  Photoproduction off protons of the $p\pi^0\eta$ three-body final state was
studied with the Crystal Barrel/TAPS detector at the electron stretcher
accelerator ELSA at Bonn for incident energies from the $\pi^0\eta$ production
threshold up to 2.5\,GeV. Differential cross sections and the total cross
section are presented. The use of linearly polarized photons gives access to
the polarization observables $\Sigma$, $I^{s}$ and $I^{c}$, the latter two
characterize beam asymmetries in case of three-body final states.
$\Delta(1232)\eta$, $N(1535){1/2^-}\pi$, and $p a_0(980)$ are the dominant
isobars contributing to the reaction. The partial wave analysis confirms the
existence of some nucleon and $\Delta$ resonances for which so far only fair
evidence was reported. A large number of decay modes of known nucleon and
$\Delta$ resonances is presented. It is shown that detailed investigations of
decay branching ratios may provide a key to unravelling the structure of
nucleon and $\Delta$ resonances.

Nuclear Experiment