Coherent photoproduction of the neutral-pion and η-meson on the deuteron, γd→π0ηd, was experimentally studied at incident photon energies ranging from the reaction threshold to 1.15 GeV. The total cross section demonstrates a rapid rise below 1 GeV. The data are underestimated by the existing theoretical calculations based on quasifree π0η photoproduction on the nucleon followed by deuteron coalescence. At the same time, the data are rather well reproduced by the calculations taking into account the final-state interaction. We also measured for the first time the differential cross sections: the π0η invariant-mass distribution dσ/dMπη, the π0d invariant-mass distribution dσ/dMπd, the ηd invariant-mass distribution dσ/dMηd, and the distribution over the deuteron emission angle dσ/dωd in the overall center-of-mass frame. The measured cross section dσ/dωd does not exhibit strongly backward-peaking behavior predicted by the calculations. At all incident energies, an increase in dσ/dMηd near the ηd threshold is observed, which indicates a bound or virtual ηd state resulting from a strong attraction between η and a deuteron. The possibilities of using coherent π0η photoproduction on a nucleus to study the η-nuclear interaction are also discussed.
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