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Description
The analysis of transverse analyzing powers $A_\text{N}^{pA}(t)$ in proton-nucleus scattering, as measured by the RHIC hydrogen gas jet target polarimeter (HJET), requires precise Coulomb corrections to both spin-flip and non-flip amplitudes. These corrections must account for a broad range of nuclear charges $Z$ and form factor slopes, while allowing flexibility to vary form factors during data fitting.
To avoid technically challenging calculations involving a small but finite fictitious photon mass, the Coulomb correction to the non-flip electromagnetic amplitude with an exponential form factor is related to the corresponding correction for the spin-flip amplitude. This approach enables evaluation of soft photon contributions for all amplitudes---including those with non-exponential form factors---in the massless photon limit, using only analytical expressions and numerically stable integrals with nonsingular integrands and finite integration limits.
Additionally, an absorptive correction to the spin-flip electromagnetic amplitude, which plays a crucial role in spin effects in forward polarized proton-nucleus scattering, is accurately calculated. These results provide a robust foundation for interpreting high-precision measurements of $A_\text{N}^{pA}(t)$ at HJET and for testing models of hadronic spin dependence.