Pion-Nucleon Processes above the First Maximum According to the Strong-Coupling Method

Abstract

A rough estimate of pion production by pion-nucleon collisions, in the range of 300-600 Mev incident kinetic energy in the lab system, is carried through on the basis of the strong-coupling method. This method, explicitly introducing the nucleon isobars, gives as the main contribution the pion production via isobaric excitation, in agreement with the conclusions of Lindenbaum and Sternheimer. Especially, a mechanism for pion productions via isobaric excitation follows without an extra $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interaction term, using only the fixed-source theory. Because of the heavier mass of the isobar and the participation of one more particle in the pion production process, the neglect of nucleon recoil in the fixed-source theory should not be taken too seriously for pion production below 1 Bev. Our results for the magnitude and energy dependence of the pion production cross section are within the same order of magnitude as the experimental results, in contradiction with the conclusions of Rodberg and Kazes who use a different kind of approximation based on the usual Chew-Low formalism and not on the strong-coupling method. We also find, as a typical result of the strong-coupling approximation, that the contributions to the isospin-$\frac{3}{2}$ states are about 4 times smaller than those to the isospin-\textonehalf{} states, which is just what the experimental results show in the energy range concerned. Thus it is shown that these important properties of the pion production cross section for pions on nucleons can already be explained by the strong-coupling approximation of the fixed-source theory without an extra $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ term. Therefore, these contributions from the fixed-source theory without an extra $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ term should be taken into account in addition to the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ mechanism which was considered as the only mechanism by Dyson, Takeda, Rodberg, Goebel and Schnitzer, Peierls, and Carruthers and Bethe. Indications are presented that maxima could arise in the production as well as in the elastic scattering cross section as a consequence of pion production via isobaric excitation and pion scattering on isobars in the intermediate states. The latter effect of pion resonance scattering on isobars also has been considered by Wong and Ross and by Tomozawa in a different kind of approach. But we did not include these last-mentioned effects in this first rough estimate.