Some theoretical aspects of the group-IIIA-ion atomic clocks: Intercombination transition probabilities

The main focus of this paper is the theoretical study of the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$ ${\to }^1$ ${\mathit{S}}_0$ intercombination transition probabilities of the group-IIIA ions that are excellent candidates for high-accuracy atomic clocks. The importance of relativistic effects on the intercombination transition probabilities is made apparent by comparing their calculated values with those of the allowed ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}_1$ ${\to }^1$ ${\mathit{S}}_0$ transition probabilities. In striking contrast to the allowed transition probabilities, the intercombination transition probabilities exhibit a strong Z dependence.