The normal and anomalous Zeeman effect

[Hymne]

Hi! I have difficulties seeing the cause that make these to concepts diffret. Haken and Wolf writes about the last one:"One speaks of the anomalous Zeeman effect when the angular momentum and magnetic moment of the two terms between which an optical transistion occurs cannot be described by just one of the two quantum numbers s or l., but are determined by both."However in the nomal Zeeman we used the J as a quantum number and therefore used both?! I am not getting this right..

 

[alxm]

However in the nomal Zeeman we used the J as a quantum number and therefore used both?! I am not getting this right..

It's not whether you use J, L and S, but their interdependence. With the ordinary Zeeman effect, you have LS-coupling, so J is conserved and J = L + S. So L and S (the total angular momentum and spin) don't change independently of each other.

 

[Hymne]

Yeah, but what is the case in the anomalous Zeeman effect then? J is still conserved right?

 

[ytuab]

In the case of the anomalous Zeeman effect, J=L+S is conserved.
(For example, in the case of L=1, and S=1/2, J=1+1/2=3/2 ...)

But each value of L and S is not conserved.
(Each value S and L is changing with time. (For example, S=1/2-0.1, L=1+0.1...)
But the sum of L and S must be conserved. (For example, J=S+L= (1/2-0.1) + (1+0.1) =3/2)...)

The spin g factor is 2, and orbital g factor is 1.
So in the anomalous Zeeman effect, these g factors of 1 and 2 are mixed, and can be different from 1 and 2, because each direction(value) of L and S is changing by the precession.

In the ordinary Zeeman effect or Paschen Back effect, the directions(values) of L and S are conserved (L=1, S=1/2)
So the g factor is 1 or 2, and the magnetic moments are the same as the Normal Zeeman effect. (1 x 1 = 2 x 1/2 = 1)