Two-body effects in coherent η-meson photoproduction on the deuteron in the region of theS11(1535)resonance

Coherent η-meson photoproduction on the deuteron has been studied, where the emphasis is on the relative importance of two-body contributions from hadronic rescattering and electromagnetic meson exchange currents besides the impulse approximation. For the elementary photoproduction amplitude a coupled resonance model developed by Bennhold and Tanabe has been used that fits reasonably well with the experimental data. The rescattering effects are treated within a coupled channel approach considering the intermediate excitation of the $P_{11}\mathrm{}\left(1440\right),$ $D_{13}\mathrm{}\left(1520\right),$ and $S_{11}\mathrm{}\left(1535\right)\mathrm{}$ nucleon resonances. The hadronic interaction between nucleon and resonances is modeled by one-boson exchange potentials, which we have considered both in the static approximation as well as fully retarded. The sum of all considered two-body effects results in an enhancement of the total cross section between 10 in the maximum and $25\%$ closer to threshold around 680 MeV if the hadronic interaction is treated retarded. This enhancement shows up in the differential cross sections mainly at backward angles. It increases steadily from only a few percent at $0°$ to more than a factor of 2 at $180°$ for a photon energy of 680 MeV. Two-body effects also become significant in certain polarization observables. Finally, no discrepancy has been found for the ratio of the isoscalar amplitude to the proton amplitude between coherent and incoherent $\eta$ photoproduction on the deuteron due to a nonvanishing complex and energy dependent phase relation.