Near-Peripheralp−pScattering from Simple One-Boson-Exchange Contributions

We fit the non-$S$-wave $p-p$ amplitude over the 0- to 345-MeV range with three pole terms utilized in a simple fashion; the pole terms are equated with the real part of the scattering amplitude. The imaginary part is then specified by elastic unitarity. The pole terms which give the fit are due to vector-meson exchange ($g_V^{}{}_{}{}^2=2.3\mathrm{}$, $\frac{f_V}{g_V}=2.3\mathrm{}$, $m_V=770\mathrm{}$ MeV), scalar-meson exchange ($g_{\sigma }^{}{}_{}{}^2=1.6\mathrm{}$, $m_{\sigma }=390\mathrm{}$ MeV), and pion exchange ($g_{\pi }^{}{}_{}{}^2=12.3\mathrm{}$, $m_{\pi }=135\mathrm{}$ MeV). The coupling constants and masses were found with an automatic search routine on an IBM 7094 or CDC 3600 computer. For experiment we took the single-energy phase-shift analyses of Arndt and MacGregor at 25, 50, 95, 142, 210, and 310 MeV. The pole parameters are consistent with other independent experiments to within the accuracy of the model. The scalar meson is postulated, but may be responsible for the $T=0\mathrm{}$, $S$-wave $\pi -\pi$ correlation observed in the reaction ${\pi }^{-}+p\to {\pi }^{+}+{\pi }^{-}+n$ at low energies.