title: Atom-dimer scattering for confined ultracold fermion gases.
abstract: We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/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)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.
authors.affiliation: Institut für Theoretische Physik, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany.
authors.forename: C
authors.initials: C
authors.lastname: Mora
authors.forename: R
authors.initials: R
authors.lastname: Egger
authors.forename: A O
authors.initials: AO
authors.lastname: Gogolin
authors.forename: A
authors.initials: A
authors.lastname: Komnik