Pion-nucleon and pion-nucleus interactions at intermediate energies

Abstract

Models of the pion-nucleon interaction must be relativistic and field theoretic. This work models those partial waves (S-, D-, and F-waves) of the interaction exhibiting resonant behavior with a new "doorway resonance model," which is both relativistic and field theoretic. This model is demonstrated to be a generalization of previous Chew-Low models with the improvement of allowing nucleon recoil and is applied to the P₁₃, P₃₁, and P₃₃ channels. Other partial waves are modelled by the relativistic generalization, developed in this work, of previous separable potential models. The results of the models are shown to compare favorably with the data. All models are free of kinematic singularities. These models are utilized to form a microscopic, momentum-space, isospin invariant optical potential to investigate the pion-nucleus iso-elastic interaction in the energy region from 300 MeV to 500 MeV where data has only recently become available and where no prior theoretical work exists. The optical potential utilizes fully relativistic kinematics, and the fermi integration is performed exactly as well as by optimal factorization. Our results are compared to recent data for 0° excitation functions for the isobaric analogue state transitions in ¹⁴C and ⁹⁰Zr. The observed rise in the cross section for energies above the resonance is reproduced by the theory, and, although not totally quantitative, the theoretical results indicate that the multiple scattering theory as defined and implemented here is significantly more convergent at the higher energies than at or below the resonance.