Are we really measuring the phase of the nuclear scattering amplitude?

Abstract

The interference at small $|t|$ of the Coulomb scattering amplitude ${f}_{c}$ and the nuclear amplitude ${f}_{n}$ is used to measure the phase of the nuclear scattering amplitude, and, hence, the $\ensuremath{\rho}$ value, where $\ensuremath{\rho}\ensuremath{\equiv}{(\frac{\mathrm{Re}{f}_{n}}{\mathrm{Im}{f}_{n}})}_{t=0}$. The normal analysis of $\overline{p}p$ and $\mathrm{pp}$ elastic scattering uses a spinless Coulomb amplitude, i.e., a Rutherford amplitude ($\frac{2\sqrt{\ensuremath{\pi}}\ensuremath{\alpha}}{t}$) multiplied by a Coulomb form factor ${G}^{2}(t)$, an ansatz that pretends that the nucleon does not have any magnetic scattering. In this article, we investigate the role of the anomalous magnetic moment of the nucleon, $\ensuremath{\kappa}\ensuremath{\approx}1.79$. Given the method of analysis currently used by most published experiments, we conclude that the current experimentally inferred values of $\ensuremath{\rho}$ for $\overline{p}p$ should be systematically lowered by \ensuremath{\approx}0.005-0.0100 and, correspondingly, the $\ensuremath{\rho}$ values for $\mathrm{pp}$ should be systematically raised by the same amount. We discuss the theoretical uncertainties and a method of experimentally minimizing them.