Hyperfine structure of hydrogenlike and lithiumlike atoms

The hyperfine splitting values of the ground state of the hydrogenlike atoms ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{}^{5+}{}_{}{}^{}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{6+}{}_{}{}^{}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}_{}^{7+}{}_{}{}^{}$ and the lithiumlike atoms ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^0{}_{}{}^{}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{4+}{}_{}{}^{}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}_{}^{6+}{}_{}{}^{}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}_{}^{8+}{}_{}{}^{}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}_{}^{9+}{}_{}{}^{}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}_{}^{10+}{}_{}{}^{}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}_{}^{11+}{}_{}{}^{}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}_{}^{14+}{}_{}{}^{}$, ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^{23+}{}_{}{}^{}$ are calculated. The calculations of the lithiumlike ions (Z≥7) are based on a combination of the 1/Z perturbation theory and the configuration interaction Hartree-Fock method. The relativistic corrections are calculated in the zeroth and first orders in 1/Z. The nuclear charge and magnetization distribution corrections and the radiative corrections are taken into account. The uncertainty of the calculations is estimated to be ∼0.02% for the hydrogenlike ions and ∼0.06% for the lithiumlike ions, except ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^{23+}{}_{}{}^{}$, for which the uncertainty is about 0.15%. The hyperfine structure constant of the ground state of Li is calculated to be A=401.5(4) MHz. The results of the calculations are compared with the theoretical values obtained with other methods and with experiment.