pi degrees photoproduction on quasi-free neutrons in the reaction gamma d->pi degrees np in the Delta region

The possibility of obtaining information about the reaction gamma n --> pi degrees n in the Delta resonance region from the reaction gamma d --> pi degrees np is analyzed. To this aim, the differential cross sections d(3) sigma/dE(n)d Omega(pi)d Omega(n) both for unpolarized particles and in case of polarized photons and deuterons as well as the asymmetry Sigma for linearly-polarized photons are calculated at photon energies from 250 to 400 MeV in the diagrammatic approach. The contributions from the pole diagrams as well as one-loop diagrams both with n-p, and pi-N-rescattering are taken into account, The main contribution to the differential cross sections of pi degrees photoproduction on the neutron in the quasi-free kinematics arises from the neutron pole diagram. The correction due to n-p rescattering decreases with increasing pion angle and becomes to be less than 8% at Theta(pi) greater than or equal to 90 degrees. The contributions of the proton pole diagram and the one of pi-N rescattering were found to be negligible. Background effects are more pronounced in the case of the asymmetry Sigma. However, they are also strongly suppressed in the neutron quasi-free kinematics at photon energies above 300 MeV.