Theory of hyperfine interactions in lithiumlike systems

Using relativistic many-body perturbation theory, we have investigated the valence, exchange core polarization, and correlation contributions to the magnetic hyperfine constants in the ground states of the lithiumlike ions ${\mathrm{Be}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, ${\mathrm{N}}^{4+}$, ${\mathrm{O}}^{5+}$, ${\mathrm{F}}^{6+}$, ${\mathrm{Ne}}^{7+}$, and ${\mathrm{Bi}}^{80+}$. Radiative corrections have also been investigated. Both the exchange core polarization and the correlation contributions as fractions of the valence-electron contribution decrease rapidly as one goes to more highly charged ions, the decrease being more drastic for the correlation effect. The radiative effect, on the other hand, increases very rapidly with increasing charge, becoming of the same order of magnitude as the correlation effect in ${\mathrm{O}}^{5+}$, ${\mathrm{F}}^{6+}$, and ${\mathrm{Ne}}^{7+}$. For ${\mathrm{Bi}}^{80+}$ the radiative effect is larger than the correlation contribution, being about 0.3% of the hyperfine field from the valence 2s electron. The significance of these results and trends will be discussed, and comparisons will be made between the net hyperfine fields obtained in the present work and available experimental results as well as with the results of earlier calculations.