Effect of Pion-Pion Interaction on Nuclear Forces

The effect of pion-pion interaction on the two-nucleon potential is investigated by using the pion-pion coupling, $H=\left(\frac{4\pi f}{c\hslash }\right):U_i{U}_i{U}_j{U}_j:$. It is found that if the coupling constant $f$ is negative, the resulting spin-orbit nuclear force in the nonrelativistic approximation is similar to that produced by the exchange of a neutral meson of mass between 3.3 and 4.1 times the pion mass. A comparison of the theoretical results for the angular dependence of the Wolfenstein coefficient ${\overline{C}}^{\prime }$ with those obtained by the phase-shift analysis of the proton-proton scattering at 310 MeV shows reasonable agreement, and gives $f=-0.262\mathrm{}$.