Exchange Splitting: Atomic Orbitals, Zeeman Effect & More

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I would like to understand what is "exchange splitting" in atomic orbitals.
For which orbitals does it happen ? Is there any similarity between this phenomenon and the Zeeman effect (which breaks the degeneracy on the magnetic quantum number and then splits the orbital into sub-orbitals having different energy according to the spin magnetic number) ?
I know that I must be confused...

Thanks.
 
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Exchange splitting is the energy difference of two electronic states due to exchange interactions, i.e. direct overlap of electronic wave functions, rather than a magnetic field.

You can sometimes calculate an equivalent magnetic field that would produce the same splitting via the Zeeman effect. These "effective" fields can be huge, 50T and more.