Importance of the Doppler Effect to the Determination of the Deuteron Binding Energy

The deuteron binding energy extracted from the reaction ${}^1H(n,\gamma){}^2H$ is reviewed with the exact relativistic formula, where the initial kinetic energy and the Doppler effect are taken into account. We find that the negligible initial kinetic energy of the neutron could cause a significant uncertainty which is beyond the errors available up to now. Therefore, we suggest an experiment which should include the detailed informations about the initial kinetic energy and the detection angle. It could reduce discrepancies among the recently reported values about the deuteron binding energy and pin down the uncertainty due to the Doppler broadening of $\gamma$ ray.