Exchange of $\pi$, $\eta$, $\rho$, $\omega$, $\phi$ mesons and a pair of pions in the relative $s$ state can account for all the important features of the nucleon-nucleon interaction. The method of dispersion relation is employed to calculate nucleon-nucleon phase shifts starting from the relativistic single-particle-exchange Feynman diagrams. Validity of the method is tested in the nonrelativistic limit where the solution of the dispersion relation is compared to the solution of the Schrödinger equation for a superposition of Yukawa potentials. For potentials that contain a long-range attraction and a strong short-range repulsion there is little difference between the two solutions. In the meson model, the attraction comes primarily from the $\pi$ and the $s$-wave two-pion exchange. The exchange of $\omega$ and $\phi$ produces the required short-range repulsive force.

Two approaches to the nucleon-nucleon scattering problem were considered. (a) The meson model was taken to be the basis of a detailed fit to the scattering data. A total of 12 adjustable parameters were introduced and a fit to the $\mathrm{pp}$ and $\mathrm{np}$ data was obtained. The accuracy is comparable to that of pure phenomenological potentials with considerably more parameters. (b) The number of parameters in the meson model is minimized using approximate symmetry considerations to clarify the physical significance of the model. With only four adjustable parameters, all the important features of the phase shift are reproduced. These results lend support to the idea that the strongly correlated multimeson systems $\rho$, $\omega$, and $\phi$ play a dominant role in the inner part (≲0.3 F) of the nucleon-nucleon potential while the exchange of two pions in a relative $s$-state accounts for the gross feature of the medium-range attraction.

DOI:https://doi.org/10.1103/RevModPhys.39.622