Energy difference between hyperfine an non hyperfine transitions

[gstefane]

If we calculate the photon energy between energy levels in the fine structure, we obtain a value of 0,093 meV approximately.

If now we take into account hyperfine splitting, we can calculate the hyperfine coupling constant A for a given magnetic field (10T). We obtain A=2.1E-4 meV, so we can see that the splitting that will be caused by the hyperfine interaction will be very small compared to the fine transitions.
For the transitions between mj=-1/2 and mj=1/2, we obtain energies of 0,093105 and 0,092893 meV, and for the transitions between mj=-3/2 and mj=-1/2, we obtain energies of 0,092963 and 0,09303675 meV.

We can conclude that the photon energy needed for the transitions in the fine structure are in the order of meV, and that the hyperfine structure splits those levels in the microeV order, so the photon energies in that case keep really similar, with slightly different values in a microeV level.

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