We report a precision measurement of the parity-violating asymmetry A(pv) in the elastic scattering of longitudinally polarized electrons from Pb-208. We measure A(pv) = 550 +/- 16(stat) +/- 8(syst) parts per billion, leading to an extraction of the neutral weak form factor F-w (Q(2) = 0.00616 GeV2) = 0.368 +/- 0.013. Combined with our previous measurement, the extracted neutron skin thickness is R-n - R-p = 0.283 +/- 0.071 fm. The result also yields the first significant direct measurement of the interior weak density of Pb-208: rho(0)(w) = -0.0796 +/- 0.0036(exp) +/- 0.0013(theo) fm(-3) leading to the interior baryon density rho(0)(w)= 0.1480 +/- 0.0036(exp) +/- 0.0013(theo) fm(-3). The measurement accurately constrains the density dependence of the symmetry energy of nuclear matter near saturation density, with implications for the size and composition of neutron stars.
