Frustrated collisions and unconventional pairing on a quantum superlattice

We consider the problem of scattering and binding of two interacting spin-(1/2) fermions on a one-dimensional tight-binding superlattice with a period of twice the lattice spacing. We solve the problem analytically for all ranges of parameters of the system. We find that, for the non-trivial case of singlet states, both bound and scattering wave functions consist of a generalized Bethe ansatz augmented with an extra scattering product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle inter-band transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision. Copyright (C) EPLA, 2010