Nucleon-nucleon scattering analyses. I. Proton-proton scattering, from 1 to 500 MeV

Energy-independent and energy-dependent analyses are given for the proton-proton scattering data from 1 to 500 MeV. These analyses are similar to those of the Livermore series, but a number of modifications have been made, particularly in the low-energy representation. First, the range of the analyses has been extended by 50 MeV (i.e., from 450 to 500 MeV) and provisions have been made to include total cross sections in the analyses. This and new data additions have resulted in a 20% expansion of the data base. The other modifications concern the low-energy data and the representation bases. To help alleviate normalization difficulties with the low-energy data, the normalization errors of all experiments in the 0- to 10-MeV energy range were floated. The $S$-wave scattering-length and effective-range parameters were adjusted to give the best fit to the data, and the energy-dependent representation was modified to account for low-energy Coulomb effects. A 28-parameter energy-dependent solution is obtained which is quite good, with ${\chi }^2=1052\mathrm{}$ for 1233 data. This is a definite improvement over the Livermore result, but the phase shifts in the 50- to 400-MeV range are virtually unchanged (with the exception of the ${}_{}{}^3{}_{}{}^{}F_4^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ phases) despite the modifications to the bases functions, a strong indication that the data place strong restrictions on the phases.