Universality in the Three-Body Problem for 4He Atoms

TL;DR

This paper explores the universal behavior of low-energy three-body observables in 4He atoms, demonstrating that they depend primarily on the scattering length and a three-body parameter, with minimal influence from the specific interaction potential.

Contribution

It provides simple universal expressions for three-body observables in 4He atoms and determines the three-body parameter from potential calculations, enhancing understanding of universality in quantum few-body systems.

Findings

Universal relations for trimer binding energy and atom-dimer scattering derived

Three-body parameter _* determined from excited trimer state energies

Estimated effective range corrections for different potentials

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 \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 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.