Low-Energy Pion Phenomena

The relation between low-energy pion-nucleon scattering and pion photoproduction is examined. Correct extrapolation to threshold of both the ${\pi }^{+}$ and ${\pi }^{-}$ photoproduction data gives agreement with theory. A recent new method for analyzing the scattering data is applied giving $a_1=0.178\mathrm{}$, $a_3=-0.087\mathrm{}$, and reasonable agreement with the Panofsky ratio $P=1.5\mathrm{}$ is obtained. An inner Coulomb correction to the scattering data helps to improve this agreement. The possibility of detecting a $\pi -\pi$ 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.