Efimovian three-body potential from broad to narrow Feshbach resonances

Abstract

We analyze 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 ${a}_{\ensuremath{-}}$ shifts away from the universal value of $\ensuremath{-}9.7\phantom{\rule{4pt}{0ex}}{r}_{\mathrm{vdW}}$, with ${r}_{\mathrm{vdW}}=\frac{1}{2}{(m{C}_{6}/{\ensuremath{\hbar}}^{2})}^{1/4}$ 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 behavior 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, while 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 nonresonant interactions.