We have developed an all-particle Fock-space relativistic coupled-cluster method to calculate the properties of two-valence atoms and ions. Using the method we compute the properties associated with a hyperfine-induced ${}^1{S}_0\to {}^3{P}_0^o$ clock transition in ${\mathrm{Al}}^{+}$. Our result of the ${}^3{P}_0^o$ metastable-state lifetime, $20.20\pm 0.91$ s, is in excellent agreement with the experimental value, $20.60\pm 1.4$ s [T. Rosenband et al., Phys. Rev. Lett. 98, 220801 (2007)]. Our studies show that the contributions from the triple excitations, and the corrections from the Breit interaction and QED effects, are essential to obtain accurate clock properties in ${\mathrm{Al}}^{+}$.

• Received 16 March 2020
• Revised 7 January 2021
• Accepted 7 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.022801