NΔ-NN interaction in the pionic disintegration of the deuteron

The cross sections for the pionic disintegration of the deuteron in the Δ-resonance region are calculated based on a unitary three-body model. The NΔ-NN transition potential is constructed from the πN $P_{11}$ and $P_{33}$ scattering amplitudes extrapolated to the off-shell region, and from the πNN 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 πN 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 Λ=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 πNN 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.