Accurate Determination of the Neutron Skin Thickness of $^{208}$Pb through Parity-Violation in Electron Scattering

Understand

We report a precision measurement of the parity-violating asymmetry $A_{PV}$ in the elastic scattering of longitudinally polarized electrons from $^{208}$Pb.

• We measure $A_{PV}=550\pm 16 {\rm (stat)}\pm 8\ {\rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_W(Q^2 = 0.00616\ {\rm GeV}^2) = 0.368 \pm 0.013$.
• Combined with our previous measurement, the extracted neutron skin thickness is $R_n-R_p=0.283 \pm 0.071$~fm.
• The result also yields the first significant direct measurement of the interior weak density of $^{208}$Pb: $\rho^0_W = -0.0796\pm0.0036\ {\rm (exp.)}\pm0.0013\ {\rm (theo.)}\ {\rm fm}^{-3}$ leading to the interior baryon density $\rho^0_b = 0.1480\pm0.0036\ {\rm (exp.)}\pm0.0013\ {\rm (theo.)}\ {\rm fm}^{-3}$.