Enhanced role of electron correlation in the hyperfine interactions in ${}^{2}D_{5∕2}$ states in alkaline-earth-metal ions

The low-lying $n(=3,4,5)d$ ${}^{2}D_{5∕2}$ states of alkaline-earth-metal ions are of vital importance in a number of different physical applications. The hyperfine structure constants of these states are characterized by unusually strong electron correlation effects. Relativistic coupled-cluster theory has been employed to carry out ab initio calculations of these constants. The role of the all-order core-polarization effects was found to be decisive in obtaining good agreement of our calculated magnetic dipole hyperfine structure constants with accurate measurements. The present work is an apt demonstration of the power of the coupled-cluster method to cope with strongly interacting configurations.

Figure 1

Goldstone diagrams representing all-order CP effects from $\overline{O}{S}_{2v}$. Arrows pointing downwards and upwards represent core $\left(a\right)$ and virtual $\left(p\right)$ electrons, respectively. The arrow inside the circle represents valence electron.

Figure 2

(Color online) Core-polarization contributions to $A∕g_I$ (MHz) for different systems.

Figure 3

(Color online) $A_{\mathrm{RCC}}∕A_{\mathrm{DF}}$ values for different systems for the RCC terms arising from Eq. (3.1). In the $X$ axis, $\overline{O}$, $\overline{O}{S}_{1v}+\mathrm{c.c.}$, $\overline{O}{S}_{2v}+\mathrm{c.c.}$, $S_{1v}^{†}\overline{O}{S}_{1v}$, $S_{2v}^{†}\overline{O}{S}_{1v}+\mathrm{c.c.}$, $S_{2v}^{†}\overline{O}{S}_{2v}$, and normalization terms are taken in a sequence in each unit distance.