Low-energy scattering and photoproduction of $\eta$-mesons on three-body nuclei

The optical potential approach for low-energy scattering of $\eta$-mesons on three-body nuclei is compared to an exact treatment of the $\eta 3N$ system using four-body scattering theory with separable interactions in s-waves only. The higher-order terms including the interaction of the struck nucleon with the surrounding nuclear medium and virtual target excitations in between successive $\eta$-scatterings are found to cause important corrections. Effects of final state interaction in $\eta$-photoproduction on $^3$H and $^3$He are also studied and sizable contributions beyond the optical model approach are found