Analytical solution of the bosonic three-body problem

Alexander O. Gogolin (1, 2) , Christophe Mora (3) , Reinhold Egger (2)

1 Department of Mathematics [Imperial College London]
2 Insitut fur Theoretische Physik I
3 LPA - Laboratoire Pierre Aigrain

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modelling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schrödinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

Domaines: Autre [cond-mat.other]

Alexander O. Gogolin, Christophe Mora, Reinhold Egger. Analytical solution of the bosonic three-body problem. Physical Review Letters, 2008, 100, pp.140404. ⟨10.1103/PhysRevLett.100.140404⟩. ⟨hal-00272446⟩