Magnetic Dipole and Electric Quadrupole Moments of the $^{229}$Th Nucleus

We determine the magnetic dipole $\ensuremath{\mu}=0.360(7){\ensuremath{\mu}}_{N}$ and the electric quadrupole $Q=3.11(6)$$e$b moments of the ${}^{229}$Th nucleus by combining our high-precision calculations of the hyperfine constants with measurements reported in Campbell et al. [Phys. Rev. Lett. 106, 223001 (2011)]. We find that the previous value $\ensuremath{\mu}=0.46(4){\ensuremath{\mu}}_{N}$ [Gerstenkorn et al., J. Phys. (Paris) 35, 483 (1974)] is incorrect by 25%. We report a method for determining the accuracy of theoretical hyperfine constants $B/Q$ and demonstrate that it can be used to extract the electric quadrupole moment $Q$ with a 1%--2% uncertainty for a large number of nuclei. This approach allowed us to identify 40% inconsistencies in measurements of Ra${}^{+}$ hyperfine constants $B$.