The unitary three-body problem in a trap
Résumé
We consider either 3 spinless bosons or 3 spin-1/2 fermions, interacting with a short range potential of infinite scattering length and trapped in an isotropic harmonic potential. In the zero-range limit, we obtain analytically the exact spectrum and eigenfunctions, and find that even the bosonic universal states have a vanishing collisional loss rate. For realistic values of the interaction range, the numerical solution of a finite range model shows that the coupling between universal and efimovian states remains weak, which confirms that the bosonic universal states are long-lived and observable.