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From reading other responses I noticed that I overlooked the fact that one can check eta to see how the system deviates from axial symmetry.
Note that the g-factors are dimensionless and the the magnetic moment values are in units of µ_N (unless it is an electron, there it is µ_B)
However, considering the studied Bohr-Weisskopf in the lecture video, it is likely that this will add some correction on the energy. This is due to the protons, charged particles, moving around in the nucleus and thus generating magnetic fields. A point like nucleus would not be able to exhibit such effects.
I see what you mean and indeed think you are correct. having thought a bit about the problem, it might have something to do with the added extra charge. Since we are looking at descriptions of atoms and we know that they are normally neutrally charged, one can probably find the explanation in the total charge which is not zero anymore.
