Non-locality and Medium Effects in the Exclusive Photoproduction of Eta Mesons on Nuclei

A relativistic model for the quasifree exclusive photoproduction of $\eta$ mesons on nuclei is extended to include both non-local and medium effects. The reaction is assumed to proceed via the dominant contribution of the S$_{11}$(1535) resonance. The complicated integrals resulting from the non-locality are simplified using a modified version of a method given by Cooper and Maxwell. The non-locality effects are found to affect the magnitude of the cross section. Some possibilities reflecting the effects of the medium on the propagation and properties of the intermediate S$_{11}$ resonance are studied. The effects of allowing the S$_{11}$ to interact with the medium via mean field scalar and vector potentials are considered. Both broadening of width and reduction in mass of the resonance lead to a suppression of the calculated cross sections.