Suppose there is an ordinary splitting of 2 electrons with ms= 1/2 & -1/2, and by raising the system to Hyperfine splitting in presence of some Teslas, corresponding nuclear spin quantum no. (mI) emerge to give us three distinct levels for each unpaired electron-coupled nuclear magnetic moment, recall the atom's nuclear spin, I=1.
The point i want to raise here is why we start to consider the upper higher-energy quantum level (mI= -1), mI=0 then mI=1 (least E), for the two ms= +- 1/2 ? It has to do with the difference in protons' (Z) which is the opposite of the electron, but doesn't it differ even a bit in either cases of (ms= 1/2 or ms=-1/2), is there a stronger illustration for that?
I am not sure I understand what you want to ask. Are you wondering about the energetic sequence of hyperfine levels in a strong magnetic field? For example, one might be interested in the hyperfine splitting of the electronic ground state in deuterium. The sequence of levels is determined by the directions of the magnetic moments of the nucleus, i. e., the deuteron, and the electron. The magnetic moment of the electron is oriented opposite to the electron spin while the magnetic moment of the nucleus is in the direction of the spin. Considering that in the hyperfine interaction term in the hamiltonian of the atom yields the sequence of levels with their associated quantum numbers.
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