Precise angular distributions have been measured for the first time for the photoproduction of $pi^{0}$-mesons off neutrons bound in the deuteron. The effects from nuclear Fermi motion have been eliminated by a complete kinematic reconstruction of the final state. The influence of final-state-interaction effects has been estimated by a comparison of the reaction cross section for quasi-free protons bound in the deuteron to the results for free protons and then applied as a correction to the quasi-free neutron data. The experiment was performed at the tagged photon facility of the Mainz Microtron MAMI with the Crystal Ball and TAPS detector setup for incident photon energies between $0.45$~GeV and $1.4$~GeV. The results are compared to the predictions from reaction models and partial-wave analyses based on data from other isospin channels. The model predictions show large discrepancies among each other and the present data will provide much tighter constraints. This is demonstrated by the results of a new analysis in the framework of the Bonn-Gatchina coupled-channel analysis which included the present data.
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