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