Nucleon-Nucleon Scattering Near 50 MeV. I. Phase-Shift Analysis of the Data

Abstract

We carry out a phase-shift analysis of $p\ensuremath{-}p$ and $n\ensuremath{-}p$ elastic scattering data in the laboratory kinetic energy range of 47.5 to 60.9 MeV. Despite the inclusion of new $n\ensuremath{-}p$ total and differential cross-section data since the phase-shift analyses of MacGregor, Arndt, and Wright (papers VI and X in particular), the ${\ensuremath{\chi}}^{2}$ vs ${\ensuremath{\epsilon}}_{1}$ curve retains its double minimum, and the anomalous value for the phase parameter $\ensuremath{\delta}(^{1}P_{1})$ persists. The data yield a range of solutions rather than a unique $I=0$ phase-shift solution, and, in fact, the ${\ensuremath{\chi}}^{2}$ vs ${\ensuremath{\epsilon}}_{1}$ curve is even flatter than it was in paper VI. The allowed range of ${\ensuremath{\epsilon}}_{1}$ is found to be from -10\ifmmode^\circ\else\textdegree\fi{} to +3\ifmmode^\circ\else\textdegree\fi{}, approximately. To find a unique solution, we constrain ${\ensuremath{\epsilon}}_{1}$ to have a reasonable theoretical value of +2.78\ifmmode^\circ\else\textdegree\fi{}, and present the corresponding constrained phase-shift solution. This yields $\ensuremath{\delta}(^{1}P_{1})=\ensuremath{-}3.52\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}1.04\ifmmode^\circ\else\textdegree\fi{}$, which is 4.5 standard deviations or more above predictions by meson-theoretical models. In fact, throughout the allowed range of ${\ensuremath{\epsilon}}_{1}$, the searched value of $\ensuremath{\delta}(^{1}P_{1})$ remains at least this far above theoretical predictions. We determine that the Harwell $n\ensuremath{-}p$ $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ data at extreme forward and extreme backward angles are responsible for the high value of $\ensuremath{\delta}(^{1}P_{1})$, and recommend that these measurements be retaken. We emphasize that contrary to popular belief, it is not sufficient just to fix the relative backward $n\ensuremath{-}p$ $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$, because incorrect forward values will result in a wrong value for $\ensuremath{\delta}(^{1}P_{1})$. With regard to forward data, good extreme forward absolute $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ data will be more effective than relative forward data spanning the 0\ifmmode^\circ\else\textdegree\fi{}-90\ifmmode^\circ\else\textdegree\fi{} range. Finally, with respect to ${\ensuremath{\epsilon}}_{1}$, we emphasize that the existing types of $n\ensuremath{-}p$ data ($\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$, ${\ensuremath{\sigma}}_{\mathrm{tot}}$, and $P$) will not remove the ambiguity in this phase parameter. Some other type of experiment must be done, as we intend to discuss in a succeeding paper.