标题： 关于$pp$和$\bar pp$散射中的库仑效应以及$ρ$的确定的一些 remarks 显示英文标题

标题： Some remarks on Coulombic effects in $pp$ and $\bar pp$ scattering and the determination of $ρ$

摘要： 我们指出了一种非常简单的计算$pp$和$\bar pp$散射振幅的混合库仑-核校正的方法，这种方法在之前关于该问题的大量研究中被忽略了。 该方法通过一个快速收敛的积分表达校正，该积分涉及核振幅的逆 Fourier-Bessel 变换和包含库仑相移以及形式因子修正的一个已知因子。 对于通常用于小动量转移高能数据拟合的指数型模型核振幅，此变换可以解析计算，并且对校正给出了非常准确的结果。 我们研究了核振幅实部中 Martin 零点可能产生的影响，以及库仑-核校正的 Bethe-West-Yennie 相位近似精度。 然后，我们将该方法应用于重新确定先前使用校正的近似版本分析高能 ISR 数据时所得到的前向散射振幅实部与虚部比值$\rho$的准确性。 相对于那些拟合的精确性，只有在 52.8 GeV 处有显著变化。 我们的方法具有更广泛的应用性，也可以用于较低能量以及质子-原子核散射。 显示英文摘要

摘要： We point out a very simple method for calculating the mixed Coulomb-nuclear corrections to the $pp$ and $\bar pp$ scattering amplitudes that has been missed in the extensive past work on this problem. The method expresses the correction in terms of a rapidly convergent integral involving the inverse Fourier-Bessel transform of the nuclear amplitude and a known factor containing the Coulomb phase shift with form-factor corrections. The transform can be calculated analytically for the exponential-type model nuclear amplitudes commonly used in fits to the high-energy data at small momentum transfers, and gives very accurate results for the corrections. We examine the possible effects of the Martin zero in the real part of the nuclear amplitude, and the accuracy of the Bethe-West-Yennie phase approximation for the Coulomb-nuclear corrections. We then apply the method to a redetermination of the ratio $\rho$ of the real to the imaginary parts of the forward scattering amplitude in fits to high-energy ISR data previously analyzed using an approximate version of the correction. The only significant changes relative the accuracy of those fits are at 52.8 GeV. Our method is applicable more generally, and can be used also at lower energies and for proton-nucleus scattering.