reported for about 20 additional nuclei from nuclear scattering experiments [@Fuller1976]. []{data-label="table:NuclearMoments"}

Most of the previous spectroscopic determinations of high-order moments of nuclei focused on extraction of octupole moments, and are compiled in Table \[table:NuclearMoments\]. This Table also lists the nuclear single-particle model [@sch55] values for the nuclear octupole moments. In addition to the listed spectroscopic determinations, the experiments were carried out in Eu [@Chi91] and Hf [@JinWakIna95]. However, due to the complexity of electronic structure calculations, these experiments only determined ratios of nuclear octupole moments between different isotopes, $\Omega(^{151}\mathrm{Eu})/\Omega(^{153}\mathrm{Eu})$ and $\Omega(^{177}\mathrm{Hf})/\Omega(^{179}\mathrm{Hf})$.

Beyond octupole order, the hexadecapole moment $\Pi$ has been spectroscopically determined for only one species: $^{165}$Ho [@DanFerGeb74]. Access to the hexadecapole moments requires $J \ge 2$ and $I \ge 2$. For example, although $^{133}$Cs nucleus has $I=7/2$ and thereby possesses hexadecapole moment, this moment can not be determined from the measured HFS of the $6\,{p_{3/2}}$ state [@GerDerTan03]. This argument prohibits the extraction of nuclear hexadecapole moments from the structure of the states used to measure magnetic octupole moments for all but two exceptions in Table \[table:NuclearMoments\]: $^{165}$Ho and $^{173}$Yb. The value for $\Pi$ that was extracted from spectroscopic measurements in $^{165}$Ho was found to be larger than the 