Determination of the Nucleon-Nucleon Scattering Matrix. VII. (p,p) Analysis from 0 to 400 MeV

All of the available ($p,p$) scattering data from 1 to 400 MeV have been analyzed, and a self-consistent set of 839 data has been chosen. Using this data selection, we investigated a number of different forms for the phase-shift energy dependence. The correct number of free parameters to use with each form was studied. The most suitable form, form $A$, gave the least-squares values ${\chi }^2=810\mathrm{}$ and ${\chi }^2=858\mathrm{}$ for 30- and 23-parameter solutions, respectively. A subset of 588 data in six narrow energy bands was used to obtain single-energy solutions. It is shown that this subset contains most of the physical content of the full set of 839 data. The value $g^2=14.72\mathrm{}\pm 0.83$ was obtained for the pion-nucleon coupling constant.