Feasibility of the observation of $η^{\prime}$ mesic nuclei in the semi-exclusive $^{12}$C($p, dp$) reaction

Abstract

We study theoretically the feasibility of the semi-exclusive $^{12}$C($p,dp$)$X$ reaction for the observation of $η^\prime$ mesic nuclei using the microscopic transport model JAM. The semi-exclusive measurements of the ($p,d$) reaction with protons from $η^\prime$ absorption are found to be significant for the observation of the $η^\prime$ bound states. Especially, the measurements of the energetic protons from $η^\prime$ non-mesic two-body absorption ($η^\prime NN \to NN$) are considered to be critically important. The Green's function method is used to calculate the expected spectrum of forward going deuterons corresponding to the excitation energy spectrum of the $η^\prime \otimes {}^{11}$C system in the semi-exclusive measurement. The semi-exclusive measurements are shown to be important in general for the $η^\prime$ mesic nucleus observation.

Figures (5)

• Figure 1: Calculated spectra of the $^{12}$C($p,d$)$^{11}$C$\otimes~\eta^\prime$ reaction for the formation of $\eta^\prime$--nucleus systems with proton kinetic energy $T_p = 2.5$ GeV and deuteron angle $\theta_d =0^\circ$ as a function of the excitation energy $E_\text{ex}$. $E_0$ is the $\eta^\prime$ production threshold. The $\eta^\prime$--nucleus optical potential is given in Eq. \ref{['eq:U_etap']}. The potential parameters are taken to be $(V, W_1, W_2) = (-100, -5 ,-5)$ MeV. The thick solid line shows the total spectrum. The dashed and dotted lines show the contributions from the one-body and two-body $\eta^\prime$ absorption processes, respectively, calculated as the conversion parts. The contribution from the $\eta^\prime$ escape process is also shown.
• Figure 2: The distributions of protons emitted in the inclusive $^{12}$C($p,d$)$X$ reaction in the plane of the proton momentum $p_p$ and $\cos \theta_p$ of the proton emission angle $\theta_p$ in the laboratory system in two independent simulations. The simulated result of the background processes is shown in (left), and that of the signal process from the $\eta^\prime$ mesic nucleus decay by the two-body absorption $\eta^\prime NN \to NN$ is shown in (right).
• Figure 3: The distributions of protons emitted from the decays of the $\eta^\prime$ mesic nuclei, which are supposed to be populated in the $^{12}\text{C}(p,d)X$ reaction, in the plane of the proton momentum $p_p$ and $\cos \theta_p$ of the proton emission angle $\theta_p$ in the laboratory system. The decay branching ratios $B_\eta$, $B_\pi$, and $B_{NN}$ for $\eta^\prime N \to \eta N$, $\eta^\prime N \to \pi N$ and $\eta^\prime NN \to NN$ processes are assumed to be (a) $(B_{\eta}, B_{\pi}, B_{NN}) = (0.2, 0.2, 0.6)$, and (b) $= (0.4,0.4, 0.2)$, respectively.
• Figure 4: The simple Feynman diagrams assumed in this article for (a) $\eta^\prime N \to \eta N^\prime$ and (b) $\eta^\prime N \to \pi N^\prime$ processes. $N$ and $N^\prime$ indicate proton and/or neutron, and $N^*$ the baryon resonances with isospine $1/2$. Because of isospin conservation, $\Delta$ resonances do not appear as the intermediate state in these diagrams.
• Figure 5: The simple one-sigma exchange Feynman diagram assumed in this article for $\eta^\prime N_1 N_2 \to N_1^\prime N_2^\prime$ process. All $N$s indicate proton and/or neutron and $N^*$ the baryon resonances with isospine $1/2$. Because of isospin conservation, $\Delta$ resonances do not appear as the intermediate state in this diagram.