Coulomb Corrections to One- and Two-Channel Strong Scattering Processes

We generalize our previous considerations of Coulomb corrections to single-channel processes to the two-channel case. Using a potential model, we derive an extremely simple formula for the corrections which does not necessitate using Coulomb wave functions. This formula is correct to lowest order in $\alpha$ but to all orders of the strong scattering. We discuss the application of our results to recent data on pion-nucleon elastic and charge-exchange scattering in the vicinity of the $N^{*}\mathrm{}\left(1236\right)\mathrm{}$ resonance. The choice of an appropriate wave equation and the question of mass-difference corrections are also discussed in an appendix.