Zeeman effect energy separation/splitting

This splitting in the energy level is similar to the Zeeman effect that causes separation of electronic states in a magnetic field. It is sometimes referred to in NMR as the Zeeman nuclear effect. 

This leads to a separation of the quantum states with different m/ and into different energies and splits the spectroscopic transition energies as well, a phenomenon called the Zeeman effect. 

As a result of the Zeeman effect, the degenerated energy levels with magnetic spin number m = 1/2 (or 1=1/2) split into two separate levels with different energy in the presence of a static magnetic field Bq. The energy difference between the two levels is... 

Fig. 10.9. The Ba spectrum in a high magnetic field with the motional Stark field compensated. The data are obtained in atomic beam experiments, and the relative intensities do not suffer from opacity or saturation effects. Both circular polarisations are separated experimentally, and are found to have the same structure (shown by presenting them as though reflected in the axis) when displaced in energy by the linear Zeeman splitting.

In most experiments the Zeeman splitting is small compared with the fine-structure separations and the effect of the magnetic field can be obtained by calculating the diagonal matrix elements of the perturbation operator. It can be shown (Problem 3.16) that the energy of the sub-level y LSJMj> is changed by an amount... 

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