We consider the reaction g+d -> pi+d in a wide energy range around and above the eta-meson photoproduction threshold at backward CM angles of the outgoing pion. Our theoretical analysis is essentially motivated by the recent measurements of the CLAS Collaboration at Jefferson Lab, where this kinematical region of the reaction has been thoroughly studied for the first time and a cusps in the energy dependence of the differential cross section in the region of Eg = 600-800 MeV has been observed. Our preliminary and qualitative analysis, based on single- and double-scattering diagrams, shows that the observed structure can be explained by the contribution of the double-scattering diagram with intermediate production of the eta meson. The effect, to a considerable extent, is formed due to the contribution of N(1535) resonance to the amplitudes of subprocesses on the nucleons.
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