Numerical Evaluation of the Pion-Nucleon Forward Scattering Amplitude

The real part of the forward elastic scattering amplitude for ${\pi }^{\pm }$-proton scattering has been evaluated from experimental cross sections by means of dispersion relations. Recent measurements indicate two peaks in the ${\pi }^{-}$-proton total cross section at 590 and 870 Mev incident pion kinetic energy. Tables of the real part of the forward scattering amplitude for ${\pi }^{\pm }$-proton scattering are presented as a function of incident pion kinetic energy in the laboratory. The forward scattering amplitudes obtained from some recent ${\pi }^{\pm }$ scattering experiments are compared with the calculations. Measurement of the forward charge-exchange cross section appears to be the most suitable way of investigating the predictions of the dispersion relation at high energies. The possibility of detecting Coulomb interference at small angles is also discussed.