The contribution of the one-pion exchange potential in the frame of a Hartree-method by using one-particle wave functions without definite parity

Abstract

In order to calculate the spin-orbit splitting and the magnetic moments of nuclei a Hartree-method was carried out with the assumption of parity-mixed one-particle wave functions. Together with a phenomenological determined scalar potential there was used a pseudoscalar potential derived as the contribution of the one-pion exchange potential selfconsistently determined. By using this method of parity-mixing, one obtains a spin-orbit splitting and also magnetic moments, which lie automatically between the Schmidt-lines in good agreement with the experimental values. Only the pion-nucleon coupling constant was used as a parameter in this selfconsistent method. It is shown that we obtain a smaller coupling constant when using the exact solution of this problem than by using perturbation theory. This effective coupling constant is of the same order of magnitude as the one obtained from the scattering data.