Zeeman interactions classical

We are interested in what happens when a magnetic moment fJt interacts with an applied magnetic field B0—an interaction commonly called the Zeeman interaction. Classically, the energy of this system varies, as illustrated in Fig. 2.1a, with the cosine of the angle between l and B0, with the lowest energy when they are aligned. In quantum theory, the Zeeman appears in the Hamiltonian operator... 

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. 

The classical Zeeman interaction between a magnetic moment and an applied magnetic field was defined above. In a quantum mechanical description the operators for the quantities need to be used, such as the nuclear spin I. With an externally applied magnetic field B the Zeeman Hamiltonian is given by... 

The above has adopted a classical picture for describing the interaction between an rf field and the magnetisation. However, just as for the interaction with the main static applied magnetic field there is an analogous quantum mechanical description. The interaction between the rf magnetic field and the nuclear spins is simply another Zeeman interaction. The difference for this field is that it is time-dependent. In practice, the sample is irradiated with a linearly polarised rf-field of strength 2Bj, frequency corf and phase a. 

The interaction of a dipole /itj with such field created by a dipole 112 is given by the classical Zeeman interaction energy —/iti The Hamiltonian describing the dipolar interaction can thus be written in the form... 

Figure 11. ESEEM spectra of the oxidized form of the Type I copper piotein msticyanin, which has the classic His2CysMet Cu(II) binding motif. These are exact cancellation-like spectra that are obtained at spectrometer operating frequencies from 7.0 to 13 GHz. The peaks are mobile, as predicted by the nuclear Zeeman dependence. The upper spectrum is derived from an engineered form of the protein in which one of the two ligand histidines is removed the spectrum is characteristic of a single hyperfine spectrum. The lower spectrum corresponds to the modulation spectrum of two nearly equivalent N interactions and features the sum/harmonic lines in the 2-3 MHz region.

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