The helium trimer with soft-core potentials

TL;DR

This paper investigates the helium trimer using soft-core potentials, demonstrating that a Gaussian potential with an added three-body force can accurately replicate the properties of the realistic LM2M2 helium-helium interaction.

Contribution

The study introduces a simplified Gaussian potential model with a three-body force to effectively describe the helium trimer's bound states and scattering properties.

Findings

Gaussian potential reproduces the two bound states of the trimer.

Low energy helium-dimer scattering phase shifts are accurately matched.

Adding a three-body force is essential for correct ground state description.

Abstract

The helium trimer is studied using two- and three-body soft-core potentials. Realistic helium-helium potentials present an extremely strong short-range repulsion and support a single, very shallow, bound state. The description of systems with more than two helium atoms is difficult due to the very large cancellation between kinetic and potential energy. We analyze the possibility of describing the three helium system in the ultracold regime using a gaussian representation of a widely used realistic potential, the LM2M2 interaction. However, in order to describe correctly the trimer ground state a three-body force has to be added to the gaussian interaction. With this potential model the two bound states of the trimer and the low energy scattering helium-dimer phase shifts obtained with the LM2M2 potential are well reproduced.