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Three identical bosons or fermions are considered in the limit of zero-rangeinteractions and finite effective range. By using a two channel model, we showthat these systems are not integrable and that the wave function verifiesspecific continuity conditions at the contact of three particles. This lastfeature permits us to solve a contradiction brought by the contact model whichcan lead to an opposite result concerning the integrability issue. Forfermions, the vicinity of integrability is characterized by large deviationswith respect to the predictions of the Bethe ansatz.

One-dimensional ultracold atomic gases: Impact of the effective range on integrability