Meson Tail Effect and Treatment of Proton-Proton Scattering Data

Abstract

The fit of experimental material on proton-proton scattering by phenomenological potentials is reviewed with the inclusion of observations by Heydenburg-Little in the 300-kev region and of Cork at 30 Mev. Weighting of data by a criterion based on internal consistency is employed. Data obtained by means of Van de Graaff machines are used to determine the best fits for different shapes of potential energy curves. Other data are compared with the resultant ($f$, $E$) plots graphically. A trend towards agreement with the long-tailed Yukawa and exponential well potentials is noticeable among the supposedly more accurate measurements of Rouvina and of Cork. The meson potential $\ensuremath{-}\frac{C{e}^{\ensuremath{-}\frac{r}{a}}}{(\frac{r}{a})}$ with $C=(93.4\ifmmode\pm\else\textpm\fi{}1.0)m{c}^{2}$, $a=(0.412\ifmmode\pm\else\textpm\fi{}0.002)\frac{{e}^{2}}{m{c}^{2}}$ fits experiment and corresponds to a meson mass of $333\ifmmode\pm\else\textpm\fi{}2m$, the limits of error being stated above somewhat arbitrarily.The effect of the tail of the Yukawa potential on scattering is studied with particular attention to its influence on the nearly linear functions of energy used in the analysis of experiment, and on the coefficients of powers of the energy in the expansion of this function ($f$).The convergence of the power series is better if the tail of the potential is chopped off. Calculation of coefficients in this series is also easier for the potential without tail. The more practical arrangements of calculations are: (a) direct calculation of $f$ for a number of energies, the tail effect being treated by a first-order approximation; and (b) calculation of coefficients of powers of $E$ in the series for $f$ for potential without tail followed by first-order calculation of effect of tail on $f$. Results obtained in these ways are compared.