Hyperfine structure of $^{173}\mathrm{Yb}^+$: towards resolving the $^{173}\mathrm{Yb}$ nuclear octupole moment puzzle

Hyperfine structure (HFS) of atomic energy levels arises due to the interaction of atomic electrons with a hierarchy of nuclear moments. These contain magnetic dipole, electric quadrupole and higher rank nuclear moments. Recently, the octupole moment of the $^{173}\mathrm{Yb}$ nucleus was extracted from HFS measurements in the ${^3P_2}$ state of neutral Yb [PRA 87, 012512 (2013)]. However, their value, $\Omega = -34.4 \,{\mathrm{b\times{\mu_N}}}$ is four orders of magnitude larger than the nuclear theory prediction, $\Omega =0.003\,{\mathrm{b\times{\mu_N}}}$. We propose to extract $\Omega$ and higher rank nuclear multipole moments from measuring hyperfine splittings in the first excited state ($4f^{13}(^2\!F^{o})6s^2$, $J=7/2$) of $^{173}\mathrm{Yb}^+$. We present results of atomic structure calculations in support of proposed measurements.