Few-body calculations of $η$-nuclear quasibound states

We report on precise hyperspherical-basis calculations of $ηNN$ and $ηNNN$ quasibound states, using energy dependent $ηN$ interaction potentials derived from coupled-channel models of the $S_{11}$ $N^{\ast}(1535)$ nucleon resonance. The $ηN$ attraction generated in these models is too weak to generate a two-body bound state. No $ηNN$ bound-state solution was found in our calculations in models where Re $a_{ηN}\lesssim 1$ fm, with $a_{ηN}$ the $ηN$ scattering length, covering thereby the majority of $N^{\ast}(1535)$ resonance models. A near-threshold $ηNNN$ bound-state solution, with $η$ separation energy of less than 1 MeV and width of about 15 MeV, was obtained in the 2005 Green-Wycech model where Re $a_{ηN}\approx 1$ fm. The role of handling self consistently the subthreshold $ηN$ interaction is carefully studied.

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