Scattering and polarization of protons by nuclei

Abstract

The relation of the polarized scattering of protons by complex nuclei to that by nucleons is investigated quantitatively. No model of nuclear forces is used, but the nucleon-nucleon scattering is directly represented by phase shifts. The agreement is found to be good for all the phase shift solutions which Stapp et al. have given for the proton-proton scattering, the deviation being from 0 to 25%. Thus the scattering by a complex nucleus can be obtained by superposition of the nucleon-nucleon scattering amplitudes. For the purpose of this comparison, the experimental data of Chamberlain et al. on the scattering and polarization of protons by carbon at small scattering angles are analyzed directly, i.e., the relevant scattering lengths are deduced from the experimental data, rather than the data synthesized from an assumed potential. The resulting nuclear absorption coefficient reproduces the observed inelastic scattering. The real part of the central potential is found to be attractive but very weak (about 4 Mev). The spin-orbit potential agrees with the nucleon-nucleon data and with some, but not all, previous theoretical values; it is only one-sixth of that required in the shell model. The analysis is facilitated by a theorem, first derived by Köhler and by Levintov, that the polarization is given correctly by the Born approximation. Simple formulas are given to obtain the Born approximation scattering (and thus the potential) from the observed scattering. A particularly simple formula relates the Born approximation scattering to the nucleon-nucleon scattering. The expressions for the relevant amplitudes in nucleon-nucleon scattering are also simplified. It is further shown that the scattering matrix for nucleon-nucleon scattering at a given angle can be completely determined if all the standard triple scattering and polarization experiments are carried out.