N Delta -NN interaction in the pionic disintegration of the deuteron.

Abstract

The cross sections for the pionic disintegration of the deuteron in the \ensuremath{\Delta}-resonance region are calculated based on a unitary three-body model. The N\ensuremath{\Delta}-NN transition potential is constructed from the \ensuremath{\pi}N ${P}_{11}$ and ${P}_{33}$ scattering amplitudes extrapolated to the off-shell region, and from the \ensuremath{\pi}NN three-body propagator. The idea of the two-potential model for the ${P}_{11}$ wave is extended to the ${P}_{33}$ wave. The parameters of the model are deduced from the fits to the \ensuremath{\pi}N scattering phase shifts. It is found that the off-shell ${P}_{11}$ and ${P}_{33}$ scattering amplitudes behave quite similarly to the monopole form factor with a cutoff momentum \ensuremath{\Lambda}=600 MeV/c as obtained earlier in the perturbation model by Gibbs, Gibson, and Stephenson. It is also found that the backward-propagating-pion component of the \ensuremath{\pi}NN propagator, which is often ignored in three-body calculations, is crucial to reproduce the magnitude of the total cross section. The three-body calculation is compared to the perturbation calculations. The second-order perturbation gives the results which closely approximate the full-order three-body calculation.