Universality in the Three-Body Problem for 4He Atoms

Abstract

The two-body scattering length a for 4He 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 Λ_*. We give simple expressions in terms of a and Λ_* for the trimer binding energy equation, the atom-dimer scattering phase shifts, and the rate for three-body recombination at threshold. We determine Λ_* for several 4He 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.