Mg}$ is  $\approx -8$ MeV with the width $\approx 19$ MeV.

On the two-nucleon decay mode of $\eta$-mesic nuclei {#on-the-two-nucleon-decay-mode-of-eta-mesic-nuclei .unnumbered}
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[r]{}[0.4]{} ![image](fig-diagram-NN.eps){width="35.00000%"}

![image](fig-etaNN.ps){width="40.00000%"}

The main novelty in our present research is exploring a new possibility for searching for $\eta$-mesic nuclei, namely through observation of their two-nucleon decay mode arising owing to the two-nucleon absorption of the captured $\eta$ in the nucleus, NN NN, \[2N-absorption\] see Fig. \[diagram-NN\]. Ejected in this process correlated back-to-back nucleons of the $NN$ pairs have very high energies ($E_N^{\rm kin}\simeq \frac12 m_\eta = 274$ MeV) and momenta ($p_N\simeq 770~{\rm MeV}/c$), so that they are to be visible (especially in coincidence) at the background of other particles emitted in photoreactions at $E_\gamma\sim 800$ MeV and thus should provide a bright signature for the $\eta$-mesic nucleus formation.

The $NN$ pair production in decays of $\eta$ in the nuclear matter was considered among other channels by Chiang, Oset and Liu [@chiang91] in terms of the self-energy of $S_{11}(1535)$ that includes a contribution of $S_{11}(1535)N\to NN$. A more direct and rather transparent evaluation of this process has been done by Kulpa and Wycech [@kulpa98b] who used available experimental data on the inverse reactions $pp\to pp\eta$, $pn\to pn\eta$ and 