  The four-body problem for an interacting two-species Fermi gas is solved
analytically in a confined quasi-one-dimensional geometry, where the two-body
atom-atom scattering length $a_{aa}$ displays a confinement-induced resonance.
We compute the dimer-dimer scattering length $a_{dd}$, and show that this
quantity completely determines the many-body solution of the associated BEC-BCS
crossover phenomenon in terms of bosonic dimers.
