Modified Analysis of Nucleon-Nucleon Scattering. I. Theory andp−pScattering at 310 Mev

Abstract

A modified method of analyzing nucleon-nucleon scattering is discussed and applied to proton-proton scattering experiments at 310 Mev. The modified scheme is based on an explicit inclusion in all higher angular-momentum states of the terms contributed by the one-pion exchange process. This procedure is suggested by Chew's conjecture that the singularities of the scattering amplitude in the $cos\theta$ plane ($\theta$ being the scattering angle in the center-of-mass system) that are closest to the physical region are due to the one-pion exchange process and are given by the Born approximation. Or, alternatively, in terms of ranges, the one-pion exchange contribution has the longest range of the forces contributing to the nucleon-nucleon interaction and hence should be primarily responsible for the contributions to the scattering amplitude in the high angular-momentum states. Since the only parameter in the Born approximation is the pion-nucleon coupling constant, the modified scheme can also provide a determination of this coupling constant. The application of the modified scheme to $p-p$ scattering at 310 Mev indicates that the first two of the five best solutions of the conventional phase-shift analysis are more satisfactory than the others for two reasons. Firstly, their goodness-of-fit parameters improve markedly when the higher angular-momentum contributions are added, whereas those of the others remain essentially unchanged. Secondly, as a function of the coupling constant, the goodness-of-fit parameters of the first two solutions show minima close to the accepted value of the coupling constant.