# Universal behavior of few-boson systems using potential models

## TL;DR

This paper investigates the universal properties of three-boson systems near the unitary limit, revealing simple parameter dependencies and applying the findings to helium-4 atom interactions.

## Contribution

It demonstrates a universal dependence of three-boson observables on few parameters using a two-parameter potential model.

## Key findings

- Dependence of three-body parameter times scattering length on angle ξ
- Ratio of boson-dimer to two-body scattering length shows similar dependence
- Computed boson-dimer scattering length for helium-4 atoms

## Abstract

The universal behavior of a three-boson system close to the unitary limit is encoded in a simple dependence of many observables in terms of few parameters. For example the product of the three-body parameter $\kappa_*$ and the two-body scattering length $a$, $\kappa_* a$ depends on the angle $\xi$ defined by $E_3/E_2=\tan^2\xi$. A similar dependence is observed in the ratio $a_{AD}/a$ with $a_{AD}$ the boson-dimer scattering length. We use a two-parameter potential to determine this simple behavior and, as an application, to compute $a_{AD}$ for the case of three $^4$He atoms.