Theory of Low-Energy Nucleon-Nucleon Scattering. IV. Numerical Results for High Partial Waves (l>~2)

Abstract

The numerical results of a dispersive theory for nucleon-nucleon scattering developed in previous papers are presented for $d$ and higher waves. Phase parameters as function of the energy are given up to 400 MeV. The ingredients of the theory—which evaluates the $2\pi$ exchanges—are amplitudes and parameters that are obtained from the theoretical analyses of simpler processes ($\pi -N$ scattering, nuclear electromagnetic form factors, etc.). Of these ingredients, those which describe the low-wave ($s$ and $p$) $N\overline{N}\to \pi \pi$ amplitudes are, at present, the least reliable. We have, therefore, presented the results in two parts: One—called "basic"—contains all contributions except for the $s$ and $p$ $N\overline{N}\to \pi \pi$ amplitudes so that they can be simply added when a better theoretical knowledge of them is available. The other part introduces the $N\overline{N}\to \pi \pi$ $s$ and $p$ waves through some phenomenological models based on the Bowcock, Cottingham, and Lurié analysis of $\pi -N$ scattering. The effect of the $\omega$ is also tentatively introduced. These last results are compared with the phase parameters obtained from experimental data: The agreement is encouraging for one of the models used up to about 250 MeV both for $T=0\mathrm{}$ and $T=1\mathrm{}$ phase parameters.