Comparison betweenNNpotential derived from dispersion relations and a model field theory

Abstract

We compare the solution of a model field theory which relates off-shell amplitudes for elastic $\mathrm{NN}$ and $\ensuremath{\pi}N$ scattering to a similar relation between on-shell amplitudes derived from a dispersive approach. The first is a dynamical realization of $s$-channel unitarity, whereas the second starts with and exploits $t(u)$ channel unitarity. Provided that ${T}_{\mathrm{NN}}$ satisfies a Mandelstam representation, equivalent approximations ought to produce equivalent results and we perform the comparison for the actually calculated ${T}_{\mathrm{NN}}$ and the subsequently extracted potentials ${V}_{\mathrm{NN}}$. Interpreting ${V}_{\mathrm{NN}}$ we caution against the simultaneous retention of contributions with pions (crossed and uncrossed) linking intermediate nucleons as well as nucleons and physical isobars.NUCLEAR REACTIONS $\mathrm{NN}$ scattering, comparison between elastic amplitude and potential derived from model field theory and dispersive approach.