Elastic Scattering of Pions onO16near the (3-3) - Resonance Energy: A Self-Consistent Calculation

An optical potential for elastic scattering of mesons on a nucleus is developed theoretically which is self-consistent at all distances from the center of the nucleus. Application is made to the case of scattering of pions on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ in the (3-3)-resonance energy region for the Fermigas model and the shell model of the nucleus. Pair correlations are included. Energy-dependent empirically fitted parameters are used as inputs for the pion-nucleon interaction. For the shell model a downward energy shift of 30-45 MeV, as well as considerable broadening, is predicted for the (3-3) pion-nucleus resonance. Graphs of the differential cross-section for various energies are included, with discussion of some significant features. Effects of inclusion and exclusion of the self-consistency requirement are considered.