Nonlinear Pseudoscalar Meson Theory

Abstract

An attempt is made to explain nuclear saturation by means of a nonlinear pseudoscalar meson field. The same nonlinearity as that introduced by Schiff for the scalar case is employed; the treatment follows similar lines, using classical field theory. The total source strength is calculated for an isolated nucleon at rest, and an expression for the two-nucleon interaction in free space is obtained. It is shown that both of these are infinite, so that a cutoff must be introduced. For the two-nucleon problem the variation method is used with a simple trial function, which is the superposition of the single-nucleon meson field amplitudes; this should be a good approximation for large separation of the nucleons. Then the nonlinear terms of the two-particle interaction are shown to be separable from the linear ones, and are repulsive. The nonlinear terms can also be separated in the many-body problem, but they are not necessarily positive definite here, and hence need not lead to saturation. A nuclear model, based on a lattice structure with stationary nucleons is discussed qualitatively.