The double-polarization observable $E$ and the helicity-dependent cross sections $sigma_{1/2}$ and $sigma_{3/2}$ have been measured for the first time for single $pi^{0}$ photoproduction from protons and neutrons bound in the deuteron at the electron accelerator facility MAMI in Mainz, Germany. The experiment used a circularly polarized photon beam and a longitudinally polarized deuterated butanol target. The reaction products, recoil nucleons and decay photons from the $pi^0$ meson were detected with the Crystal Ball and TAPS electromagnetic calorimeters. Effects from nuclear Fermi motion were removed by a kinematic reconstruction of the $pi^{0}N$ final state. A comparison to data measured with a free proton target showed that the absolute scale of the cross sections is significantly modified by nuclear final-state interaction (FSI) effects. However, there is no significant effect on the asymmetry $E$ since the $sigma_{1/2}$ and $sigma_{3/2}$ components appear to be influenced in a similar way. Thus, the best approximation of the two helicity-dependent cross sections for the free neutron is obtained by combining the asymmetry $E$ measured with quasi-free neutrons and the unpolarized cross section corrected for FSI effects under the assumption that the FSI effects are similar for neutrons and protons.
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