BOUND STATES AND SCATTERING LENGTHS OF THREE TWO-COMPONENT PARTICLES WITH ZERO-RANGE INTERACTIONS UNDER ONE-DIMENSIONAL CONFINEMENT
Kartavtsev O.I., Malykh A.V., Sofianos S.A.

Received: August 19, 2008

PACS: 31.15.ac, 03.65.Ge, 34.50.-s

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The universal three-body dynamics in ultracold binary gases confined to one-dimensional motion is studied. The three-body binding energies and the (2+1)-scattering lengths are calculated for two identical particles of mass m and a different particle of mass m₁, whose interaction is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio m/m₁ at which three-body states occur and the (2+1)-scattering length vanishes are determined for both zero and infinite interaction strength λ₁ of the identical particles. A number of exact results are listed and asymptotic dependences for both m/m₁ → ∞ and λ₁ → -∞ are derived. Combining the numerical and analytic results, we deduce a schematic diagram showing the number of three-body bound states and the sign of the (2+1)-scattering length in the plane of the mass ratio and the interaction-strength ratio. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.