Elastic Scattering of Protons and Neutrons by Deuterons

Abstract

Phase shifts for $p-d$ and $n-d$ scattering are calculated in Born approximation for partial waves with $l\ge 1$. 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 $l\ge 1$, 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 "$kcot\delta$" 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 $a_4=6.2\mathrm{}\pm 0.2\times {10}^{-13\mathrm{}} \mathrm{cm}, a_2=0.8\mathrm{}\pm 0.3\times {10}^{-13\mathrm{}} \mathrm{cm}.$ 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. $N-d$ 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 ${}_{}{}^3{}_{}{}^{}S$ and ${}_{}{}^1{}_{}{}^{}S-n-p$ potentials. However, the ${}_{}{}^2{}_{}{}^{}S$ 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.