Precise and accurate nuclear electric quadrupole moment of $^{223}$Ra from molecular spectroscopy

Nuclear electric quadrupole moments of unstable isotopes are commonly extracted from laser spectroscopy of the atomic hyperfine structure, where the accuracy is limited to the several-percent level by the available electric-field-gradient (EFG) calculations. In this study, we determine the spectroscopic quadrupole moment of $^{223}$Ra (half-life $t_{1/2} = 11.4$ d) from hyperfine-resolved collinear resonance ionization spectroscopy of the radioactive molecule $^{223}$Ra$^{19}$F. The $X\,^2Σ^+$ electronic ground state of RaF provides a large axial EFG at the radium nucleus that can be calculated with relativistic coupled-cluster theory to sub-percent accuracy. Together with a three-fold improvement in spectral resolution over previous fast-beam measurements of radioactive molecules, this yields $Q_s = +1.211(7)_\mathrm{stat}(2)_\mathrm{syst}(5)_\mathrm{theo}\,e\mathrm{b}$ for $^{223}$Ra with a total uncertainty of 0.73%, approximately three times better than atomic and ionic determinations. This result demonstrates that molecular spectroscopy can provide access to the electromagnetic structure of unstable nuclei with a precision competitive with, and in favorable cases better than, atomic spectroscopy, and may thus be envisioned for studies beyond the limitations of current radioactive-atom experiments.