for four and five-body bosonic systems, highlighting the universality of excited states and the potential non-universality of larger ground states.

Findings

Ground and first excited states are below the N-1 particle threshold.

Root mean square radii approach constants in weak binding limit.

Excited states may exhibit universal structures, while ground states for more than five particles are likely non-universal.

Abstract

We compute binding energies and root mean square radii for weakly bound systems of $N=4$ and $5$ identical bosons. Ground and first excited states of an $N$-body system appear below the threshold for binding the system with $N-1$ particles. Their root mean square radii approach constants in the limit of weak binding. Their probability distributions are on average located in non-classical regions of space which result in universal structures. Radii decrease with increasing particle number. The ground states for more than five particles are probably non-universal whereas excited states may be universal.