N}$ has appropriately a bigger width than the width of the $\eta$-mesic nucleus.

Neglecting binding and Fermi motion of nucleons and $\eta$, we have the following kinematical characteristics of the ejected correlated $\pi N$ pairs (as for energies, momenta and velocities): && s = E\_+ E\_N = m\_+m\_N = 1486 MeV, && E\_\^[kin]{} = 313 [MeV]{},E\_N\^[kin]{} = 94 [MeV]{}, p\_= p\_N = 431 [MeV]{}/c, && \_= 0.95,\_N=0.42. \[kinema-piN\] A simple simulation that takes into account the Fermi motion of nucleons and $\eta$ as well as binding of these particles reveals that fluctuations around these ideal parameters are substantial (see Fig. \[simulation-piN\]) \[specifically, we used in this simulation the $\eta$-meson binding energy of 10 MeV with the width 25 MeV; for nucleons, we assumed a Fermi-gas distribution with binding energies distributed between 5 and 30 MeV\]. In particular, the angle $\theta_{\pi N}$ between the emitted pion and nucleon may not be so close to $180^\circ$, and a subtraction of background events with $\theta_{\pi N} \ne 180^\circ$ used sometimes in practice should be done cautiously. A shift of the peak down to 1486 MeV in the distribution of the total energy $E_{\pi N}=E_\pi+E_N$ seen in Fig. \[simulation-piN\] is related with binding of 