Precision Beam Control in Parity Violating Electron Scattering Measurements of the Neutral Weak Form Factor of ²⁰⁸Pb and ⁴⁸Ca

The RMS radii of the neutron distribution in both ²⁰⁸Pb and ⁴⁸Ca have been precisely measured by the PREX and CREX experiments via the parity violating asymmetry in longitudinally polarized elastic electron-nucleus scattering. The advantage of these parity violating electron scattering measurements lies in the use of an electroweak probe to measure these quantities, significantly reducing uncertainties from theoretical interpretations. The PREX measurement of the large ²⁰⁸Pb nucleus, for which nuclear density functional theory can be applied, provides meaningful constraints on the density dependence of the symmetry energy of neutron-rich nuclear matter; an important parameter for the nuclear equation of state. The complimentary CREX measurement of the modestly sized, neutron rich ⁴⁸Ca nucleus, for which edge effects are significant, provides an important benchmark for nuclear theory to help bridge ab-initio theoretical approaches and the nuclear density functional theory. While the electroweak nature of the interaction lends itself to a clean interpretation of the results it also presents significant experimental hurdles, including the need to employ innovative precision beam control techniques. This talk will give an overview of the recently published experimental results from the PREX and CREX collaborations, will touch upon the tension observed between these results and select theoretical calculations and measurements, and will describe the techniques employed to meet the stringent systematic uncertainty goals arising from beam asymmetries during the PREX-II and CREX experiments. These beam control techniques will also be used in the upcoming extreme-precision MOLLER experiment.