Four-body system of ${}^4\mathrm{He}$ atoms: Dimer-dimer scattering

TL;DR

This paper introduces a novel approach to accurately solve four-body helium atom systems by gradually softening the potential, enabling better understanding of binding energies, scattering, and correlations in weakly-bound few-body systems.

Contribution

It presents a new method for solving four-body helium atom problems with realistic potentials by potential softening and extrapolation, improving accuracy and resolving previous disagreements.

Findings

Accurate four-body helium atom energies and scattering results.

Observation of linear correlations between three- and four-body quantities.

Establishment of a Phillips correlation line for dimer-dimer scattering length.

Abstract

The strong short-range repulsion, characteristic to realistic interatomic potentials, complicates the description of weakly-bound few-body systems such as those of \He atoms. The present work proposes an approach for solving this problem and applies it to a realistic system of four ${}^4\mathrm{He}$ atoms. The potential is gradually softened such that rigorous four-body equations for bound and scattering tates can be accurately solved in the momentum-space framework, and the results are extrapolated back to the limit of the original potential. Linear correlations between three- and four body quantities are observed, and the accuracy of the procedure is improved by extrapolating in one of the three-body quantities. Results for the ${}^4\mathrm{He}$ tetramer ground and excited state binding energies and atom-trimer scattering agree well with at least some of earlier determinations and shed light on the existing disagreements. An additional case of the Phillips correlation line is established for the dimer-dimer scattering length. The trimer production rate via the ultracold two-dimer collisions is estimated, it exhibits significant finite-range effects despite the weak binding of the dimer.