  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.
