标题： 库仑校正的数值计算：前向弹性散射中的 $\boldsymbol{p}^\uparrow\!\!\;\boldsymbol{p}$ 和 $\boldsymbol{p}^\uparrow\!\boldsymbol{A}$ 散射 显示英文标题

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

摘要： RHIC氢气喷射靶极化仪对质子-核散射中横向分析功率$A_\text{N}(t)$的测量数据分析需要对自旋翻转和非自旋翻转振幅进行精确的库仑修正。这些修正必须涵盖广泛的原子序数$Z$和形式因子斜率，并且在数据拟合过程中具有调整形式因子的灵活性。为了避免涉及小但有限的虚构光子质量的技术上具有挑战性的计算，与指数形式因子相关的非自旋翻转电磁振幅的库仑修正被关联到相应的自旋翻转振幅的修正。这种方法允许使用仅含解析表达式和数值稳定的积分（具有非奇异的被积函数和有限的积分限）来计算所有振幅（包括那些具有非指数形式因子的振幅）的软光子贡献，这些计算均在无质量光子极限下完成。此外，对自旋翻转电磁振幅的吸收性修正进行了准确评估，该修正在向前极化质子-核散射中的自旋效应中起着关键作用。 显示英文摘要

摘要： 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.