Electromagnetic corrections to $\pi ^-$p scattering length from pionic   hydrogen
  We derive a closed, model space independent, expression for the electromagnetic correction factor $\delta $ to the scattering length $a$ extracted from a hydrogenic atom with an extended charge to order $\alpha ^2$ and $a^3$ in the limit of a short ranged hadronic interaction. 
T. E. O. Ericson (CERN, Geneva, Switzerland, and TSL, Uppsala, Sweden)   B. Loiseau (LPNHE, Universite P. & M. Curie, Paris,...