$\eta$-nucleus interaction from the $d+d$ reaction around the $\eta$ production threshold

The $\eta$ mesic nucleus is considered to be one of the interesting exotic many body systems and has been studied since 1980's theoretically and experimentally. Recently, the formation of the $\eta$ mesic nucleus in the fusion reactions of the light nuclei such as $d + d \rightarrow (\eta + \alpha) \rightarrow X$ has been proposed and the experiments have been performed by WASA-at-COSY. We develop a theoretical model to evaluate the formation rate of the $\eta$ mesic nucleus in the fusion reactions and show the calculated results. We find that the $\eta$ bound states could be observed in the reactions in cases with the strong attractive and small absorptive $\eta$-nucleus interactions. We compare our results with existing data of the $d + d \rightarrow \eta + \alpha$ and the $d + d \rightarrow {^3 \rm He} + N + \pi$ reactions. We find that the analyses by our theoretical model with the existing data can provide new information on the $\eta$-nucleus interaction.