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We analyze the data on the total cross sections for the $dd \to \eta{}^4{\rmHe}$ reaction close to threshold and look for possible $\eta ^4 {\rm He}$ boundstates. We develop a framework in which the $\eta ^4{\rm He}$ optical potentialis the key ingredient, rather than parameterizing the scattering matrix, as isusually done. The strength of this potential, together with some productionparameters, are fitted to the available experimental data. The relationship ofthe scattering matrix to the optical potential is established using theBethe-Salpeter equation and the $\eta ^4{\rm He}$ loop function incorporatesthe range of the interaction given by the experimental $^4 {\rm He}$ density.However, when we look for poles of the scattering matrix, we get poles in thebound region, poles in the positive energy region or no poles at all. If wefurther restrict the results with constraints from a theoretical model with allits uncertainties the bound states are not allowed. However, we find a bumpstructure in $|T|^2$ of the $\eta ^4{\rm He} \to \eta ^4{\rm He}$ amplitudebelow threshold for the remaining solutions.

$\boldsymbol{\eta}$-$\boldsymbol{^4{\rm He}}$ interaction from the $\boldsymbol{d d \to \eta ^4{\rm He}}$ reaction near threshold