The isospin structure of photoproduction of pi-eta pairs from the nucleon in the threshold region

Photoproduction of $\pi \eta$-pairs from nucleons has been investigated from threshold up to incident photon energies of $\approx$~1.4~GeV. The quasi-free reactions $\gamma p\to p{\pi }^0\eta$, $\gamma n\to n{\pi }^0\eta$, $\gamma p\to n{\pi }^{+}\eta$, and $\gamma n\to p{\pi }^{-}\eta$ were for the first time measured from nucleons bound in the deuteron. The corresponding reactions from a free-proton target were also studied to investigate final-state interaction effects (for neutral pions the free-proton results could be compared to previous measurements; the $\gamma p\rightarrow n\pi^+\eta$reactionwasmeasuredforthefirsttime)\mathrm{.}Forthe$\pi^0\eta$finalstatecoherentproductionviathe$\gamma d\rightarrow d\pi^0\eta$ reaction was also investigated. The experiments were performed at the tagged photon beam of the Mainz MAMI accelerator using an almost $4\pi$ coverage electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. The total cross sections for the four different final states obey the relation $\sigma (p{\pi }^0\eta )$ $\approx$ $\sigma (n{\pi }^0\eta )$ $\approx$ $2\sigma (p{\pi }^{-}\eta )$ $\approx$ $2\sigma (n{\pi }^{+}\eta )$ as expected for a dominant contribution from a ${\mathrm{\Delta }}^{\star }\to \eta \mathrm{\Delta }(1232)\to \pi \eta N$ reaction chain, which is also supported by the shapes of the invariant-mass distributions of nucleon-meson and $\pi$-$\eta$ pairs. The experimental results are compared to the predictions from an isobar reaction model.