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The energy transfer spectra have been calculated for the coherent $\eta$meson production in the proton nucleus reaction. The elementary reactionoccurring in the nucleus is considered as $ pN \to pN^*(1535) $; $ N^*(1535)\to N\eta $. The $N^*(1535)$ excitation for the forward going proton and $\eta$meson is occurred due to the $\pi^0$ and $\eta$ meson exchange interactions,other mesons do not contribute in this process. The cross sections arecalculated for the $\pi^0$ and $\eta$ meson exchange interactions, and theeffect of their interference on the cross section is also studied. The initialand final state interactions as well as the $N^*(1535)$ nucleus interaction areaddressed by the optical potentials. The distorted wave functions for protonand $\eta$ meson are described by the eikonal form. The sensitivity of thecross section to the hadron nucleus potential is presented.

$\pi^0$ and $\eta$ meson exchange interactions in the coherent $\eta$ meson production in the nucleus