Coulomb corrections for the non-flip and spin-flip electromagnetic $\boldsymbol{p}^\uparrow\!\boldsymbol{A}$ amplitudes

TL;DR

This paper demonstrates that Coulomb corrections to elastic proton-nucleus amplitudes are identical for non-flip and spin-flip cases under certain conditions, enabling precise numerical calculations for phenomenological use.

Contribution

It introduces a method to compute Coulomb corrections for both electromagnetic and hadronic amplitudes using analytical expressions and numerical integrations, applicable in the massless-photon limit.

Findings

Coulomb corrections are identical for non-flip and spin-flip amplitudes with the same form factors.

The method allows high-precision numerical calculations of Coulomb corrections.

The approach is practical and systematically controlled for phenomenological applications.

Abstract

It is demonstrated that, within the eikonal approach, the Coulomb corrections to the elastic electromagnetic non-flip 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 $p^{\uparrow}A$ 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.