Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

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.