Determination of the Nucleon-Nucleon Scattering Matrix. VIII. (p,p) Analysis from 350 to 750 MeV

Abstract

All of the available ($p,p$) data from 350 to 750 MeV have been analyzed together with matrix representations for the data at lower energies. Several energy-dependent forms for the phase shifts were investigated, including forms using contributions from $\sigma$, $\rho$, and $\omega$ resonances. The most useful form, form $A$ with 31 free parameters, gave a least-squares value ${\chi }^2=1575\mathrm{}$ for a fit to data and matrices representing 1147 individual data from 23 to 736 MeV. Several different methods of including the inelastic scattering effects were studied. Although the inelastic scattering has an important effect on the elastic phases, an analysis of the elastic scattering data gives little information about the inelastic phases. A single-energy analysis at 425 MeV, where inelastic effects are very small, gave a well-defined result. However, a similar analysis at 630 MeV, where the total inelastic cross section is almost as large as the total elastic cross section, gave only qualitatively correct values for $S$, $P$, and $D$ phases, and gave little information about the $F$ and higher phases. The ($p,p$) elastic scattering matrix can now be defined accurately at energies from 0 to 450 MeV, but at energies above 450 MeV more experimental and theoretical information is still needed before a reliable analysis can be carried out.