Mehta, Nirav P.Hazzard, Kaden R.A.Ticknor, Christopher2019-01-182019-01-182018Mehta, Nirav P., Hazzard, Kaden R.A. and Ticknor, Christopher. "Model for scattering with proliferating resonances: Many coupled square wells." <i>Physical Review A,</i> 98, no. 6 (2018) American Physical Society: https://doi.org/10.1103/PhysRevA.98.062703.https://hdl.handle.net/1911/105095We present a multichannel model for elastic interactions, composed of an arbitrary number of coupled finite square-well potentials, and derive semianalytic solutions for its scattering behavior. Despite the model's simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple but physically realistic statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed-channel coupling strength.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlePhysRevA.98.062703https://doi.org/10.1103/PhysRevA.98.062703