for comparison. The INC model takes into account production of various mesons and baryon resonances, their free propagation in the nuclear matter, and then various $2\to 2$ collisional reactions including $\eta N\to\pi N$. This model successfully describes many photoreactions in wide kinematical ranges as was demonstrated, beyond [@pschenichnov97], in simulations of the GRAAL experiment at energies 500–1500 MeV [@ignatov08]. Binding effects for $\eta$ and reactions like $\eta NN\to NN$ were not included into the model, so one can try to find effects arising due to formation and decay of $\eta$-mesic nuclei through characteristic deviations of the model predictions from the experimental data.

The simulation shows that the selection (\[eq:selection\]) of particles with sufficiently long ranges distinguishes very well protons (as particles with $\beta_C \leq 0.7$) and pions (as particles with $\beta_C \geq 0.7$): the overlap is less than 1%.

![Two-dimensional $\Delta E{-}\beta_C$ distribution, the INC model.[]{data-label="2-dim-bE-INC"}](fig-2dim-bE.eps){width="60.00000%"}

![Two-dimensional $\Delta E{-}\beta_C$ distribution, the INC model.[]{data-label="2-dim-bE-INC"}](fig-2dim-bE-INC.eps){width="60.00000%"}

Considering one-dimensional spectra over $\beta_C$ of events selected according to the condition (\[eq:selection\]) of sufficiently long ranges and imposing the additional cut-off $0.3 <\beta_N < 0.7$ for neutron velocities, we find rather interesting structures in the spectra. Shown in Fig. \[bC\] are experimental data (blue areas) together 