Atom-dimer scattering for confined ultracold fermion gases

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a(perpendicular to) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a(perpendicular to)/aapproximate to1.46, and a dimer state for arbitrary a(perpendicular to)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a(perpendicular to)/amuch greater than1, we find a repulsive zero-range atom-dimer interaction. For a(perpendicular to)/amuch less than-1, however, the potential has long range, with a(ad)>0 and b(ad)much greater thana(ad). There is no trimer state, and despite a(ad)=0 at a(perpendicular to)/aapproximate to2.6, there is no resonance enhancement of the interaction.