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The PREX-2 and CREX experiments in Hall A at Jefferson Lab are precision measurements of parity violating elastic electron scattering from complex nuclei. One requirement was that the incident electron beam polarization, typically $\approx$90\%, be known with 1\% precision. We commissioned and operated a M{\o}ller polarimeter on the beam line that exceeds this requirement, achieving a precision of 0.89\% for PREX-2, and 0.85\% for CREX. The uncertainty is purely systematic, accumulated from several different sources, but dominated by our knowledge of the target polarization. Our analysis also demonstrates the need for accurate atomic wave functions in order to correct for the Levchuk Effect. We describe the details of the polarimeter operation and analysis, as well as (for CREX) a comparison to results from a different polarimeter based on Compton scattering.

We report a precise measurement of the parity-violating asymmetry $A_{\rm PV}$ in the elastic scattering of longitudinally polarized electrons from $^{48}{\rm Ca}$. We measure $A_{\rm PV} =2668\pm 106\ {\rm (stat)}\pm 40\ {\rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_{\rm W} (q=0.8733$ fm$^{-1}) = 0.1304 \pm 0.0052 \ {\rm (stat)}\pm 0.0020\ {\rm (syst)}$ and the charge minus the weak form factor $F_{\rm ch} - F_{\rm W} = 0.0277\pm 0.0055$. The resulting neutron skin thickness $R_n-R_p=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$~fm is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter., Comment: 8 pages, 5 figures Replace 6-16-22: included ancillary files, corrected errors in references, author affiliations. Small text changes for clarity

The M{\o}ller polarimeter in Hall A at Jefferson Lab in Newport News, VA, has provided reliable measurements of electron beam polarization for the past two decades reaching the typically required $\pm$1\% level of absolute uncertainty. However, the upcoming proposed experimental program including MOLLER and SoLID have stringent requirements on beam polarimetry precision at the level of 0.4\% \cite{MOLLER2014, SoLID2019}, requiring a systematic re-examination of all the contributing uncertainties. M{\o}ller polarimetry uses the double polarized scattering asymmetry of a polarized electron beam on a target with polarized atomic electrons. The target is a ferromagnetic material magnetized to align the spins in a given direction. In Hall A, the target is a pure iron foil aligned perpendicular to the beam and magnetized out of plane parallel or antiparallel to the beam direction. The acceptance of the detector is engineered to collect scattered electrons close to 90$^{\circ}$ in the center of mass frame where the analyzing power is a maximum (-7/9). One of the leading systematic errors comes from determination of the target foil polarization. Polarization of a magnetically saturated target foil requires knowledge of both the saturation magnetization and $g^\prime$, the electron $g$-factor which includes components from both spin and orbital angular momentum from which the spin fraction of magnetization is determined. This paper utilizes the existing world data to provide a best estimate for target polarization for both nickel and iron foils including uncertainties in magnetization, high-field and temperature dependence, and fractional contribution to magnetization from orbital effects. We determine the foil electron spin polarization at 294~K to be 0.08020$\pm$0.00018 (@4~T applied field) for iron and 0.018845$\pm0.000053$ (@2~T applied field) for nickel.

We report precision determinations of the beam normal single spin asymmetries ($A_n$) in the elastic scattering of 0.95 and 2.18~GeV electrons off $^{12}$C, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb at very forward angles where the most detailed theoretical calculations have been performed. The first measurements of $A_n$ for $^{40}$Ca and $^{48}$Ca are found to be similar to that of $^{12}$C, consistent with expectations thus demonstrating the validity of theoretical calculations for nuclei with Z~$\leq20$. We also report $A_n$ for $^{208}$Pb at two new momentum transfers (Q$^2$) extending the previous measurement. Our new data confirm the surprising result previously reported, with all three data points showing significant disagreement with the results from the $Z\leq 20$ nuclei. These data confirm our basic understanding of the underlying dynamics that govern $A_n$ for nuclei containing $\lesssim 50$ nucleons, but point to the need for further investigation to understand the unusual $A_n$ behaviour discovered for scattering off $^{208}$Pb., Comment: 7 pages, 2 figures

We report a precision measurement of the parity-violating asymmetry $A_{PV}$ in the elastic scattering of longitudinally polarized electrons from $^{208}$Pb. We measure $A_{PV}=550\pm 16 {\rm (stat)}\pm 8\ {\rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_W(Q^2 = 0.00616\ {\rm GeV}^2) = 0.368 \pm 0.013$. Combined with our previous measurement, the extracted neutron skin thickness is $R_n-R_p=0.283 \pm 0.071$~fm. The result also yields the first significant direct measurement of the interior weak density of $^{208}$Pb: $\rho^0_W = -0.0796\pm0.0036\ {\rm (exp.)}\pm0.0013\ {\rm (theo.)}\ {\rm fm}^{-3}$ leading to the interior baryon density $\rho^0_b = 0.1480\pm0.0036\ {\rm (exp.)}\pm0.0013\ {\rm (theo.)}\ {\rm fm}^{-3}$. The measurement accurately constrains the density dependence of the symmetry energy of nuclear matter near saturation density, with implications for the size and composition of neutron stars.