New theory of nuclear forces. Relativistic origin of the repulsive core

Abstract

A relativistic, three-dimensional wave equation which restricts one of the two interacting particles to its mass shell is applied to the study of nuclear forces. In the nonrelativistic limit, the equation reduces to a Schr\odinger equation with effective potentials composed of two parts. One part, with longer range, is similar to nonrelativistic potentials obtained from other theories, while a second short-range part, which arises solely from the relativistic nature of this equation, is repulsive and dominates over the longer-range part at short distances. The resulting soft-core potentials are evaluated numerically for a simple one-particle-exchange model limited to the exchange of $\ensuremath{\pi}$, $\ensuremath{\rho}$, $\ensuremath{\omega}$, and a neutral spinless meson. By adjusting four of the parameters we obtain good fits to the Reid soft-core potentials, especially in the $S$ states. The couplings obtained are very reasonable, and the results are compared with other recent models. The general features of the theory and the quantitative details of the model are thoroughly discussed.