Elastic Scattering of Pions by Nucleons and Pion Production in Nucleon-Nucleon Collisions

Abstract

If the ideas about the pion-nucleon interaction discussed by Chew are taken seriously, it is important to know the accuracy of his calculation of the phase shifts for pion-nucleon scattering resulting from the second-order Tamm-Dancoff approximation. In this paper, exact solutions (found by numerical methods) of the integral equations for the scattering amplitudes resulting from the second-order Tamm-Dancoff approximation are compared with his approximate results.Aitken, Mahmoud, and Watson have shown that a similar integral equation occurs in a theory (based on the same ideas as those discussed by Chew) of pion production in nucleon collisions. The accuracy of their approximate solution of this integral equation is discussed.