Eur. Phys. J. B (2012) 85: 386
https://doi.org/10.1140/epjb/e2012-30841-3

Regular Article

Efimov physics beyond universality

Physik Department, Technische Universität München, 85747 Garching, Germany

^a e-mail: richard.schmidt@ph.tum.de

Received: 14 September 2012
Received in final form: 24 September 2012
Published online: 29 November 2012

Abstract

We provide an exact solution of the Efimov spectrum in ultracold gases within the standard two-channel model for Feshbach resonances. It is shown that the finite range in the Feshbach coupling makes the introduction of an adjustable three-body parameter obsolete. The solution explains the empirical relation between the scattering length a₋ where the first Efimov state appears at the atom threshold and the van der Waals length l_vdw for open-channel dominated resonances. There is a continuous crossover to the closed-channel dominated limit, where the scale in the energy level diagram as a function of the inverse scattering length 1 / a is set by the intrinsic length r^⋆ associated with the Feshbach coupling. Our results provide a number of predictions for the deviations from universal scaling relations between energies and scattering lengths that can be tested in future experiments.