Pion-nucleon scattering at intermediate energies

A study of pion-nucleon scattering at intermediate energies, P/sub π/ from 2 to 5 GeV/C, using a relativistic optical model is made. This model is based on the Bethe-Salpeter Equation and its reduced form, the Blackenbecler-Sugar equation, which is simpler to solve. The numerical work involves solving singular integral equations numerically using Simpson's rule to obtain the scattering amplitudes and hence the cross sections. The scattering data are fitted by changing the various potential parameters in this model. In addition to the potential created by the exchange of a scalar (sigma) and rho-meson as performed in earlier work, the exchange of a S/sup */ meson is also investigated. For simplicity, most of the coupling parameters are kept fixed with energy except for the energy varying imaginary part of the sigma-meson coupling constant. π/sup +/-/-P and charge exchange data agree very well with the experimental values. The polarizations agree only qualitatively. Further investigation shows that the polarizations are sensitive to the rho-meson parameters. Further extensions to this work are also suggested