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(q̄), the weak charge radius R_W, and the point neutron radius R_n of 208Pb 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 q̄=0.475 fm^-1. We find F_W(q̄)=0.204±0. 028(exp)±0.001(model). We use the Helm model to infer the weak radius from F_W(q̄). 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 σ 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 R_W 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.