The first study of quasi-free Compton scattering on the neutron in the energy range of $E_{gamma}=0.75 - 1.5$ GeV is presented. The data reveals a narrow peak at $Wsim 1.685$ GeV. This result, being considered in conjunction with the recent evidence for a narrow structure at $Wsim 1.68$GeV in the $eta$ photoproduction on the neutron, suggests the existence of a new nucleon resonance with unusual properties: the mass $Msim 1.685$GeV, the narrow width $Gamma leq 30$MeV, and the much stronger photoexcitation on the neutron than on the proton.
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