Coherent Photoproduction ofπ0from Deuterium

The calculation of elastic photoproduction of ${\pi }^0$ mesons from deuterium, $\gamma +d\to {\pi }^0+d$, is carried out in the impulse approximation at photon energies around 500 Mev. The single nucleon photoproduction amplitudes are taken from dispersion formulas and are corrected for kinematic effects due to internal momentum of the nucleons in the deuteron. We include the $D$-state part of the deuteron wave function and use different models with Yukawa type or repulsive core wave functions. We give formulas connecting the cross section with the deuteron form factors. For small momentum transfers the formulas are of course model independent and reduce to the usual ones. The presence of a 7% $D$ state in a repulsive-core model leads to a cross section which falls typically more slowly at high momentum transfers, e.g., at a momentum transfer 2.74 ${\mathrm{f}}^{-1\mathrm{}}$, the cross section is larger by about 40% than the cross section calculated in the absence of the $D$ state. The experimental points favor this model.