Isobar contributions to the two-nucleon interaction derived from noncovariant perturbation theory

Abstract

The fourth-order iterative diagrams involving $N\Delta$ and $\Delta \Delta$ intermediate states and including $\pi$ as well as $\rho$ exchange are calculated in momentum space without any approximation. It turns out that, due to retardation effects in the propagators, these contributions are by a factor of 3 smaller than former models using twice-iterated transition potentials with simple propagators of pion (and $\rho$) range. This fact allows the use of much shorter-range cutoffs at the $N\Delta$ vertices than before. $\mathrm{NN}$ scattering phase shifts are calculated using these diagrams together with a suitably modified one-boson exchange potential, likewise derived from noncovariant perturbation theory. The effect of the $N\Delta \rho$ vertex is different in various partial waves; its decisive role in getting a consistent description, especially of the important ${}_{}{}^3{}_{}{}^{}P$ phases, is demonstrated. It is shown that the static limit (necessarily used by other groups working in $r$ space) is not a good approximation and, moreover, its effect cannot be mocked up by a mere change of parameters.