Efimov Physics in small bosonic clusters

TL;DR

This paper investigates Efimov physics in small bosonic clusters with resonant interactions, analyzing their spectra and scale invariance using hyperspherical harmonics, and exploring effects of two- and three-body forces.

Contribution

It provides a detailed analysis of Efimov states in small bosonic clusters, including the impact of three-body forces, using a hyperspherical harmonics approach.

Findings

Clusters exhibit two states: deep and shallow near the $A-1$ threshold.

Scale invariance is confirmed for these states across different interaction regimes.

Adding a three-body force reproduces the trimer binding energy accurately.

Abstract

We study small clusters of bosons, $A=2,3,4,5,6$, characterized by a resonant interaction. Firstly, we use a soft-gaussian interaction that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with LM2M2 potential, a widely used $^4$He-$^4$He interaction. We change the intensity of the potential to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length and we report the clusters' energies on Efimov plot, which makes the scale invariance explicit. Secondly, we repeat our calculation adding a repulsive three-body force to reproduce the trimer binding energy. In all the region explored, we have found that these systems present two states, one deep and one shallow close to the $A-1$ threshold, and scale invariance has been investigated for these states. The calculations are performed by means of Hyperspherical Harmonics basis set.