$7/2$. Since $^{173}\mathrm{Yb}$ has nuclear spin of $5/2$, the grand total angular momentum $F$ is an integer in the interval $[1,6]$. The $^{173}\mathrm{Yb}$ isotope possesses five distinct nuclear electromagnetic moments. The nucleus has an unpaired valence neutron in the $f_{5/2}$ state. The observed [@Stone2005] nuclear magnetic dipole $\mu$ and electric quadrupole moments $Q$ are equal to $-0.680\,\mathrm{\mu_N}$ and $2.80\mathrm{\,b^2}$, respectively. The nuclear single-particle shell model is not adequate for this isotope as it predicts zero value for the quadrupole moment (the valence nucleon is a neutron for this isotope, whereas the electric moments arise from the distribution of protons in the core). This discrepancy points to a strong nuclear deformation of $^{173}\mathrm{Yb}$. Following the theoretical proposal [@BelDerJoh08], the value for the octupole moment was deduced [@Singh] from the HFS in neutral $^{173}\mathrm{Yb}$ atom in the metastable $6s6p\,^3\!P_2$ state. However, the deduced value, $\Omega = -34.4 \,{\mathrm{b\times{\mu_N}}}$, is $\sim 200$ times larger and of opposite sign compared to the prediction of the single-particle nuclear shell model [@Schwartz1955]. A more sophisticated nuclear structure calculation [@Williams1962] (axially-symmetric collective model in strong coupling) yields $\Omega =0.003\,{\mathrm{b\times{\mu_N}}}$, bringing the discrepancy with the spectroscopic determination in neutral Yb to four orders of magnitudes. As to the 