Coulomb corrections for the nonflip and spin-flip electromagnetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>p</mml:mi> <mml:mo stretchy="false">↑</mml:mo> </mml:msup> <mml:mi>A</mml:mi> </mml:math>

It is demonstrated that, within the eikonal approach, the Coulomb corrections to the elastic electromagnetic nonflip and spin-flip proton-nucleus amplitudes are identical when the two amplitudes share the same exponential form factors. This result allows Coulomb corrections to be computed numerically, and with high precision, for both electromagnetic and hadronic elastic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>p</a:mi> <a:mo stretchy="false">↑</a:mo> </a:msup> <a:mi>A</a:mi> </a:math> amplitudes in the massless-photon limit, including the effects of soft magnetic photon exchange. The method relies on analytical expressions and numerical integrations over a finite impact-parameter range with nonsingular integrands, providing a practical and systematically controlled framework for phenomenological applications.