@sokol00] (see also a summary in [@sokol08]). It was triggered [@sokol94; @lebedev95a] by a suggestion [@sokol91] to seek $\eta$-mesic nuclei through observing decay products of $\eta$-mesic nuclei, namely two correlated back-to-back particles, a pion and a nucleon, ejected in the process of annihilation of captured $\eta$-mesons in the nucleus, Eq. (\[etaNpiN\]). It was hoped that a background for the two very energetic particles (the pion and the nucleon) ejected in decays of $\eta$-mesic nuclei transversely to the beam would be lower than that for ejection of forward protons in the inclusive processes. Besides, it was hoped that background conditions in photon-induced reactions would be generally better than those in pion-induced ones.

Studies of the reaction + \^[12]{}[C]{} (\_[ ]{}\^[11]{}[Be]{} [  or  ]{} \_[ ]{}\^[11]{}[C]{}) + N \^+ + n + X + N \[reac-C:piN\] done in the middle of 1990’s at the LPI electron synchrotron indeed showed a signal of an enhanced production of the correlated back-to-back $\pi^+n$ pairs ejected transversely to the photon beam when the photon energy exceeded the $\eta$-meson photoproduction threshold. Energy resolution of the experimental setup was, however, not sufficient to resolve a peak similar to that shown in Fig. \[spectral-function\] and to determine whether the 