Electron Zeeman interaction, basic

The basic idea of the slow-motion theory is to treat the electron spin as a part of the lattice and limit the spin part of the problem to the nuclear spin rather than the IS system. The difficult part of the problem is to treat, in an appropriate way, the combined lattice, now containing the classical degrees of freedom (such as rotation in condensed matter) as well as quantized degrees of freedom (such as the electron Zeeman interaction). The Liouville superoperator formalism is very well suited for treating this type of problems. 

We have seen in Chapter 2 that the electronic Zeeman term, the interaction between unpaired electrons in molecules and an external magnetic field, is the basis of EPR, but we have also discussed in Chapter 4 the fact that if a system has more than one unpaired electron, their spins can mutually interact even in the absence of an external field, and we have alluded to the fact that this zero-field interaction affords EPR spectra that are quite different from those caused by the Zeeman term alone. Let us now broaden our view to include many more possible interactions, but at the same time let us be systematic and realize that this plethora of possibilities is eventually reducible to five basic types only, two of which are usually so weak that they can be ignored. 

Originally the three-spin effect was postulated to explain the positive enhancements observed for certain fluorine nuclei in solvents also containing protons.The possibility arose that the fluorine nuclei were being influenced by the proton polarization as well as by the direct coupling to the electron spins. The basic idea behind the three-spin effect can be seen by considering the transitions among the Zeeman energy levels shown in Fig. 20. Since the electron—proton interaction is of the dipolar kind, the predominant coupled transition will be an... 

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