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Abstract
We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting
via a short range potential of infinite scattering length and trapped in an isotropic
harmonic potential. For a zero-range model, we obtain analytically the exact spectrum
and eigenfunctions: for fermions all the states are universal; for bosons there is
a coexistence of decoupled universal and efimovian states. All the universal states,
even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we
numerically find for bosons a coupling between zero angular momentum universal and
efimovian states; the coupling is so weak that, for realistic values of the interaction
range, these bosonic universal states remain long-lived and observable.