  We derive a closed, model independent, expression for the electromagnetic
correction factor to a phenomenological hadronic scattering length extracted
from a hydrogenic atom. It is obtained in a non-relativistic approach and in
the limit of a short ranged hadronic interaction to terms of order
((alpha)**2)(log(alpha)) using an extended charge distribution. A hadronic
negatively charged pion-proton scattering length of 0.0870(5), in units of
inverse charged pion-mass, is deduced, leading to a pion-nucleon coupling
constant from the GMO relation equals to 14.04(17).
