Gaussian characterization of the unitary window for $N=3$: bound, scattering and virtual states

TL;DR

This paper uses a gaussian potential model to analyze three-body systems near the unitary limit, capturing universal low-energy properties and correlations in systems like helium atoms and nucleons.

Contribution

It introduces a gaussian characterization of the unitary window that links real systems to the universal limit, explaining low-energy states and correlations.

Findings

Gaussian trajectories effectively describe low-energy states

Universal behavior links real systems to the unitary limit

Strong correlations between observables are explained

Abstract

The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having $1/2$ spin-isospin symmetry. We perform a gaussian characterization of the window using a gaussian potential to define trajectories for low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the gaussian characterization of the window, thought as a contact interaction plus range corrections, captures the main low-energy properties of real systems as for example three helium atoms or three nucleons. The mapping of real systems on the gaussian trajectories is taken as indication of universal behavior. The trajectories continuously link the physical points to the unitary limit allowing for the explanation of strong correlations between observables appearing in real systems and which are known to exist in that limit. In the present study we focus on low-energy bound, scattering and virtual states.