The Low Energy Elastic Scattering of Neutrons by Deuterons

The elastic scattering of neutrons by deuterons at energies less than 166 MeV incident neutron energy has been calculated using a scattering equation similar to that of Buckingham and Massey and a central nuclear potential with Gaussian form. Five values of the effective range are considered, covering all values of physical significance. For analytical convenience, a deuteron wave function consisting of two Gaussians is used, the deuteron binding energy being minimized with respect to three parameters. S and P phases for several energies were evaluated with the aid of electronic computers (Pilot ACE and DEUCE) for Serber, ordinary and symmetrical exchange forces. From the total cross section below 2 MeV it appears that the potentials of larger effective range agree best with experiment, although the doublet scattering length considerably exceeds the experimentally estimated value for all these potentials, probably because of polarization effects at low energies. From the P phases, conclusions are drawn about the validity of the Born approximation used by Christian and Gammel. The problem is then resolved for the short range potential using an adaptation of the variational methods of Hulthen and Kohn. The results at low energies compare favourably with the exact solution obtained previously. It therefore seems that the variational method may be used successfully when polarization of the deuteron is explicitly allowed for, and further calculations including this effect and using the Kohn method are in progress.