The photoproduction of isolated photons has been measured in diffractive events recorded by the ZEUS detector at HERA. Cross sections are evaluated in the photon-proton transverse-energy and pseudorapidity ranges 5<ET(gamma)<15 GeV and -0.7<eta(gamma)<0.9 inclusively and also with a jet with transverse energy and pseudorapidity in the range 4<ET(jet)<35 GeV and -1.5<eta(jet)<1.8, using a total integrated electron-proton luminosity of 374 pb-1. A number of kinematic variables were studied and compared to predictions from the RAPGAP Monte Carlo model. An excess of data is observed above the RAPGAP predictions for z|P(meas)>0.9, where z|P(meas) is the fraction of the longitudinal momentum of the colourless Pomeron exchange that is transferred to the photon-jet final state, giving evidence for direct Pomeron interactions.
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