The Influence of External Fields hfs

In a weak external magnetic field B there will be a spHtting of magnetic sublevels for the hyperfine structure (hfs) case as for the previously discussed case, where the influence of the nucleus was omitted. However, also in the hyperfine structure case the electronic shell is responsible for the interaction. Because of the coupling between I and J, these vectors process about F. Thus, the direction in relation to B of the electronic magnetic moment, which is associated with J, is influenced. The situation is illustrated in Fig. 2.19. 

In strong magnetic fields, the Paschen-Back effect for the hyperfine structure will result. As for the fine structure case the mathematical expression is simple, i.e., 

In intermediate fields the calculation is more complicated. For J or J = 1/2, the Breit-B,abi formula can be expressed in analogy with the fine structure case, see (2.31). For. 7 — 1/2 we have 

Here the plus sign refers to the higher F value. In Fig. 2.20 the dependence of the sublevels on the magnetic field for a. J = lj2,1 — 3/2 state is shown. 

The Zeeman and Paschen-Back regions can be identified and the relevant quantum numbers Mp, Mr, and Mj, are indicated Mp = Mr + j)-The Mp = 2 levels have no mixing partner and proceed linearly into the Paschen-Back region. 

In the presence of hyperfine structure, gj now takes the place of gj in describing the gear ratio between the magnetic energy contribution and 

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