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 FW(q¯), the weak charge radius RW, and the point neutron radius Rn 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 q¯=0.475 fm−1. We find FW(q¯)=0.204±0.028(exp)±0.001(model). We use the Helm model to infer the weak radius from FW(q¯). We find RW=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 RW 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 Rn=5.751±0.175(exp)±0.026(model)±0.005(strange)fm fromRW. Here there is only a very small error (strange) from possible strange quark contributions. We find Rn to be slightly smaller than RW because of the nucleon's size. Finally, we find a neutron skin thickness of Rn−Rp=0.302±0.175(exp)±0.026 (model) ± 0.005 (strange) fm, where Rp is the point proton radius.