Efimov physics beyond universality

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 non-universal ratios between energies and scattering lengths that can be tested in future experiments.