Phase-Parameter Representation of Proton-Proton Scattering from 9.7 to 345 Mev

Abstract

Results of gradient searches for phase parameters by means of an IBM-704 machine representing proton-proton scattering are reported on and the procedure used is described. The analysis made use of most available measurements. The number of "measurements" used by the machine was 541. In some cases each "measurement" was a composite of two or more measurements found in the literature. The fits join smoothly to the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ phase-shift energy curve below 9.7 Mev. A family of fits has been obtained employing as a starting point the extended source+spin-orbit potential representation below 150 Mev extrapolated to one or another of the several Stapp, Ypsilantis, Metropolis fits at 312 Mev. Other searches started out with phase parameters corresponding to the Gammel-Thaler phenomenological potential. Evidence is presented to the effect that the better fits of both families are essentially the same. Error limits of phase parameters derived are estimated by various procedures. Some of the accumulated evidence for the applicability of the one-pion exchange potential (OPEP) to the calculation of phase parameters for the higher $L$ and $J$ is described and the basis for previously published inferences regarding the spatial extension within which the major part of the potential is the OPEP is illustrated. In the case of the best fit, referred to as YLAM below, tests indicating the existence of potentials for separate $J$ have been made showing therefore that there is no serious question regarding the energy rates of change of logarithmic derivatives of radial wave functions being negative. A brief discussion of the relationship of this requirement to the meson theory of nuclear forces is included.