Simple model of Feshbach resonance in the strong-coupling regime

TL;DR

This paper presents an analytic model for s-wave Feshbach resonances in strong-coupling regimes, revealing that resonances can occur without bound states in the closed channel, using dressed potentials and piecewise constant interactions.

Contribution

It introduces a simple analytic model for Feshbach resonances in the strong-coupling regime, including cases where the closed channel lacks a bound state.

Findings

Feshbach resonances can exist without a bound state in the closed channel.

Analytic expressions for scattering length and resonance count are derived.

Numerical validation confirms the analytical predictions.

Abstract

We use the dressed potentials obtained in the adiabatic representation of two coupled channels to calculate s-wave Feshbach resonances in a 3D spherically symmetric potential with an open channel interacting with a closed channel. Analytic expressions for the s-wave scattering length $a$ and number of resonances are obtained for a piecewise constant model with a piecewise constant interaction of the open and closed channels near the origin. We show analytically and numerically that, for strong enough coupling strength, Feshbach resonances can exist even when the closed channel does {\em not} have a bound state.