Low-Energy Pion Phenomena

Abstract

The relation between low-energy pion-nucleon scattering and pion photoproduction is examined. Correct extrapolation to threshold of both the ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ photoproduction data gives agreement with theory. A recent new method for analyzing the scattering data is applied giving ${a}_{1}=0.178$, ${a}_{3}=\ensuremath{-}0.087$, and reasonable agreement with the Panofsky ratio $P=1.5$ is obtained. An inner Coulomb correction to the scattering data helps to improve this agreement. The possibility of detecting a $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interaction by low-energy pion scattering is examined. A new dispersion relation connects the $s$- and $p$-wave phase shifts at low energies; this relation excludes some well-known sets of phase-shift curves.