Zeeman terms

Hfi includes a nuclear Zeeman term, a nuclear dipole-dipole term, an electron-nuclear dipole term and a term describing the interaction between the nuclear dipole and the electron orbital motion. 

The electron-electron dipolar term, Ho, equals S1.D.S2. The tensor D is completely anisotropic and only mixes T-states with one another. It is therefore dropped. The nuclear Zeeman term, tlzi =... 

When a magnetic field, B, is applied to a ferromagnetic or ferrimagnetic particle with magnetic moment, p, the magnetic energy has a contribution from the Zeeman term... 

The time dependence result evidently from the angle 6 and, considering from a quantum mechanical point of view the interaction between a magnetic moment and the static magnetic field B0 (Zeeman term), we can invoke a local field of the form... 

The g tensor can be easily related to more fundamental properties of the spin system by comparing the energy from the Zeeman term in the spin... 

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. 

Before we develop the resonance conditions for systems with hyperhne and with zero-held interactions, we return to the electronic Zeeman term S B as an example interaction to discuss a hitherto ignored complexity that is key to the usefulness of EPR spectroscopy in (bio)chemistry, namely anisotropy the fact that all interactions... 

What would happen if we were to lower the microwave frequency from X-band to L-band (1 GHz). The Zeeman term for g 2.2 (an average value for copper) would correspond to a held of circa 325 gauss at 1 GHz, and so the two interactions S B and S I would be of comparable magnitude. In such situations the perturbation expressions become extremely complicated and lose all practical significance. 

Suppose we have an isolated system with a single unpaired electron and no hyper-fine interaction. Mononuclear low-spin Fe111 and many iron-sulfur clusters fall in this category (cf. Table 4.2). The only relevant interaction is the electronic Zeeman term, so the spin Hamiltonian is... 

As mentioned in Sect. 3.3, the electron Zeeman term contributes to Wba if first order base functions. Explicit first order expressions of Wba for l.h. and r.h. rotating fields, I = 1/2 and an isotropic or purely dipolar hfs tensor are given in Table 2. 

Interaction of particle spin magnetic moment with the external magnetic field (Zeeman term). 

The total Hamilton operator for solid state NMR, including the Zeeman term (Hq), is given in equation (1) ... 

The nuclear Zeeman term describes the interaction of the nuclear spins with the external magnetic field. Just as the hyperfine splitting, this term is not incorporated in the original purely electronic Breit-Pauli Hamiltonian as presented in Eqs. (59) and (60) but becomes relevant for ESR spectroscopy. 

For a hydrogen atom in an external field of 10,000 G, draw a figure that shows the effect on the original 1 s energy level of including first the electron Zeeman term, then the nuclear Zeeman term, and finally the hyperfine coupling term in the Hamiltonian. 

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