A One Dimensional Model for a Non-Linear Meson Field

Abstract

<p> A repulsive meson-meson interaction was suggested many years ago (1951 by Schiff) as a possible mechanism for nuclear saturation, but very little has been done since then. This is mainly because the meson field equation becomes nonlinear due to the meson-meson interaction. We realized that the nonlinear field equation is analytically solvable, within classical and adiabatic approximations, if the space is reduced to a one-dimensional one. Within the above context we investigate the effect of the meson-meson interaction on nuclear forces. The approximations which Schiff used are critically examined. A variational method for determining the meson field, which Schiff suggested but did not fully investigate, is found to be a very efficient approximation. Finally, quantum corrections are briefly examined.</p>