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Coherent photoproduction of the neutral pion and eta meson on the deuteron,$\gamma{d}${$\to$}$\pi^0\eta{d}$, has been experimentally studied at incidentphoton energies ranging from the reaction threshold to 1.15 GeV. The totalcross section demonstrates a rapid rise below 1 GeV. The data areunderestimated by the existing theoretical calculations based on quasi-free$\pi^0 \eta$ photoproduction on the nucleon followed by deuteron coalescence.At the same time, the data are rather well reproduced by the calculationstaking into account the final-state interaction. We have also measured for thefirst time the differential cross sections: the $\pi^0 \eta$ invariant-massdistribution $d\sigma/dM_{\pi \eta}$, the $\pi^0 d$ invariant-mass distribution$d\sigma/dM_{\pi d}$, the $\eta d$ invariant-mass distribution$d\sigma/dM_{\eta d}$, and the distribution over the deuteron emission angle$d\sigma/d\Omega_d$ in the overall center-of-mass frame. The measured crosssection $d\sigma/d\Omega_d$ does not exhibit strongly backward-peaking behaviorpredicted by the calculations. At all incident energies, an increase in$d\sigma/dM_{\eta d}$ near the $\eta d$ threshold is observed, which indicatesa bound or virtual $\eta d$ state resulting from a strong attraction between$\eta$ and a deuteron. The possibilities of using coherent $\pi^0\eta$photoproduction on a nucleus to study the $\eta$-nuclear interaction are alsodiscussed.

Coherent photoproduction of the neutral pion and eta meson on the deuteron at incident energies below 1.15 GeV