Elastic and Inelastic Scattering of 100- to 200-Mev Protons or Neutrons by Deuterons

Abstract

Expressions have been obtained, on the Born approximation, for the elastic and the total scattering cross section of protons or neutrons by deuterons, on the basis of the three forms of nucleon potentials suggested by Rarita and Schwinger, including tensor forces but with a Gaussian function for the radial part $V(r)$. Numerical calculations have, however, been carried through without tensor forces for (i) the angular distribution and total cross section of elastic scattering at 100, 150, and 200 Mev, (ii) the energy spectrum of protons scattered (elastically plus inelastically) in different directions from that of the incident protons and total cross section, and (iii) the energy spectra of neutrons ejected in directions making angles 0\ifmmode^\circ\else\textdegree\fi{} and 30\ifmmode^\circ\else\textdegree\fi{} with the direction of the incident protons, for 200 Mev. The three potentials predict considerable differences in both the differential and the total cross sections for both elastic and total scattering. The proton-deuteron total cross sections for 100 Mev is 0.424, 0.212, ${0.089\ifmmode\times\else\texttimes\fi{}10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$ according to the ordinary, exchange, and symmetrical force, respectively, as compared with the observed value ${0.117\ifmmode\times\else\texttimes\fi{}10}^{\ensuremath{-}24}$ recently reported from Berkeley for 90 Mev. The calculations show that the interference of the amplitudes scattered by the two particles of the deuteron plays an important role in the determination of the total cross section for proton-deuteron scattering. It is therefore not a good approximation to set the total $p\ensuremath{-}d$ cross section equal to the sum of the $p\ensuremath{-}n$ and $p\ensuremath{-}p$ cross sections for free particle collisions.