Improved Coupled Channels and R-Matrix Models: Predictions to 1 Gev
The $NN$ scattering near inelastic threshold is sensitive to the long-range diagonal interaction in the produced isobar channel. Earlier models included meson exchange potentials in the $NN$ sector and connecting that sector to isobar channels, as well as an $R$-matrix description of short-range quark effects. Including the diagonal pion exchange contributions in the $N\Delta$ channels coupled to the very inelastic ${}^1D_2$ and ${}^3F_3$ $NN$ channels substantially improves those phase parameters and the observables $\Delta\sigma_{L}$ and $\Delta\sigma_{T}$. The same improvement is made to the other $I=1$ $NN$ channels. In the ${}^1S_0$ $NN$ channel coupling to the $\Delta\Delta$ channel is unusually important due to the $L=2$ angular momentum barrier in the $N\Delta$ channel. The pion exchange transition potentials between isobar channels are included in this partial wave to obtain the correct equilibrium between one- and two-pion decay channels. Other improvements to earlier models have been made, in the specification of isobar channels and the inclusion of decay width effects in more channels. A comparison is made with all the $pp$ data for $T_L \le 800$~MeV, producing a very good fit over the whole energy range.