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($$\bar{q}$$), the weak charge radius RW, and the point neutron radius Rn, of 208Pb 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 FW($$\bar{q}$$) = 0.204 ± 0.028(exp) ± 0.001(model). We use the Helm model to infer the weak radius from FW($$\bar{q}$$). 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 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, from RW. 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. As a result, 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.