Hyperfine structure of the metastable ${{}^{3}P}_2$ state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments

Measuring the hyperfine structure (HFS) of long-lived ${{}^{3}P}_2$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in ${}^{87}\text{S}\text{r}$ needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. The results of similar analyses for ${}^9\text{B}\text{e}$, ${}^{25}\text{M}\text{g}$, and ${}^{43}\text{C}\text{a}$ are also reported.

Figure 1

Sample Brueckner-Goldstone diagrams included in the effective $\text{CI}+\text{MBPT}$ Hamiltonian. (a) Coulomb interaction between the two valence electrons. The double arrows indicate that the single-particle states originate or terminate in the model space. (b) Brueckner (core-polarization) diagrams. (c) Screening diagrams.