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

Abstract

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 $X{}^2{\Sigma }^{+}$ 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.