Pion Reactions in One Nucleon System and Nucleon Isobars

Abstract

In this paper, we try to interpret the pion-nucleon interaction on the basis of the nucleon isobar model. As a complementary way to the strong coupling and phenomenological theories, we start from the field theoretical viewpoint which will be useful to connect the present phenomenological theory of pions to the future theory of fields. We treat the nucleon isobars as elementary particles and describe them by the Rarita-Schwinger equation of particles with spin 3/2. Hence the familiar Feynman-Dyson method is immediately applicable to the calculation of matrix elements of such processes involving nucleon isobars as the pion-proton scattering and the pion-production by γ-rays on proton. The qualitative features are governed mainly by the mass, width, spin and isotopic spin of the isobar, so that our results roughly agree with those of the strong coupling and phenomenological theories. In some detailed respects, however, our results show differences from other theories; the agreement with experiments is improved for the angular distributions of γ-p scattering and photo-production of charged pions, but becomes a little worse for that of neutral pions. Our method is applied only to pion reactions in one nucleon system, for we know too little about two or more nucleon systems to extract the pure pion-nucleon interaction. Lastly, we discuss the validity of the nucleon isobars.