Single pion production in pion-nucleon scattering

Abstract

We describe a model for single pion production, π+N → π+π+N, which includes a pion-pion interaction in the (3/2, 3/2) channel in the final state. We use a static model Hamiltonian with the addition of direct π-π interaction terms. The lowest order amplitude is obtained by selecting the appropriate graphs and a simple method is used to introduce the resonant final state interaction into the lowest order graphs. There are two parameters in the theory which are related to the s- and p-wave π-π scattering lengths, a0 and a1. These are determined by fitting the theory to the observed total cross sections for the process π-+p → π++π-+n in the energy range from threshold to 450 MeV. We can fit the major features of this cross section. The scattering lengths are found to be a0 = -0.046 μ-1 and a1 = 0.016 μ-1. The fit to the observed energy distributions indicates a value for the ratio a1/a0 slightly different from that for the total cross section. The fit to the angular distributions is less satisfactory. The reason for this is discussed in relation to an approximation made in evaluating the production amplitude.