Electromagnetic corrections for the analysis of low energy $π^- p$ scattering data

We calculate the electromagnetic corrections to the isospin invariant mixing angle and to the two eigenphases for the $s$-, $p_{1/2}$- and $p_{3/2}$-partial waves for $\pi^- p$ elastic and charge exchange scattering. These corrections have to be applied to the nuclear quantities in order to obtain the two hadronic phase shifts for each partial wave. The calculation uses relativised Schr\"{o}dinger equations containing the sum of an electromagnetic potential and an effective hadronic potential. The mass differences between $\pi^-$ and $\pi^0$ as well as between $p$ and $n$ are taken into account. We compare our results with those of previous calculations and qualitatively estimate the uncertainties in the corrections.