A Precision Measurement of the Neutron Radius in $^{208}$Pb

The upcoming $^{208}$Pb Radius Experiment (PREx) at Jefferson Lab's Hall A will determine the neutron radius R$_{\mathrm{n}}$ of Lead with $\pm1\%$ projected precision. The experiment will measure the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from $^{208}$Pb at an energy of 1.05 GeV and scattering angle of 5$^{\circ}$. In this way, the neutrons are isolated by the weak charge probe and thus allow for a model independent measurement of R$_{\mathrm{n}}$ analogous to the classic measurements of the proton radius R$_{\mathrm{p}}$. The theoretical corrections to the measured asymmetry are either small or well understood providing a clean extraction of the neutron form factor and charge density. In addition to being a fundamental test of nuclear theory, a precise measurement of R$_{\mathrm{n}}$ pins down the density dependence of the symmetry energy of neutron rich nuclear matter which has impacts on neutron star structure, heavy ion collisions, and atomic parity violation experiments.