Revisiting the nuclear magnetic octupole moment

The nuclear magnetic octupole moment is revisited as a potentially useful observable for nuclear structure studies. The magnetic octupole moment, $\mathrm{\Omega }$, is examined in terms of the nuclear collective model including weak and strong coupling. Single-particle formulation is additionally considered in the overall comparison of theoretical predictions with available experimental data. Mirror nuclei symmetry is examined in terms of the magnetic octupole moment isoscalar and isovector terms. A full list of predictions for $\mathrm{\Omega }$ of odd-proton and odd-neutron nuclei in medium-heavy mass regimes of the nuclear chart is produced aiming at providing starting values for future experimental endeavors.