Fock-space relativistic coupled-cluster calculation of hyperfine induced ${}^1{\mathbf{S}}_0\to {}^3{\mathbf{P}}_0^{\mathbf{o}}$ clock transition in Al${}^{+}$

Abstract

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 hyperfine induced ${}^1{S}_0{-}^3{P}_0^o$ clock transition in Al${}^{+}$. Our result of the ${}^3{P}_0^o$ metastable state life time, $20.20\pm 0.91$ s, is in excellent agreement with the experimental value, $20.60\pm 1.4$ s [Phys. Rev. Lett. {\bf 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 Al${}^{+}$.

12 pages, 6 figures, 6 tables