Determination of the Nucleon-Nucleon Elastic-Scattering Matrix. IV. Comparison of Energy-Dependent and Energy-Independent Phase-Shift Analyses

Abstract

($p, p$) and ($n, p$) scattering data in six energy bands centered at 25, 50, 95, 142, 210, and 330 MeV, have been analyzed. First an energy-dependent analysis was carried out. Then phase-shift energy derivatives were extracted from this analysis and used in carrying out accurate energy-independent analyses. The energy-dependent phase-shift forms were chosen to have a singularity structure consistent with the requirements of partial-wave dispersion equations. A very rapid search procedure was utilized. The isotopic spin-1 scattering matrix was accurately determined over the energy range under consideration. The isotopic spin-0 scattering matrix was also determined, but not to the same accuracy, because of the incompleteness of the ($n, p$) data selection. The phase-shift analyses were carried out, and the pion-nucleon coupling constant ${g}^{2}$ was determined, using first ($p, p$) and then ($p, p$) plus ($n, p$) data selections. The results were a further substantiation of the charge independence hypothesis. Matrix methods used for the search procedures are discussed, and it is shown how the data normalization constants can be eliminated from the search. A discussion is also included of the use of the inverse error matrix in obtaining quantitative fits with theoretical models.