section of $\eta$-mesic nuclei formation off light nuclei (like carbon or oxygen implied in the following) turns out to be a few $\mu$b [@kohno89; @lebedev89; @lebedev91; @lebedev95; @tryasuchev99; @tryasuchev01], i.e. $\simeq 2{-}7\%$ of the total cross section $\sigma_{\gamma
A}^\eta$ of inclusive $\eta$ photoproduction, with the exact value strongly dependent on the assumed strength of the optical potential $U$.

![a) $\eta$-mesic nuclei formation and decay with the emission of back-to-back $\pi N$ pairs. b) Background creation of back-to-back $\pi N$ pairs by unbound $\eta$.[]{data-label="diagrams-piN"}](fig-diagram-piN.eps){width="80.00000%"}

Energies $E[{}_\eta(A-1)]$ of the produced $\eta$-mesic nuclei can, in principle, be determined through missing mass measurements in the reaction $(\gamma,p)$ using tagged photons $\gamma$ and a magnetic spectrometer for $N'=p$. Indirectly, the same energy E\[\_(A-1)\] = E\_+ E\_[A-1]{} = E\_[N]{} + E\_[A-2]{} \[eq:E-eta-(A-1)\] can also be found from the observed energy of a correlated back-to-back $\pi N$ pair produced at the second stage of the reaction (\[reac:piN\]) where the captured $\eta$ meson annihilates through the subprocess N N. \[etaNpiN\] The energy excitation of $(A-2)$ in (\[eq:E-eta-(A-1)\]) is not a fixed value. It rather depends on whether an $s$-shell or $p$-shell nucleon $N$ is knocked out in the process (\[etaNpiN\]). Therefore a distribution of the experimental observable $E_{\pi 