Numerical Calculation of Coulomb Corrections in Forward Elastic $p^\uparrow\!\!\;{p}$ and ${p}^\uparrow\!{A}$ Scattering

TL;DR

This paper develops a precise, flexible method for calculating Coulomb corrections in proton-nucleus scattering, essential for analyzing polarization measurements at RHIC, by relating spin-flip and non-flip amplitudes without complex small photon mass calculations.

Contribution

It introduces an analytical approach to compute Coulomb corrections for both spin-flip and non-flip amplitudes across various nuclear charges and form factors, improving accuracy and computational stability.

Findings

Coulomb corrections can be related for spin-flip and non-flip amplitudes without small photon mass calculations.

The method accurately accounts for absorptive corrections in spin-flip amplitudes.

The approach enhances the analysis of polarization data in proton-nucleus scattering.

Abstract

The analysis of RHIC hydrogen gas jet target polarimeter measurements of transverse analyzing powers $A_\text{N}(t)$ in proton-nucleus scattering requires accurate Coulomb corrections to both spin-flip and non-flip amplitudes. These corrections must cover a wide range of nuclear charges $Z$ and form factor slopes, with 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 was related to the corresponding correction for the spin-flip amplitude. This approach allows soft photon contributions to all amplitudes, including those with non-exponential form factors, to be calculated in the massless photon limit using only analytical expressions and numerically stable integrals with nonsingular integrands and finite integration limits. In addition, an absorptive correction to the spin-flip electromagnetic amplitude, which plays a critical role in spin effects in forward polarized proton-nucleus scattering, was accurately evaluated.