Nonlinear approach toNNinteractions using self-interacting meson fields

Abstract

Motivated by the success of models based on chiral symmetry in $\mathrm{NN}$ interactions, we investigate self-interacting scalar, pseudoscalar, and vector meson fields and their impact for $\mathrm{NN}$ forces. We parametrize the corresponding nonlinear field equations and get analytic wavelike solutions. A probability amplitude for the propagation of particle states is calculated and applied in the framework of a boson-exchange $\mathrm{NN}$ potential. Using a proper normalization of the meson fields makes all self-scattering amplitudes finite. The same normalization is able to substitute for the phenomenological form factors used in conventional boson-exchange potentials and thus yields a phenomenological understanding of this part of the $\mathrm{NN}$ interaction. We find an empirical scaling law which relates the meson self-interaction couplings to the pion mass and self-interaction coupling constant. Our model yields $\mathrm{np}$ phase shifts comparable to the Bonn B potential results and deuteron properties, in excellent agreement with experimental data.