Saturation properties of helium drops from a Leading Order description

TL;DR

This paper investigates helium drops using a leading order effective theory, linking short-range interactions to saturation properties, and demonstrates that simple models can accurately describe many-body behavior near the unitary limit.

Contribution

It introduces a leading order effective theory model for helium drops that captures saturation properties and extends universal behavior from few-boson systems to many-body systems.

Findings

Energy per particle can be accurately predicted at leading order.

The model successfully describes saturation properties of helium drops.

Universal behavior extends from few-boson to many-body systems.

Abstract

Saturation properties are directly linked to the short-range scale of the two-body interaction of the particles. The case of helium is particular, from one hand the two-body potential has a strong repulsion at short distances. On the other hand, the extremely weak binding of the helium dimer locates this system very close to the unitary limit allowing for a description based on an effective theory. At leading order of this theory a two- and a three-body term appear, each one characterized by a low energy constant. In a potential model this description corresponds to a soft potential model with a two-body term purely attractive plus a three-body term purely repulsive constructed to describe the dimer and trimer binding energies. Here we analyse the capability of this model to describe the saturation properties making a direct link between the low energy scale and the short-range correlations. We will show that the energy per particle, $E_N/N$, can be obtained with reasonable accuracy at leading order extending the validity of this approximation, characterizing universal behavior in few-boson systems close to the unitary limit, to the many-body system.