Weak charge form factor and radius of 208 Pb through parity violation in electron scattering
We use distorted wave electron scattering calculations to extract the weak charge form factor F W ($\bar{q}$), the weak charge radius R W , and the point neutron radius R n , of 208 Pb from the PREX parity violating asymmetry measurement. The form factor is the Fourier transform of the weak charge density at the average momentum transfer $\bar{q}$ = 0.475 fm -1 . We find F W ($\bar{q}$) = 0.204 ± 0.028(exp) ± 0.001(model). We use the Helm model to infer the weak radius from F W ($\bar{q}$). We find RW = 5.826 ± 0.181(exp) ± 0.027(model) fm. Here the exp 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. As a result, 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.