  The coherent $\eta$ meson energy $E_\eta$ distribution spectra in the proton
nucleus reaction have been calculated to investigate the $\pi^0 - \eta$ mesons'
interference, in addition to the study of resonance $N^*$ dynamics in the
nucleus. The elementary reaction occurring in the nucleus is assumed to proceed
as $ pN \to pN^* $; $ N^* \to N\eta $. Born terms in the intermediate state is
also considered. In a scalar-isovector nucleus, this reaction occurs because of
$\pi^0$ and $\eta$ meson exchange interactions for the forward going proton and
$\eta$ meson; other meson exchange potentials do not contribute in this
process. The sensitivity of the cross section to the hadron nucleus
interactions, and the beam energy dependence of the cross section are studied
for this reaction.
