Pion-Nucleon Scattering at High Energies

Abstract

The pseudoscalar theory in the Tamm-Dancoff approximation is applied to high-energy pion-nucleon scattering with a view to explaining the observed maximum in ${\pi }^{-}-p$ scattering around 1 Bev as a resonant interaction. The integral equation is solved for the $D_{\frac{5}{2}}$ state of $T=\frac{1}{2}$ which is attractive. The various singularities in the kernel and the wave function are taken into account in a semianalytical fashion. A short derivation is given of the complex intefral equation which takes the effects of meson production into account, and it is solved in an approximate manner.