Efimov Physics and the Three-Body Parameter within a Two-Channel Framework

TL;DR

This paper investigates Efimov physics in three-body systems considering both scattering length and effective range, revealing how narrow Feshbach resonances influence the three-body parameter and spectrum beyond universal predictions.

Contribution

It introduces a two-channel framework that incorporates effective range effects, providing new insights into the relation between two- and three-body physics in atomic systems.

Findings

Universal spectrum recovered for shallow states

Non-monotonic behavior near narrow Feshbach resonances

Corrections to universal scaling laws for deeper bound states

Abstract

We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. The universal spectrum is recovered for the least bound states, whereas for larger binding energies we find corrections to the universal scaling laws. We recover known results for broad Feshbach resonances with small effective range, whereas in the case of narrow resonances we find a distinct non-monotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. To address the issue of the physical origin of the three-body parameter we provide a physically clear model for the relation between three-body physics and typical two-body atom-atom interactions. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down the relation of two- and three-body physics in atomic systems.