We use distorted wave electron scattering calculations to extract the weak charge form factor $F_W\left(\overline{q}\right)$, the weak charge radius $R_W$, and the point neutron radius $R_n$ of ${}^{208}$Pb from the Lead Radius Experiment (PREX) parity-violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer $\overline{q}=0.475$ fm${}^{-1}$. We find $F_W\left(\overline{q}\right)=0.204\pm 0.028\left(\exp \right)\pm 0.001\left(\mathrm{model}\right)$. We use the Helm model to infer the weak radius from $F_W\left(\overline{q}\right)$. We find $R_W=5.826\pm 0.181\left(\exp \right)\pm 0.027\left(\mathrm{model}\right)\mathrm{fm}$. Here the experimental error includes PREX statistical and systematic errors, while the model error describes the uncertainty in $R_W$ from uncertainties in the surface thickness $\sigma$ of the weak charge density. The weak radius is larger than the charge radius, implying a “weak charge skin” where the surface region is relatively enriched in weak charges compared to (electromagnetic) charges. We extract the point neutron radius $R_n=5.751\pm 0.175\left(\exp \right)\pm 0.026\left(\mathrm{model}\right)\pm 0.005\left(\mathrm{strange}\right)\mathrm{fm}$ from $R_W$. Here there is only a very small error (strange) from possible strange quark contributions. We find $R_n$ to be slightly smaller than $R_W$ because of the nucleon's size. Finally, we find a neutron skin thickness of $R_n-R_p=0.302\pm 0.175\left(\exp \right)\pm 0.026$ (model) $\pm$ 0.005 (strange) fm, where $R_p$ is the point proton radius.

• Received 7 February 2012

DOI:https://doi.org/10.1103/PhysRevC.85.032501