Analysis of Proton-Proton Scattering by Means of thefFunction

The approximately linear relationship between the $f$ function and the energy, $E$, is discussed by elementary methods. Formulas for the comparison of derivatives of $f$ with respect to $E$ are given for potentials of different shapes. The comparison of potentials is reduced to that of wave functions at a standard energy. A discussion of the relation between the meson mass corresponding to experiments on proton-proton scattering and the mass of the $\pi$-meson is included. The variation in the comparison owing to lack of reproduction of the curvature of the ($f,E$) plot is estimated and the uncertainties caused by relativistic corrections as well as modifications of the Yukawa potential at distances of the order of the Compton wave-length for the proton are considered.