Optical Model Potential for Pion-Nucleus Scattering

Abstract
The assumption that two-body forces are not appreciably modified within nuclei offers the possibility of calculating the optical-model potential from two-body scattering phenomena. For instance, the dispersion relations recently proposed by Goldberger permit one to make a calculation of the pion-nucleus well depth directly from observed pion-nucleon scattering cross sections. The results predict a rather striking variation with energy for this potential and appear to be in fair agreement with the available experimental data. The physical basis for the potential is investigated. Numerical calculations using meson theory (in the form proposed by Chew) are in disagreement with the results from the dispersion relations (as well as the experimental values). This involves solving an equation closely related to that used by Brueckner et al. in their study of nuclear saturation. The relations of the potential to various nuclear properties are discussed—for instance, it is shown in detail that the resolution of the nuclear radius is limited to the range of the two-body interaction.