Nuclear Forces in Pseudoscalar Meson Theory

The nuclear forces in pseudoscalar meson theory are evaluated using a nonrelativistic approximation to the relativistic interaction. The potential is obtained in a form which allows explicit evaluation of the contribution due to the multiple scattering of the virtual mesons between the two nucleons. An approximate expression for the potential, including the multiple scattering of a single meson, is obtained in closed form. For $r<\mathrm{}\frac{0.5\hslash }{\mu c}$, the multiple-scattering terms predominate and a power series expansion of the potential is non-convergent. On the other hand, for $r>\mathrm{}\frac{0.5\hslash }{\mu c}$ the potential obtained can be approximated by the second- and fourth-order terms as obtained from perturbation theory. With these latter two terms and a phenomenological "repulsive core," quite satisfactory results are obtained for the low-energy properties of the two-nucleon system.