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