\_= 10.76 [MeV for\^[16]{}\_[ ]{}O]{}, E\_= -6.39 [MeV]{}, && \_= 13.20 [MeV for\^[26]{}\_[ ]{}Mg]{}. \[eq:EB-Liu\] Note, however, that a stronger $\eta N$ scattering amplitude was inferred in some other analyses. For example, using a $K$-matrix model for coupled channels $\pi N$, $\eta N$, $\gamma N$ and $\pi\pi N$, Green and Wycech [@green97; @green05] found from fit to available data a\_[N]{} = (0.910.06) + i (0.270.02) fm. With such a big strength of $\eta N$ interaction lighter $\eta$-mesic nuclei could also exist.

As an example of different predictions for binding energies and widths of $\eta$-mesic nuclei we mention very elaborated calculations [@oset02a; @oset02b; @oset02c], in which a model for meson-baryon interaction with dynamically generated resonances was build using a unitarized chiral perturbation theory for coupled channels $\pi N$, $\eta N$, $K\Lambda$, $K\Sigma$ and $\pi\pi N$ and then self-energies of all the particles in the nuclear matter were evaluated consistently. This approach leads to the $\eta N$ scattering length $a_{\eta N} =
0.264 + i\, 0.245~\rm fm$ close to that obtained in Eq. (\[a-etaN-BL\]). The resulting $\eta A$ potential is, however, found stronger owing to nonlinear dressing effects: $U = -54 -i\, 29$ MeV at normal nuclear density. Also stronger are $\eta$-meson 