Determination of the Nucleon-Nucleon Elastic Scattering Matrix. I. Phase-Shift Analysis of Experiments Near 140 MeV

A phase-shift analysis has been carried out for ($p, p$) and ($n, p$) experiments near 140 MeV. The two kinds of data were analyzed separately and combined (with charge independence assumed). Investigations were made on the accuracy of the data, the search procedure, the significance of error-matrix calculations, the significance of the absolute value of $x^2$ (the least-squares sum), and the importance of using an energy dependence for the phase shifts and for the data. A single solution was obtained that gives a good fit to both the ($p, p$) and the ($n, p$) data. The gross features of charge independence were found to be accurately verified. Determinations of the pion-nucleon coupling constant $g^2$ and the pion mass gave results consistent with previous nucleon-nucleon analyses. The ($n, p$) data, although they include five kinds of experiments, are not complete enough by themselves to permit an accurate phase-shift analysis. The ($p, p$) data are complete. The combined ($p, p$) plus ($n, p$) data give $T=1\mathrm{}$ phase shifts that agree with the phase shifts from the ($p, p$) analysis alone, and they give accurate values for the $T=0\mathrm{}$ phase shifts.