A resonance model for pion production in nucleon-nucleon collisions at fairly low energies

Abstract

Cross-sections for pion production in nucleon-nucleon collisions are calculated on the assumption that the production takes place into a few angular momentum states only, and that the matrix element for each particular transition is constant except for factors due to the final-state pion-nucleon and nucleon-nucleon interactions. The outgoing pion is assumed to be in a resonant (3/2, 3/2) state with one of the nucleons. The angular momentum states introduced are compared with those of Rosenfeld (1954) and Gell-Mann & Watson (1954). It is found that a three-parameter theory can give a good account of most of the experiments on pion production, both total and differential, up to 660 MeV, except near threshold when non-resonance production is important and further parameters are necessary. Energy distribution and angular correlation experiments bring out the importance of the pion-nucleon resonance. The cross-section for neutral pion production is predicted fairly accurately in terms of that for positive pion production from threshold to 660 MeV; at 660 MeV, the calculated positive:neutral ratio is 3⋅9. The difference between this value and that of Peaslee (1954) is partly due to the mass difference between the positive and neutral pion and partly to the inclusion of interference effects between the outgoing nucleons.