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Total cross sections, angular distributions, and invariant-mass distributionshave been measured for the photoproduction of $\pi^0\pi^0$ pairs off freeprotons and off nucleons bound in the deuteron. The experiments were performedat the MAMI accelerator facility in Mainz using the Glasgow photon taggingspectrometer and the Crystal Ball/TAPS detector. The accelerator deliveredelectron beams of 1508 and 1557~MeV, which produced bremsstrahlung in thinradiator foils. The tagged photon beam covered energies up to 1400~MeV. Thedata from the free proton target are in good agreement with previousmeasurements and were only used to test the analysis procedures. The resultsfor differential cross sections (angular distributions and invariant-massdistributions) for free and quasi-free protons are almost identical in shape,but differ in absolute magnitude up to 15\%. Thus, moderate final-stateinteraction effects are present. The data for quasi-free neutrons are similarto the proton data in the second resonance region (final state invariant massesup to $\approx$1550~MeV), where both reactions are dominated by the$N(1520)3/2^-\rightarrow \Delta(1232)3/2^+\pi$ decay. At higher energies,angular and invariant-mass distributions are different. A simple analysis ofthe shapes of the invariant-mass distributions in the third resonance region isconsistent with strong contributions of an $N^{\star}\rightarrow N\sigma$ decayfor the proton, while the reaction is dominated by a sequential decay via a$\Delta\pi$ intermediate state for the neutron. The data are compared topredictions from the Two-Pion-MAID model and the Bonn-Gatchina coupled channelanalysis.

Photoproduction of $\pi^0$-pairs off protons and off neutrons