Magnetic field Zeeman interaction

The interaction of the spin magnetic moment with the orbital magnetic moment of the unpaired electron leads to an orientationally dependent shift of the resonance frequency. This effect is normally described by an effective spin operator S and an anisotropic g matrix. The quantimi-mechanical Hamilton operator for the interaction of the electron spin with the external magnetic field Zeeman interaction) can, therefore, be described by... 

Spins are magnetic moments that are associated with angular momentum they interact with external magnetic fields (Zeeman interaction) and with each other (couplings). In most cases, the Zeeman interaction of the electron spin is the largest interaction in the spin system (high-field limit). The electron Zeeman (EZ) interaction can generally be described by the Hamiltonian below. 

The spin state of a paramagnetic system with total spin S wiU lift its (25 + l)-fold degeneracy under the influence of ligand fields (zero-field interaction) and applied fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei is different for the 25 + 1 spin states in magnitude and direction. Therefore, the absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how the electronic states are occupied at a certain temperature. 

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

In the presence of a strong static magnetic field, all interactions are described as perturbations to the dominant Zeeman interaction, given by... 

INTRAMOLECULAR ELECTRONIC-ROTATIONAL INTERACTIONS, MAGNETIC FIELD DEPENDENT INTERACTIONS, AND THE MOLECULAR ZEEMAN EFFECT... 

It is instructive to consider the mechanism by which the hyperfine coupling arises. In a strong magnetic field, the interaction between an unpaired electron and a magnetic nucleus acts as a small perturbation 8E to the Zeeman levels E and 2 of the electron spin. This perturbation is composed of two components. 

The large static applied magnetic field (Bq) produces the Zeeman interaction (= where is the z-... 

Zeeman Unitary 10 -10 Interaction with main magnetic field... 

The first temi describes the electronic Zeeman energy, which is the interaction of the magnetic field with the two electrons of the radical pair with the magnetic field, Bq. The two electron spins are represented by spin... 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

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... 

When we include the Zeeman interaction term, gpBB-S, in the spin Hamiltonian a complication arises. We have been accustomed to evaluating the dot product by simply taking the direction of the magnetic field to define the z-axis (the axis of quantization). When we have a strong dipolar interaction, the... 

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. 

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