Simultaneous Determination of Multiple Nuclear Parameters of $^{229}$Th Using Highly Charged Ions

Development of a $^{229}$Th nuclear optical clock requires precise and model-insensitive nuclear-structure parameters, which presently suffer from limited accuracy and poor consistency. We propose a joint spectroscopy scheme using two highly charged $^{229}$Th ions with $J=1/2$ electronic ground states, where the lowest electronic excitation energy of each ion far exceeds the nuclear transition energy. This configuration effectively forms a three-level system comprising the electronic ground state and the nuclear ground ($g$) and isomeric ($m$) states, resulting in strongly enhanced nuclear hyperfine mixing. Within this framework, a unified analysis of precision measurements on both ions enables the simultaneous determination of five key nuclear parameters without relying on external nuclear inputs: the magnetic dipole moments $μ_g$ and $μ_m$, the bare-nucleus transition energy $ω_n$, the charge-radius difference $δ\langle r^{2}\rangle_{gm}$, and the $M1$ transition matrix element $T_{M1}$. With this approach, the uncertainties in $ω_n$ and $δ\langle r^{2}\rangle_{gm}$ are estimated to be reduced by factors of 3 and 2, respectively, relative to their current uncertainties. %compared with current values. This work could provide a useful benchmark for nuclear theory and serve as a foundation for future development of a $^{229}$Th-based nuclear optical clock.