Pathologies in three-body molecular clusters when using δ-shell potentials

Abstract

In this work the calculation of the binding energy of three ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms is carried out using δ-shell binary potential models, hyperspherical harmonic expansions, and adiabatic approximations. The results obtained with a one δ-shell potential are well within the range of those obtained by other workers using different techniques. The ones with the two δ-shell potentials are not. We show that attractive δ-shells lead to pathologies in calculations of the eigenpotentials, and in the resulting binding energies—and that those effects are expected to become more important for the two δ-shell binary potentials.