Small eta-N scattering lengths favour eta-d and eta-alpha states

Unstable states of the eta meson and the 3He nucleus predicted using the time delay method were found to be in agreement with a recent claim of eta-mesic 3He states made by the TAPS collaboration. Here, we extend this method to a speculative study of the unstable states occurring in the eta-d and eta-4He elastic scattering. The T-matrix for eta-4He scattering is evaluated within the Finite Rank Approximation (FRA) of few body equations. For the evaluation of time delay in the eta-d case, we use a parameterization of an existing Faddeev calculation and compare the results with those obtained from FRA. With an eta-N scattering length, $a_{\eta N} = (0.42, 0.34)$ fm, we find an eta-d unstable bound state around -16 MeV, within the Faddeev calculation. A similar state within the FRA is found for a low value of $a_{\eta N}$, namely, $a_{\eta N} = (0.28, 0.19)$ fm. The existence of an eta-4He unstable bound state close to threshold is hinted by $a_{\eta N} = (0.28, 0.19)$ fm, but is ruled out by large scattering lengths