Ondes partielles et modèles d'échange dans les réactions πN → ππN (Deuxième note)

Abstract

We present a theoretical framework to be used in the analysis of the experimental data for the reaction πN → ππN in terms of partial wave amplitudes and amplitudes corresponding to peripheral production of N* and ρ. In a previous paper, we expressed the amplitudes describing πN → ππN in terms of Pauli spinors and matrices. Here we derive results in terms of spherical harmonics and Clebsch-Gordan coefficients. The final amplitude contains various admixtures of partial wave and exchange amplitudes. We calculate the probability distributions and also the recoupling coefficients corresponding to different final state interactions. We develop the partial wave expansion of exchange amplitudes and finally we examine the case in which the initial nucleon is polarized.