$FSI$ Corrections For Near Threshold Meson Production In Nucleon-Nucleon Collisions

A procedure is proposed which accounts for final state interaction corrections for near threshold meson production in nucleon-nucleon scattering. In analogy with the Watson-Migdal approximation, it is shown that in the limit of extremely strong final state effects, the amplitude factorizes into a primary production amplitude and an elastic scattering amplitude describing a $3 \to 3$ transition. This amplitude determines the energy dependence of the reaction cross section near the reaction threshold almost solely. The approximation proposed satisfies the Fermi-Watson theorem and the coherence formalism. Application of this procedure to meson production in nucleon-nucleon scattering shows that, while corrections due to the meson-nucleon interaction are small for s-wave pion production, they are crucial for reproducing the energy dependence of the $\eta$ production cross section.