Coulomb Effects in Pion Scattering by Protons under the Charge Independence Hypothesis

Abstract

The differential cross sections for scattering of charged $\ensuremath{\pi}$-mesons by protons, observed so far at energies and angles for which Coulomb effects are negligible, were found compatible with the assumption of charge independence for the nuclear interaction between pion and nucleon. For the future discussion of scattering experiments now being performed at lower energies, the Coulomb effects are calculated, retaining the charge independence hypothesis for the nuclear part of the interaction and describing it by the phase shifts used in the higher energy region. For 35-Mev pions, an estimate based on the known magnitude of the total ${\ensuremath{\pi}}^{+}\ensuremath{-}p$ cross section shows the Coulomb effects to reach 50 percent for a scattering angle of the order of 50\ifmmode^\circ\else\textdegree\fi{} in the center-of-mass system.