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

Abstract

The energy transfer spectra have been calculated for the coherent $\eta$ meson production in the proton nucleus reaction. The elementary reaction occurring in the nucleus is considered as $pN\to p{N}^{\ast }(1535)$; $N^{\ast }(1535)\to N\eta$. The $N^{\ast }(1535)$ 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 are calculated for the ${\pi }^0$ and $\eta$ meson exchange interactions, and the effect of their interference on the cross section is also studied. The initial and final state interactions as well as the $N^{\ast }(1535)$ nucleus interaction are addressed by the optical potentials. The distorted wave functions for proton and $\eta$ meson are described by the eikonal form. The sensitivity of the cross section to the hadron nucleus potential is presented.

Comments: 12 pages, 3 figures