Theory of hyperfine interactions in alkaline-earth ions isoelectronic with alkali-metal atoms:Mg+25ground state

Relativistic many-body perturbation theory has been used to investigate the hyperfine structure of the singly ionized magnesium ion. These investigations were carried out to explain the recent experimental data in the ground state $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ of ${\mathrm{Mg}}^{+}$ as well as to compare the hyperfine interaction results, both experimental and theoretical, in alkali-metal atoms with those in the corresponding isoelectronic alkaline-earth positive-ion series. The one-electron contribution to the hyperfine constant in ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}_{}^{+}{}_{}{}^{}$ was found to be -553 MHz composed of the direct and exchange core-polarization contribution of -466 and -87 MHz, respectively, the many-electron correlation contribution being -48 MHz. The net theoretical hyperfine constant comes out to be -(602±8) MHz, which agrees very well with the recent experimental value of -596.25 MHz obtained with the use of ion-storage techniques.