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

Abstract

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 $A_{PV}=550\pm 16(\mathrm{stat})\pm 8(\mathrm{syst})$ parts per billion, leading to an extraction of the neutral weak form factor $F_W(Q^2=0.00616{\mathrm{GeV}}^2)=0.368\pm 0.013$. 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: ${\rho }_W^0=-0.0796\pm 0.0036(exp.)\pm 0.0013(theo.){\mathrm{fm}}^{-3}$ leading to the interior baryon density ${\rho }_b^0=0.1480\pm 0.0036(exp.)\pm 0.0013(theo.){\mathrm{fm}}^{-3}$. 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.

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