Dependence of calculated binding energies and widths of η-mesic nuclei on treatment of subthreshold η-nucleon interaction

We demonstrate that the binding energies εη and widths Γη of η-mesic nuclei depend strongly on the subthreshold η-nucleon interaction. This strong dependence is made evident from comparing three different η-nucleus optical potentials: (1) a microscopic optical potential taking into account the full effects of the off-shell ηN interaction; (2) a factorization approximation to the microscopic optical potential where a downward energy shift parameter is introduced to approximate the subthreshold ηN interaction; and (3) an optical potential using the on-shell ηN scattering length as the interaction input. Our analysis indicates that the in-medium ηN interaction for bound-state formation is about 30 MeV below the free-space ηN threshold, which causes a substantial reduction of the attractive force between the η and nucleon with respect to that implied by the scattering length. Consequently, the scattering-length approach overpredicts the εη and caution must be exercised when these latter predictions are used as guide in searching for η-nucleus bound states. We also show that final-state-interaction analysis cannot provide an unequivocal determination of the existence of the η-nucleus bound state. More direct measurements are, therefore, necessary