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

N. G. Kelkar·K. P. Khemchandani·B. K. Jain
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Abstract

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, $a_{ηN} = (0.42, 0.34)$ 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 $a_{ηN}$, namely, $a_{ηN} = (0.28, 0.19)$ fm. The existence of an eta-4He unstable bound state close to threshold is hinted by $a_{ηN} = (0.28, 0.19)$ fm, but is ruled out by large scattering lengths.

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N. G. Kelkar, K. P. Khemchandani, B. K. Jain. 2006-06-16. Small eta-N scattering lengths favour eta-d and eta-alpha states. https://doi.org/10.1088/0954-3899%2F32%2F8%2F007

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