text: If the spin–orbit interaction dominates over the effect of the external magnetic field,  and  are not separately conserved, only the total angular momentum  is. The spin and orbital angular momentum vectors can be thought of as precessing about the (fixed) total angular momentum vector . The (time-)"averaged" spin vector is then the projection of the spin onto the direction of :
  and for the (time-)"averaged" orbital vector:
  Thus,
  Using  and squaring both sides, we get
  and:
  using  and squaring both sides, we get
  Combining everything and taking , we obtain the magnetic potential energy of the atom in the applied external magnetic field,
  where the quantity in square brackets is the Landé g-factor g of the atom ( and ) and  is the z-component of the total angular momentum. 
  For a single electron above filled shells  and , the Landé g-factor can be simplified into:
  Taking  to be the perturbation, the Zeeman correction to the energy is