Elastic Scattering of Protons and Neutrons by Deuterons

Phase shifts for p-d and n-d scattering are calculated in Born approximation for partial waves with l1. These are used as a starting point for a phase shift analysis of the p-d data in the energy range 0-10 Mev. For l1, the phase shifts resulting from the phase shift analysis agree with those calculated in Born approximation. The ^4S and ^2S phase shifts have a reasonable energy dependence; that is, the "kcot" plots are smooth functions of the energy and extrapolate to a set of scattering lengths near one of the known sets of n-d scattering lengths. It is concluded that the correct set of n-d scattering lengths is a₄=6. 20. 210^-13 cm, a₂=0. 80. 310^-13 cm. Since this is in disagreement with some previous theoretical conjectures, the scattering lengths and S phase shifts in the energy region 0-10 Mev are calculated using a variational method with neglect of polarization (a theoretical estimate of the effect of polarization is made) and the results support the conclusion. N-d angular distributions are calculated and compared with experiments. The agreement of the theoretical results with the experimental ones provides a strong a fortiori justification of conclusions drawn from the theory about the importance of the internucleonic potentials in low energy p-d and n-d scattering. The scattering is nearly independent of the odd parity n-p potentials and of the forces between like particles. Furthermore, it is nearly independent of the shape of the ^3S and ^1S-n-p potentials. However, the ^2S scattering length is sensitive to the singlet even parity n-n potential, and is calculated as a function of the depth of this potential. It is insensitive to other n-n potentials.