Theoretical calculations of hyperfine splitting,Zeeman shifts,and isotope shifts of 27Al+ and logical ions in Al+ clocks

Based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, similar models are employed to simultaneously calculate the first-order and second-order Zeeman coefficients as well as the hyperfine interaction constants of the related energy levels of ²⁷Al⁺ and its logical ions ⁹Be⁺ and ²⁵Mg⁺ in the ²⁷Al⁺ optical clock. With less than 0.34% deviations from experimental values in Zeeman coefficients of ²⁷Al⁺, these calculated parameters will be of great help for better evaluation of the systematic uncertainty. We also calculate the isotope shift parameters of the related energy levels, which could extend our knowledge and understanding of nuclear properties of these ions.