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Simple model of Feshbach resonance in the strong-coupling regime

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.