On the Mechanism of Nucleon-Nucleon Attraction by Pion Exchange

Abstract

A formula is derived for the central nucleon-nucleon potential, based on an analysis of the physical origin of the nucleon-nucleon attraction by pion exchange. The decrease of the dynamical mass of the interaction field, exchanged pion in this case, is the principal mechanism responsible for the nuclear attraction in a similar way that the decrease of the kinetic energy of the exchange electron in the diatomic molecule is directly responsible for the covalent molecular attraction. The minimum value of this central nucleon-nucleon potential and the position of the minimum are similar with the values reported in literature for a potential calculated by lattice QCD, which shares the features of the phenomenological nucleon-nucleon potentials. The Schrodinger equation with this central nucleon-nucleon potential was solved numerically for different values of the pion mass. The binding energy increases with the decrease of the pion mass. For masses higher than the real pion mass the nucleon-nucleon system is unbound. We discuss on the two pion exchange and hard core repulsion. The minimum value of the potential for two pion exchange is comparable with the minimum value of the CD Bonn potential. For a hard core radius of 0.5 fm the binding energy is equal to the deuteron binding energy.