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

Abstract

The fourth-order iterative diagrams involving $N\ensuremath{\Delta}$ and $\ensuremath{\Delta}\ensuremath{\Delta}$ intermediate states and including $\ensuremath{\pi}$ as well as $\ensuremath{\rho}$ 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 $\ensuremath{\rho}$) range. This fact allows the use of much shorter-range cutoffs at the $N\ensuremath{\Delta}$ 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 $N\ensuremath{\Delta}\ensuremath{\rho}$ 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.NUCLEAR REACTIONS Nucleon-nucleon interaction, $\mathrm{NN}\ensuremath{\rightarrow}N\ensuremath{\Delta}$ and $\mathrm{NN}\ensuremath{\rightarrow}\ensuremath{\Delta}\ensuremath{\Delta}$ transition potentials with $\ensuremath{\pi}$ and $\ensuremath{\rho}$ exchange, noncovariant perturbation theory.