Pion-Nucleon Scattering at High Energies

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.

It is found that, contrary to the original expectation of a resonant interaction, the increase of $D_{\frac{5}{2},\frac{1}{2}}$ phase shift over the Born approximation is not large. Also the effects of meson production are not found to be very significant over the energy range 1 Bev to 2 Bev. This last is contrary to the observations in this energy range.