Weak charge form factor and radius of 208Pb through parity violation in electron scattering

We use distorted wave electron scattering calculations to extract the weak charge form factor F-W ((q) over bar), the weak charge radius R-W, and the point neutron radius R-n of Pb-208 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 (q) over bar = 0.475 fm(-1). We find F-W ((q) over bar) = 0.204 +/- 0.028 (exp) +/- 0.001 (model). We use the Helm model to infer the weak radius from F-W ((q) over bar). We find R-W = 5.826 +/- 0.181 (exp) +/- 0.027 (model) 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 +/- 0.175 (exp) +/- 0.026 (model) +/- 0.005 (strange) 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 RW because of the nucleon's size. Finally, we find a neutron skin thickness of R-n - R-p = 0.302 +/- 0.175 (exp) +/- 0.026 (model) +/- 0.005 (strange) fm, where R-p is the point proton radius.