Elastic Scattering of Protons and Neutrons by Deuterons

Abstract

Phase shifts for $p\ensuremath{-}d$ and $n\ensuremath{-}d$ scattering are calculated in Born approximation for partial waves with $l\ensuremath{\ge}1$. These are used as a starting point for a phase shift analysis of the $p\ensuremath{-}d$ data in the energy range 0-10 Mev. For $l\ensuremath{\ge}1$, the phase shifts resulting from the phase shift analysis agree with those calculated in Born approximation. The $^{4}S$ and $^{2}S$ phase shifts have a reasonable energy dependence; that is, the "$kcot\ensuremath{\delta}$" plots are smooth functions of the energy and extrapolate to a set of scattering lengths near one of the known sets of $n\ensuremath{-}d$ scattering lengths. It is concluded that the correct set of $n\ensuremath{-}d$ scattering lengths is ${a}_{4}=6.2\ifmmode\pm\else\textpm\fi{}0.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13} \mathrm{cm}, {a}_{2}=0.8\ifmmode\pm\else\textpm\fi{}0.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13} \mathrm{cm}.$ 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. $N\ensuremath{-}d$ 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 $p\ensuremath{-}d$ and $n\ensuremath{-}d$ scattering. The scattering is nearly independent of the odd parity $n\ensuremath{-}p$ potentials and of the forces between like particles. Furthermore, it is nearly independent of the shape of the $^{3}S$ and $^{1}S\ensuremath{-}n\ensuremath{-}p$ potentials. However, the $^{2}S$ scattering length is sensitive to the singlet even parity $n\ensuremath{-}n$ potential, and is calculated as a function of the depth of this potential. It is insensitive to other $n\ensuremath{-}n$ potentials.