Soft Pion Production in Nucleon-Nucleon Collisions

The emission of soft pions in nucleon-nucleon collisions is studied for lab energies in the range 500-800 MeV. Following the prescription of the Adler-Dothan theorem, we consider the dominant contribution to arise from processes involving emission from external nucleon lines only. The amplitudes are calculated in the helicity representation, the invariant functions for the nucleon-nucleon scattering being obtained from phase shifts. Cross sections for $\mathrm{pp}\to \mathrm{np}{\pi }^{+}$ are given in some detail.