Efimovian three-body potential from broad to narrow Feshbach resonances

TL;DR

This paper investigates how the Efimovian three-body potential evolves from broad to narrow Feshbach resonances, revealing that the three-body parameter shifts due to changes in potential depth and spin interactions.

Contribution

It models the three-body system with a separable two-body interaction considering full zero-energy behavior, providing new insights into the potential's universality and the origin of the three-body parameter shift.

Findings

Short-range repulsive barrier remains universal for narrow resonances.

The three-body parameter shift is due to a decrease in potential depth.

Dominance of the resonant channel influences the three-body potential.

Abstract

We analyse the change in the hyperradial Efimovian three-body potential as the two-body interaction is tuned from the broad to narrow Feshbach resonance regime. Here, it is known from both theory and experiment that the three-body dissociation scattering length $a_-$ shifts away from the universal value of $-9.7 \ r_{\mathrm{vdW}}$, with $r_{\mathrm{vdW}} = \frac{1}{2} \left(m C_6/\hbar^2 \right)^{1/4}$ the two-body van der Waals range. We model the three-body system using a separable two-body interaction that takes into account the full zero-energy behaviour of the multichannel wave function. We find that the short-range repulsive barrier in the three-body potential characteristic for single-channel models remains universal for narrow resonances, whilst the change in the three-body parameter originates from a strong decrease in the potential depth. From an analysis of the underlying spin structure we further attribute this behavior to the dominance of the two-body interaction in the resonant channel compared to other background interactions.