Small ηN scattering lengths favour ηd and ηα states
نویسندگان
چکیده
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 η-mesic 3He states made by the TAPS collaboration. Here, we extend this method to a speculative study of the unstable states occurring in the ηd and η4He elastic scattering. The T -matrix for η 4He scattering is evaluated within the Finite Rank Approximation (FRA) of few body equations. For the evaluation of time delay in the ηd case, we use a parameterization of an existing Faddeev calculation and compare the results with those obtained from FRA. With an ηN scattering length, aηN = (0.42, 0.34) fm, we find an ηd unstable bound state around −16 MeV, within the Faddeev calculation. A similar state within the FRA is found for a low value of aηN , namely, aηN = (0.28, 0.19) fm. The existence of an η 4He unstable bound state close to threshold is hinted by aηN = (0.28, 0.19) fm, but is ruled out by large scattering lengths. PACS numbers: 14.40.Aq, 03.65.Nk,14.20.Gk
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