Three identical bosons or fermions are considered in the limit of zero-range
interactions and finite effective range. By using a two channel model, we show
that these systems are not integrable and that the wave function verifies
specific continuity conditions at the contact of three particles. This last
feature permits us to solve a contradiction brought by the contact model which
can lead to an opposite result concerning the integrability issue. For
fermions, the vicinity of integrability is characterized by large deviations
with respect to the predictions of the Bethe ansatz
