Modeling of a microscopic optical pion-nucleon potential at energies in the (3, 3)-resonance region and nuclear-matter effect on the pion-nucleon amplitude

Differential cross sections for elastic pion scattering on a number of nuclei at energies between 130 and 290 MeV are calculated. For this purpose, use is made of a microscopic optical pion-nucleus potential that was obtained on the basis of the Glauber theory of high-energy scattering and which is determined by the density distribution of pointlike target nucleons and by the pion-nucleon scattering amplitude. The calculation of the cross sections in question is based on solving the respective relativistic wave equation. Three parameters of the pion-nucleon amplitude are fitted in performing a comparison with experimental data. These are the total cross section for pion-nucleon scattering, the ratio of the real to the imaginary part of the forward pion-nucleon scattering amplitude, and the slope parameter. The resulting values of these parameters are then compared with their counterparts for scattering on free nucleons. The character of nuclear-matter-induced changes in these parameters is studied.