Finite-range effects in Efimov physics beyond the separable approximation

TL;DR

This paper investigates the limitations of the separable approximation in Efimov physics for three bosons with finite-range interactions, highlighting the importance of including multiple bound states and higher partial waves for accurate predictions.

Contribution

It introduces improved methods beyond the separable approximation, accounting for multiple bound states and higher partial waves to accurately describe Efimov and non-Efimov trimer states.

Findings

Separable approximation is accurate for potentials with one bound dimer state.

Including multiple bound states improves Efimov spectrum predictions.

Higher partial-wave components are necessary for accurate three-body calculations.

Abstract

We study Efimov physics for three identical bosons interacting via a pairwise square-well potential, analyze the validity of the separable approximation as a function of the interaction strength, and investigate what is needed to improve this approximation. We find separable approximations to be accurate for potentials with just one (nearly) bound dimer state. For potentials with more bound or almost bound dimer states, these states need to be included for an accurate determination of the Efimov spectrum and the corresponding three-body observables. We also show that a separable approximation is insufficient to accurately compute the trimer states for energies larger than the finite-range energy even when the two-body T matrix is highly separable in this energy regime. Additionally, we have analyzed three distinct expansion methods for the full potential that give exact results and thus improve on the separable approximation. With these methods, we demonstrate the necessity to include higher partial-wave components of the off-shell two-body T matrix in the three-body calculations. Moreover, we analyze the behavior of the Efimov states near the atom-dimer threshold and observe the formation of non-Efimovian trimer states as the potential depth is increased. Our results can help to elaborate simpler theoretical models that are capable of reproducing the correct three-body physics in atomic systems.