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We analyze the data on cross sections and asymmetries for the $pd (dp) \to\eta ^3{\rm He}$ reaction close to threshold and look for bound states of the$\eta ^3 {\rm He}$ system. Rather than parameterizing the scattering matrix, asis usually done, we develop a framework in which the $\eta ^3 {\rm He}$ opticalpotential is the key ingredient, and its strength, together with someproduction parameters, are fitted to the available experimental data. Therelationship of the scattering matrix to the optical potential is establishedusing the Bethe-Salpeter equation and the $\eta ^3 {\rm He}$ loop functionincorporates the range of the interaction given by the empirical $^3 {\rm He}$density. We find a local Breit Wigner form of the $\eta^3$He amplitude $T$below threshold with a clear peak in $|T|^2$, which corresponds to an $\eta^3{\rm He}$ binding of about 0.3 MeV and a width of about 3 MeV. By fitting thepotential we can also evaluate the $\eta ^3 {\rm He}$ scattering length,including its sign, thus resolving the ambiguity in the former analyses.

Determination of the $\boldsymbol{\eta ^3{\rm He}}$ threshold structure from the low energy $\boldsymbol{pd \to \eta ^3{\rm He}}$ reaction