${}_{229}\mathrm{Th}_{3+}$ as an ionic optical clock for fine-structure-constant variations

In this paper, we propose the $5f_{5/2}\to 5f_{7/2}$ transition in ${}_{229}\mathrm{Th}_{3+}$ as an ionic clock with accuracy of ${10}^{-18}$ level, which can be also used together with the nuclear clock transition for measuring variations of fine-structure constant with common-mode rejection of certain systematic effects. The many-body perturbation theory and Dirac-Fock plus core polarizability method are used to perform theoretical calculations. Calculation results show that several systematic frequency shifts can be suppressed to ${10}^{-18}$ level or even below. Assuming the accuracy of ionic clock frequency can be achieved in ${10}^{-18}$ level, ${}_{229}\mathrm{Th}_{3+}$ potentially offers a precision of drift of fine-structure constant of $\dot{\alpha }/\alpha$ in ${10}^{-21}\text{−}{\mathrm{yr}}^{-1}$ level by measuring the frequency ratio of nuclear clock frequency and ionic clock frequency.