Hadron interferences in the proton-induced coherent $\eta$-meson-production reaction on a scalar-isovector nucleus

The coherent $\eta$-meson energy $E_{\eta }$ distribution spectra in proton nucleus reactions 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 $pN\to p{N}^{*}$; $N^{*}\to N\eta$. Born terms in the intermediate state are 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 the $\eta$ meson; other meson exchange potentials do not contribute to 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.

Figure 1

Schematic diagrams describing the mechanism of the considered reaction (see text): (a) direct (or postemission) and (b) cross (or preemission) diagrams.

Figure 2

The $\eta$-meson energy $E_{\eta }$ distribution spectra for the ${}^{14}\mathrm{C}$ nucleus at 2.5 GeV. The cross section due to the $N\left(1520\right)$ resonance is distinctly the largest (dot-dot-dashed curve). The coherently added cross section (dot-dashed curve) is less than the previous cross section because of the interference of the Born terms and resonances quoted in the figure.

Figure 3

(a) Contributions of ${\pi }^0$- and $\eta$-meson exchange potentials to the cross section arising due to the $N\left(1520\right)$ resonance only. The peak position is shifted to the higher value of $E_{\eta }$ because of the interference of these potentials (dot-dot-dashed curve). (b) Same as those presented in the panel (a) but for the coherently added cross sections due to Born terms and resonances (see text).

Figure 4

The sensitivity of the cross section to the hadron nucleus interaction (optical potential). The cross section is reduced drastically (by a factor of $\simeq 12$), and the peak position is shifted by 40 MeV towards the higher value of $E_{\eta }$ because of these interactions.

Figure 5

Beam energy dependence of the cross section. The cross section increases and the peak position shifts towards the higher $E_{\eta }$ with the enhancement in the beam energy.