"Soft-pion" production in the reactionNN→NNπ

We examine the reaction $\mathrm{NN}\to \mathrm{NN}\pi$ for "soft-pion" kinematics (${\overrightarrow{\mathrm{p}}}_{\pi }=0\mathrm{}$ in the center of mass). An earlier calculation based on the Adler-Dothan theorem severely underestimated the ${\overrightarrow{\mathrm{p}}}_{\pi }=0\mathrm{}$ cross section for $\mathrm{pp}\to \mathrm{np}{\pi }^{+}$ at 740 MeV. We attempt to understand this discrepancy in the context of a relativistic, unitary, three-body isobar model. The postemission $\Delta$-pole contributions are shown to be very important, even for these "soft-pion" kinematics. Relatively high partial waves in the $\mathrm{NN}\to N\Delta$ isobar amplitude are significant. However, after summing all the postemission and preemission diagrams, the discrepancy with experiment is only partially removed.