Two-Nucleon Potentials from Dispersion Relations

Abstract

Dispersion relations are applied to obtain the two-pion-exchange nuclear potentials including the first order non-static effects. Calculation is made within the approximation in which only the contribution from the single nucleon intermediate state is considered for pion-nucleon scattering, though the S-wave suppression is correctly taken into account. All the potentials obtained are expressed in a spectral representation. It is shown that this form is suitable to distinguish the effects of low energy pion exchange from those of high energy pion exchange. Only the former can be reliably estimated, while the latter are subjected to a cutoff and substituted by adjustable parameters. The potentials thus obtained are compared with phenomenological ones in terms of the spectral distributions of exchanged pions. Comparison of the present method with the others for potential construction is also made in relation to the problem of the coupling type between pions and nucleons.