Effective Field Theory for Few-Boson Systems

TL;DR

This paper develops an effective field theory approach to universal bosonic few-body systems, calculating energies and scattering lengths, and demonstrating convergence without additional interactions, with applications to helium atoms.

Contribution

It introduces a leading-order EFT framework for bosonic systems, showing convergence and correlations between few-body energies, and applies it successfully to helium atomic systems.

Findings

Convergence to zero-range interaction limit demonstrated.

No additional few-body interactions needed at leading order.

Results agree well with sophisticated helium potentials.

Abstract

We study universal bosonic few-body systems within the framework of effective field theory at leading order (LO). We calculate binding energies of systems of up to six particles and the atom-dimer scattering length. Convergence to the limit of zero-range two- and three-body interactions is shown, indicating that no additional few-body interactions need to be introduced at LO. Generalizations of the Tjon line are constructed, showing correlations between few-body binding energies and the binding energy of the trimer, for a given dimer energy. As a specific example, we implement our theory for 4He atomic systems, and show that the results are in surprisingly good agreement with those of sophisticated 4He-4He potentials. Potential implications for the convergence of the EFT expansion are discussed.