Hyperfine structure constants and <i>g</i> factors of clock-states of Al-like ions

The highly charged Al-like ions are the potential candidates for the next-generation atomic optical clocks, and their atomic parameters are also useful in plasma and nuclear physics. In the present work, the hyperfine interaction constants and Landé g factors of 3s²3p ²P_{1/2, 3/2} states in the ground configuration for Al-like ions in a range between Si⁺ and Kr²³⁺ ions are calculated by using the multi-configuration Dirac-Hartree-Fock method. Owing to the fact that hyperfine interaction constant is sensitive to electron correlation effect, we systematically investigate its influence on the hyperfine interaction constants, particularly for the high-order correlation related to the 2p electrons. According to this investigation and by taking into account the Breit interaction and QED corrections, we achieve the computational accuracy at a level of 1% and 10^–5 for the hyperfine interaction constant and Landé g factor, respectively, except for Si⁺ ion. Furthermore, the electronic part of hyperfine interaction constant and g factor each as a function of atomic number are obtained. The deviations of the hyperfine structure constant and g factor from these fitted formulas from the ab initio calculations are less than 2% and 10^–5, respectively. As a result, the hyperfine structure constants and g factors of all isotopes can be determined for Al-like ions with 14 ≤ Z ≤ 54.