On the existence of magnetic octupole moment of hydrogen-like atoms in the 1S1/2 and 2P1/2 states

Hydrogen-like atom in 1S1/2- and 2P1/2-states with total angular momentum F≥3/2 is shown to possess one more quantum characteristic - magnetic octupole momentum (OM), caused by hyperfine interaction (HFI) between the nucleus and electron. By means of direct solution of the Dirac disturbed equation the necessary corrections to the wave functions are found. Using them, analytical expressions for OM are obtained, which take into account the contributions of both magnetic dipole and electric quadrupole HFI