Suppression of Pair Coupling in Nuclear Forces

It is demonstrated that for the nuclear force problem the effective coupling constant for the emission of a pair of mesons is the same as the renormalized coupling constant, $\frac{{g_s}^2}{4\pi }$, which occurs in the matrix element for meson-nucleon scattering in the low energy limit. The proof involves an adaptation of the techniques developed by Deser, Thirring, and Goldberger for the scattering problem. The relatively small value of the coupling constant thus obtained, $\frac{{g_s}^2}{4\pi }\sim 1$, can be interpreted as the consequence of a net pair suppression, although not in the narrow sense associated with the nucleon propagation function alone. Radiative corrections to multiple pair vertices are considered briefly.