Effect of the Failure of Isotopic Spin Conservation on the Pion-NucleonSWaves

The charge-dependent effects of the ${\pi }^{-}-{\pi }^0$ mass difference, the Coulomb interaction, and the ${\pi }^{-}+p\to \gamma +n$ radiative transition are calculated phenomenologically using a charge-independent potential model for the pion-nucleon nuclear $S$-state interaction. It is found that the charge-exchange $S$-wave-scattering is little affected but that the transition rate for a bound ${\pi }^{-}$ meson (Panofsky effect) is suppressed about 10%, removing the discrepancy between the difference in scattering lengths as calculated from scattering and from the Panofsky effect. However, it is also found that there can be 25% corrections to the ${\pi }^{-}$ elastic scattering amplitude of either sign, making the precise analysis of low-energy ${\pi }^{-}$ elastic scattering experiments difficult.