Bounds on the bound eta-3He system

We investigate the relation between the eta-He-3 binding energy and width and the (complex) eta-He-3 scattering length. Following our systematic analysis of the eta-He-3 scattering length we set limits on the eta-He-3 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 He-3 quasibound 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