Coherent pion photoproduction on the deuteron is studied in the threshold region spanning photon lab energies from threshold at 139.83 MeV to 160 MeV. Unlike previous similar calculations which used the now obsolete value for the $s$-wave $E_{0+}$ multipole, our work relies on the latest information on the elementary amplitudes which are in excellent agreement with recent precise data on the $\gamma \overrightarrow{p}{\pi }^{0}p$ reaction. We compare the exact treatment of pion propagation against various approximations often used in the literature and their impact on the very important pion rescattering contribution. We have investigated the sensitivity of the $\gamma \overrightarrow{D}{\pi }^{0}D$ cross section to various choices of the values of the elementary multipoles and in particular the neutron $s$-wave amplitude $E_{0+}^{{\pi }^{0}n}.$ The Fermi motion, corrections due to the boost from the nucleon to the deuteron frames as well as the deuteron $D$-state are all taken into account. The predicted total and differential cross sections are compared with the very recent experimental data from the Saskatchewan Accelerator Laboratory.

• Received 31 March 1998

DOI:https://doi.org/10.1103/PhysRevC.58.1777