The unitary three-body problem in a trap

Felix Werner; Yvan Castin

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arXiv · cond-mat/0507399

The unitary three-body problem in a trap

Felix Werner·Yvan Castin

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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.

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Felix Werner, Yvan Castin. 2026-07-21. The unitary three-body problem in a trap. https://arxiv.org/abs/cond-mat/0507399

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