Universality in the three-body problem for 4He atoms -: art. no. 042706

The two-body scattering length a for He-4 atoms is much larger than their effective range r(s). As a consequence, low-energy few-body observables have universal characteristics that are independent of the interaction potential. Universality implies that, up to corrections suppressed by r(s)/a, all low-energy three-body observables are determined by a and a three-body parameter Lambda(*). We give simple expressions in terms of a and Lambda(*) for the trimer binding-energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine Lambda(*) for several He-4 potentials from the calculated binding energy of the excited state of the trimer and use it to obtain the universality predictions for the other low-energy observables. We also use the calculated values for one potential to estimate the effective range corrections for the other potentials.