Bounds on the bound η ³He system

We investigate the relation between the \eta ^3He binding energy and width and the (complex) \eta ^3He scattering length. Following our systematic analysis of the eta 3He scattering length we set limits on the \eta ^3He binding. If bound states exist the binding energy (width) should not exceed 5 MeV (10 MeV). In addition, we comment on a recently claimed observation of an \eta-mesic ^3He quasi-bound state by the TAPS collaboration based on \eta photoproduction data. Although our limits are in reasonable agreement with the values reported by this collaboration, our analysis of these data does not lead to a solid conclusion concerning the existence of an \eta-mesic bound state. More dedicated experiments are necessary for further clarification.