Nonlinear Meson Theory of Nuclear Forces. I. Neutral Scalar Mesons with Point-Contact Repulsion

Abstract

This paper develops an attempt to account for nuclear saturation and shell structure in terms of manybody forces that are derived from mesons that obey a nonlinear wave equation. Classical field theory is used, and in some cases the practical difficulties of obtaining numerical answers are reduced by employing a variation method. Apart from a cutoff, which appears in this particular form of the theory but could be eliminated, there are two parameters in the theory; they can be chosen so that nuclear matter has a stable density equal to the observed value, and a variational binding energy equal to 42 percent of the observed value, thus approximately accounting for saturation. The two-nucleon interaction has the observed order of magnitude in empty space, and is greatly reduced within nuclei. This suppression of two-body interactions in favor of the interaction of each nucleon with the average nucleon density in heavy nuclei may account for the independent-particle model and hence for shell structure. Although the theory does not account for magnetic moments, it indicates that a more realistic version (for example, a nonlinear pseudoscalar theory) may predict a reduction of the anomalous magnetic moments of nucleons within nuclei. According to a recent suggestion of Bloch, this could account for the deviations of the magnetic moments of even-odd nuclei from the Schmidt lines. The nonlinearity also has the consequence that mesons are scattered from nuclei as though by a strong repulsive potential. The relation of this effect to current observations on interactions between mesons and nuclei is briefly discussed.