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Precise helicity-dependent cross sections and the double-polarizationobservable $E$ were measured for $\eta$ photoproduction from quasi-free protonsand neutrons bound in the deuteron. The $\eta\rightarrow 2\gamma$ and$\eta\rightarrow 3\pi^0\rightarrow 6\gamma$ decay modes were used to optimizethe statistical quality of the data and to estimate systematic uncertainties.The measurement used the A2 detector setup at the tagged photon beam of theelectron accelerator MAMI in Mainz. A longitudinally polarized deuteratedbutanol target was used in combination with a circularly polarized photon beamfrom bremsstrahlung of a longitudinally polarized electron beam. The reactionproducts were detected with the electromagnetic calorimeters Crystal Ball andTAPS, which covered 98\% of the full solid angle. The results show that thenarrow structure observed earlier in the unpolarized excitation function of$\eta$ photoproduction off the neutron appears only in reactions withantiparallel photon and nucleon spin ($\sigma_{1/2}$). It is absent forreactions with parallel spin orientation ($\sigma_{3/2}$) and thus veryprobably related to partial waves with total spin 1/2. The behavior of theangular distributions of the helicity-dependent cross sections was analyzed byfitting them with Legendre polynomials. The results are in good agreement witha model from the Bonn-Gatchina group, which uses an interference of $P_{11}$and $S_{11}$ partial waves to explain the narrow structure.

Helicity-dependent cross sections and double-polarization observable E in eta photoproduction from quasi-free protons and neutrons