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We have developed an all-particle Fock-space relativistic coupled-clustermethod to calculate the properties of two-valence atoms and ions. Using themethod we compute the properties associated with hyperfine induced $^1S_0 -^3P^o_0$ clock transition in Al$^+$. Our result of the $^3P^o_0$ metastablestate life time, $20.20 \pm 0.91$ s, is in excellent agreement with theexperimental 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 toobtain accurate clock properties in Al$^+$.

Fock-space relativistic coupled-cluster calculation of hyperfine induced $\bf {^1S_0 \rightarrow {^3P^o_0}}$ clock transition in Al$^+$