Pion-nucleon charge exchange and scattering at low energies

An analysis of low energy pion-nucleon charge exchange and elastic scattering data is presented. A system of coupled channels with nonlocal potentials is used to include the effects of the Coulomb interaction, pion and nucleon mass differences, and the photoabsorption channel. By using recent accurate charge exchange data, redundancies exist, allowing cross checks between data sets. The cross section for ${\pi }^{+}$n→${\pi }^0$p is deduced and a value of $a_1$-$a_3$=0.290±0.008 ${\mu }^{\mathrm{-}1}$ is extracted.