Subject Zeeman spin

Systems with more than one unpaired electron are not only subject to the electronic Zeeman interaction but also to the magnetic-field independent interelectronic zero-field interaction, and the spin Hamiltonian then becomes... 

Let us calculate the frequencies of transitions between Zeeman eigenstates s) and r), assuming that the nuclei are only subjected to an isotropic chemical shift and the first- and second-order quadrupolar interaction. As seen in Sect. 2.1, the Hamiltonian that governs the spin system in the frame of the Zeeman interaction (the rotating frame) is... 

Fig. 3. Energy level diagram for a spin f nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. Frequency of the central transition (shown in bold lines) is independent of the quadrupolar interaction to first order, but is subject to second-order quadrupolar effects (see text).

Low-spin Fe(iii) porphyrins have been the subject of a number of studies. (638-650) The favourably short electronic spin-lattice relaxation time and appreciable anisotropic magnetic properties of low-spin Fe(iii) make it highly suited for NMR studies. Horrocks and Greenberg (638) have shown that both contact and dipolar shifts vary linearly with inverse temperature and have assessed the importance of second-order Zeeman (SOZ) effects and thermal population of excited states when evaluating the dipolar shifts in such systems. Estimation of dipolar shifts directly from g-tensor anisotropy without allowing for SOZ effects can lead to errors of up to 30% in either direction. Appreciable population of the excited orbital state(s) produces temperature dependent hyperfine splitting parameters. Such an explanation has been used to explain deviations between the measured and calculated shifts in bis-(l-methylimidazole) (641) and pyridine complexes (642) of ferriporphyrins. In the former complexes the contact shifts are considered to involve directly delocalized 7r-spin density... 

The experimental spectrum of atomic H shows good agreement with this model, except when it is subjected to a magnetic field, which results in a splitting of the spectrum lines. This phenomenon, also known as the anomalous Zeeman effect, can be explained by assuming that, in addition to its orbital momentum, an electron possesses an intrinsic angular momentum, p, with value p = [s(s + l)y h, where s is the spin quantum... 

Nuclear magnetic resonance (NMR) experiments subject a sample to a strong, static homogeneous magnetic field B = (0,0, B) that splits the energy levels of degenerate nuclear spin states. Transitions between these Zeeman levels are induced with an oscillating field (radio frequencies around 10 cm i). 

If an electron (or nuclear) spin S is subjected to a magnetic field Hq in the direction z then the Zeeman interaction... 

When a spectral line source is subject to a magnetic field, the spectral lines display hyperfine structure (Zeeman effect). In order to explain hyperfine structure it is postulated that the electron rotates on its axis with spin angular momentum S ... 

Figure 8. Level (anti-)crossing of nuclear sublevels S=l/2, 1=1 by adjusting the nuclear Zeeman splitting. Only the m=l transitions are shown in the diagram. As in Figure 7, the ENDOR transitions are mobile and subject to a critical point as the magnitude of the nuclear zeeman energy assumes a value that leads to the crossing condititm in (me electrcm spin...

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