Meson Theory of Nucleon—Nucleon Interaction

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.