Direct-Interaction Model Calculation of High-Energy Proton-Carbon Scattering

An optical potential has been derived which includes, to first order in $q^2$, the effect of the nucleon-nucleon angular dependence. Nucleon-nucleon scattered amplitudes calculated from the 310-Mev nucleon-nucleon phase shifts have been put into the potential and the proton-carbon scattered amplitudes calculated from it by WKB approximation. Good agreement was obtained with the scattered amplitudes as derived directly from the 313-Mev proton-carbon data using an extension of the analysis employed previously by Bethe. The inclusion of the nucleon-nucleon angular dependence in the potential was found to be important in order to obtain the correct value of the imaginary part of the forward scattered amplitude and the correct proton-carbon angular dependence at moderately small angles. Phase shift solutions 1 and 6 of Stapp et al. were investigated and found to give essentially the same agreement with the differential cross section at small angles. Solution 6 was found to give a better fit to the polarization data than solution 1, but the significance of this is not clear.