Abstract
In this work the calculation of the binding energy of three $^{4}\mathrm{He}$ atoms is carried out using \ensuremath{\delta}-shell binary potential models, hyperspherical harmonic expansions, and adiabatic approximations. The results obtained with a one \ensuremath{\delta}-shell potential are well within the range of those obtained by other workers using different techniques. The ones with the two \ensuremath{\delta}-shell potentials are not. We show that attractive \ensuremath{\delta}-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 \ensuremath{\delta}-shell binary potentials.
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