Finite-range model potentials for resonant interactions

Abstract

We show that it is possible to model two-body resonant interactions at low energy with a class of finite-range potentials based on the methods of Jost and Kohn. These potentials are expressed in terms of the effective range [Formula: see text] and the [Formula: see text]-wave scattering length [Formula: see text]. We derive continuum solutions of these potentials. By writing [Formula: see text], where the sign [Formula: see text] refers to positive(negative) scattering length, [Formula: see text] is of the form of Pöschl–Teller potential and [Formula: see text] is expressed as a power series of the small parameter [Formula: see text] when [Formula: see text] is large, we derive Green’s function of [Formula: see text]. Using the Green’s function, solutions of [Formula: see text] for [Formula: see text] can be obtained numerically by treating [Formula: see text] as a perturbation. We describe the threshold behavior of scattering phase shift for [Formula: see text]. This study may be important for developing a better understanding of physics of strongly interacting ultracold atomic gases with tunable interactions.