Meson theory of nucleon-nucleon scattering up to 2 GeV

Abstract

We show that it is possible to construct a meson-exchange Hamiltonian for $\mathrm{N},\ensuremath{\pi},\ensuremath{\Delta}$, and ${\mathrm{N}}^{*}$ (1470 MeV) to describe NN scattering up to 2 GeV. The model consists of: (a) vertex interactions $\ensuremath{\pi}\mathrm{N}\ensuremath{\leftrightarrow}\ensuremath{\Delta} or {\mathrm{N}}^{*}$, and $\ensuremath{\pi}\ensuremath{\Delta}\ensuremath{\leftrightarrow}\ensuremath{\Delta} or {\mathrm{N}}^{*}$ with which an isobar model is constructed to describe the ${P}_{33}$ and ${P}_{11}\ensuremath{\pi}\mathrm{N}$ scattering phase shifts up to 1 GeV; (b) the transition interactions from $\mathrm{NN}\mathrm{to}\mathrm{N}\ensuremath{\Delta},\ensuremath{\Delta}\ensuremath{\Delta},\mathrm{N}{\mathrm{N}}^{*}, \mathrm{and} {\mathrm{N}}^{*}{\mathrm{N}}^{*}$ are determined from one-pion and one-rho exchange mechanisms; (c) the $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}$ interaction is directly derived from the Paris potential by using a momentum-dependent procedure to subtract the contributions from intermediate states involving $\ensuremath{\Delta}$ or ${\mathrm{N}}^{*}$. The $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}$ scattering equation is cast into the familiar coupled-channel form, but with a highly nonlocal isobar self-energy $\ensuremath{\Sigma}(E,p)$ calculated from the vertex interactions $\ensuremath{\pi}\mathrm{N}\ensuremath{\leftrightarrow}\ensuremath{\Delta} or {\mathrm{N}}^{*}$ in a dynamical three-body approach. Both the isospin $T=1$ and $T=0$ NN scattering phase shifts of Arndt et al. up to 1 GeV can be described to a very large extent by the model. The fits are, on the average, better than most of the previous NN calculations. The model also describes reasonably well both the magnitudes and signs of the NN total cross sections ${\ensuremath{\sigma}}^{\mathrm{tot}}$, $\ensuremath{\Delta}{\ensuremath{\sigma}}_{T}^{\mathrm{tot}}$, and $\ensuremath{\Delta}{\ensuremath{\sigma}}_{L}^{\mathrm{tot}}$ up to 2 GeV, except the strong energy dependences in the region near 800 MeV. We discuss the origin of this problem in connection with future necessary improvements of the model and the questions about the dibaryon resonances. The model can be used for a unified approach to study the isobar-nucleus dynamics at both low and intermediate energies.[NUCLEAR REACTIONS Isobar model for $\ensuremath{\Delta}$ and ${\mathrm{N}}^{*}$ excitation, mesonexchange theory of NN scattering from 0 to 2 GeV.]