  The energies and widths of bound states of the $\eta$ meson in different
nuclei are obtained using the results for its selfenergy in a nuclear medium,
which is evaluated in a selfconsistent manner using techniques of unitarized
chiral perturbation theory. We find bound states in all studied nuclei (from
$^{12}{C}$ on) and the half widths obtained are larger than the separation of
the levels, what makes the experimental observation of peaks unlikely. We have
paid a special attention to the region of nuclei where only the $1s$ state
appears and the binding energies are of the order of magnitude of the half
width, which would magnify the chances that some broad peak could be observed.
This is found in the region of $^{24}{Mg}$ with a binding energy around 12.6
MeV and half width of 16.7 MeV. In heavy nuclei like $^{208}{Pb}$ there are
many bound states which would be difficult to disentangle and the deepest state
has a binding energy about 21 MeV and half width around 16 MeV. Such an
overlapping accumulation of states could be seen as an extension of the
continuum of $\eta$ strength into the bound region in $\eta$ production
experiments.

Nuclear Theory