Pion-nucleon interaction model for the P 11 and P 33 channels and the unitary three-body calculation of nn scattering

Abstract

We extend the isobar-dominated model for the πN P 33 channel in such a manner as to incorporate a background (non-pole) interaction. The pion-nucleon potential has two driving terms, a pole part generated by the πNΔ vertex and a background part. The πrN P 11 interaction is constructed in a similar way by including a pole part generated by the πNN vertex and a non-pole part. Motivated by a quark-model picture for baryons, we choose the common cut-off form factor for the πNN and πNΔ vertices. The parameters of the model are determined by the fit to the empirical πN phase shifts. Using this πN interaction model as an input, we calculate nucleon-nucleon elastic-scattering phase parameters based on a unitary, relativistic, pion-exchange model. We find that our model adequately reproduces the 1D 2 phase parameters as well as those of peripheral partial waves. We also find that the longitudinal total cross section difference Δσ L(pp → NNπ) comes closer to the data. We discuss the different choice of the irN relative momentum, the backward pion propagation, and the Pauli-principle violating states for the background P 11 interaction.