Quark Model, Multiple Scattering, and Regge Theory

The quark model for meson-nucleon scattering is treated by means of Glauber theory, using Reggeized quark scattering amplitudes. The multiple-scattering effects are calculated, and numerical estimates of their magnitudes are obtained by fitting the resulting forms to the available data. We find that the correction terms obtained in this way are generally subtractive and amount to 15% of the total cross sections. They disappear at a rate intimately connected with the shrinking of the diffraction peak; when the latter phenomenon begins to occur, our model predicts that total cross sections will show an increase of several millibarns. The multiple-scattering terms are essentially Regge-cut effects, and therefore may be helpful in explaining the nonvanishing polarization observed in $\pi p$ charge exchange. Using a simple model of this type, we obtain reasonably good fits to all types of pion-nucleon scattering data including both elastic and charge-exchange polarizations as well as total and differential cross sections.