Nucleon--nucleon scattering near 50 MeV. I. Phase shift analysis of the data

We carry out a phase-shift analysis of p-p and n-p elastic scattering data in the laboratory kinetic energy range of 47.5 to 60.9 MeV. Despite the inclusion of new n-p total and differential cross-section data since the phase-shift analyses of MacGregor, Arndt, and Wright (papers VI and X in particular), the χ² vs ε₁ curve retains its double minimum, and the anomalous value for the phase parameter δ(¹P₁) persists. The data yield a range of solutions rather than a unique I=0 phase-shift solution, and, in fact, the χ² vs ε₁ curve is even flatter than it was in paper VI. The allowed range of ε₁ is found to be from -10° to +3°, approximately. To find a unique solution, we constrain ε₁ to have a reasonable theoretical value of +2.78°, and present the corresponding constrained phase-shift solution. This yields δ(¹P₁)=-3.52°±1.04°, which is 4.5 standard deviations or more above predictions by meson-theoretical models. In fact, throughout the allowed range of ε₁, the searched value of δ(¹P₁) remains at least this far above theoretical predictions. We determine that the Harwell n-p dσ/dΩ data at extreme forward and extreme backward angles are responsible for the high value of δ(¹P₁), 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-p dσ/dΩ, because incorrect forward values will result in a wrong value for δ(¹P₁). With regard to forward data, good extreme forward absolute dσ/dΩ data will be more effective than relative forward data spanning the 0°-90° range. Finally, with respect to ε₁, we emphasize that the existing types of n-p data (dσ/dΩ, ${\sigma }_{tot}$, 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.