Feasibility of the observation of $\eta^{\prime}$ 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 $\eta^\prime$ mesic nuclei using the microscopic transport model JAM. The semi-exclusive measurements of the ($p,d$) reaction with protons from $\eta^\prime$ absorption are found to be significant for the observation of the $\eta^\prime$ bound states. Especially, the measurements of the energetic protons from $\eta^\prime$ non-mesic two-body absorption ($\eta^\prime NN \to NN$) 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 $\eta^\prime \otimes {}^{11}$C system in the semi-exclusive measurement. The semi-exclusive measurements are shown to be important in general for the $\eta^\prime$ mesic nucleus observation.