Formation of $\eta$-mesic Nuclei Using the Recoilless (d,$^3$He) Reaction

Abstract

We propose to use the recoilless (d,$^3$He) reaction to produce $\eta$-mesic nuclei. This reaction has been used to observe deeply bound pionic states and proven to be powerful recently. We calculate $\eta$-mesic bound states in the nucleus using an optical potential and their formation cross section with the Green function method. Then, we carefully check the experimental feasibility. We find that $\eta$-mesic nuclei can be observed experimentally using the (d,$^3$He) reaction. We also mention the possibility to study the formation of $\omega$-mesic nuclei.