Traces of integrability in scattering of one-dimensional dimers on a barrier

Understand

We consider molecules made of two one-dimensional short-range-interacting bosonic atoms.

• We show that in the process of scattering of these molecules off a narrow barrier, odd incident waves produce \emph{no unbound atoms, even when the incident energy exceeds the dissociation threshold}.
• This effect is a consequence of a prohibition on chemical reactions acting in a generally unphysical Bethe Ansatz integrable system of a $C_{2}$-type, with which our system shares the spatially odd eigenstates.
• We suggest several experimental implementations of the effect.