The Four-Boson System with Short-Range Interactions

TL;DR

This paper analyzes the four-boson system with short-range interactions, demonstrating that two- and three-body forces suffice for renormalization and exploring correlations in binding energies, with applications to helium atoms.

Contribution

It constructs an effective interaction model for four-boson systems and shows that no four-body force is needed for renormalization, applying it to helium atoms.

Findings

Four-body binding energies are cutoff independent without a four-body force.

A linear correlation exists between trimer and tetramer binding energies.

The model accurately predicts the helium tetramer's binding energy.

Abstract

We consider the non-relativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energy of the 4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4He atoms, the correlation is approximately linear.