Nuclear hyperfine interaction general

In eqn (4.1), g and A-t are 3x3 matrices representing the anisotropic Zeeman and nuclear hyperfine interactions. In general, a coordinate system can be found - the g-matrix principal axes - in which g is diagonal. If g and A, are diagonal in the same coordinate system, we say that their principal axes are coincident. 

This mechanism is identical to the one arising from the contact interaction between an unpaired electron and a nuclear spin (41). In that case, the hyperfine coupling (generally denoted by Asc or A and exists only if the electron density is non-zero at the considered nucleus, hence the terminology of contact ) replaces the J coupling and the earlier statement (i) may be untrue because it so happens that T becomes very short. In that case, dispersion curves provide some information about electronic relaxation. These points are discussed in detail in Section II.B of Chapter 2 and I.A.l of Chapter 3. 

Type I and 2 mononuclear copper centers in enzymes and proteins are distinguished by theit different EPR spectra for Cu(ll). Type 1 and 2 spectra exhibit comparatively narrowly and widely spaced hyperfine lines, respectively, for the electton-nuclear spin interaction. The more narrow the spacing, the weaker is the interaction. Type 1 cupric centers generally have an intensely blue color, whereas type 2 centets are virtually colotless. 

Inequations (7.155) and (7.158) we have taken the diagonal = 0 component of the second-rank spherical tensors T2(/ . S) and T2(/a, Ia). In general, these interactions and others like them will have off-diagonal terms also, with q = 1 and 2. The q = 2 components are particularly interesting because, for a molecule in a Id electronic state, they connect the A = +1) and A = — 1) components directly. They therefore make additional hyperfine contributions to the /I-doubling of molecules in Id electronic states. As a result, the nuclear hyperfine splitting of one component of a A-doublet is different from that of the other component. The two contributions are ... 

NMR spin lattice relaxation measurements provide very direct information about the Fourier transform of the spin susceptibility x( w) in a one-dimensional conductor [39]. The spin degrees of freedom constitute a relaxation channel for nuclear spin due to the modulation of the hyperfine interaction by the electron spin time dependence, which is given generally... 

In a paper that appeared in 1979, R.P.J. Merks and R. DeBeer pointed out that the sinusoidal dependence of the stimulated echo ESEEM experiment on x and T (equation 8), presented the opportunity to collect ESEEM data in both time dimensions and then apply a two-dimensional EFT to derive two important benefits. The first benefit was that suppression-free spectra should be obtained along the zero-frequency axis for each dimension while the second benefit would be the appearance of cross-peaks at (tUo, cofs) and (tw, co ) that would allow one to identify peaks that belonged to the same hyperfine interaction. This ESEEM version of the NMR COSY experiment (see Nuclear Magnetic Resonance (NMR) Spectroscopy of Metallobiomolecules) would prove invaluable for ESEEM analysis of complex spin systems. However, the disparity in spin relaxation times in the x and T time dimensions precluded the general application of this method. 

The isotropic g and a values are now replaced by two 3x3 matrices representing the g and A tensors and which arise from the anisotropic electron Zeeman and hyperfine interaction. Other energy terms may also be included in the spin Hamiltonian, including the anisotropic fine term D, for electron-electron interactions, and the anisotropic nuclear quadrupolar interaction Q, depending on the nucleus. Usually the quadrupolar interachons are very small, compared to A and D, are generally less than the inherent linewidth of the EPR signal and are therefore invisible by EPR. They are readily detected in hyperfine techniques such as ENDOR and HYSCORE. All these terms (g. A, D) are anisotropic in the solid state, and must therefore be defined in terms of a tensor, which will be explained in this section. 

In actual practice the unpaired electron is not free. It is generally associated with one or more nuclei, which may have a nuclear spin magnetic moment. This moment generates a magnetic field at the location of the unpaired electron, due to the so-called contact or Fermi hyperfine interaction (the electron has a finite probability of penetrating to the atomic nucleus) and to the through-space dipolar interaction between nuclear and electronic magnetic spin moment, represented by... 

One key aspect of ENDOR spectroscopy is the nuclear relaxation time, which is generally governed by the dipolar coupling between nucleus and electron. Another key aspect is the ENDOR enhancement factor, as discussed by Geschwind [294]. The radiofrequency frequency field as experienced by the nucleus is enhanced by the ratio of the nuclear hyperfine field to the nuclear Zeeman interaction. Still another point is the selection of orientation concept introduced by Rist and Hyde [276]. In ENDOR of unordered solids, the ESR resonance condition selects molecules in a particular orientation, leading to single crystal type ENDOR. Triple resonance is also possible, irradiating simultaneously two nuclear transitions, as shown by Mobius et al. [295]. 

The magnetic interaction between the electron spin S and nuclear spin I is called the hyperfine interaction. Since these are vector quantities, the general hyperfine interaction must be represented by a second-rank tensor... 

The general cases of symmetric and asymmetric tops have been reviewed.56 For deuterium, the nuclear quadrupole interaction is small and the hyperfine structure is not always resolved, so that the deuteron quadrupole coupling constant must be obtained by curve-fitting. The accuracy of the data diminishes as the size and the asymmetry of the molecule increases. 

Seventy-live per cent of all papers on experimental Mossbauer spectroscopy are concerned with the first excited-state decay of Fe indeed, because of this, Fe and Mossbauer spectroscopy are synonymous to many people. The sheer volume of published work makes a completely exhaustive survey impossible, but in the following chapters a series of critical reviews will be given of specific areas defined by chemical classification. In this way a comprehensive view of the field can be obtained. The nuclear parameters of the s Fe y-decay have also received more attention than usual. This chapter summarises the currently available data on the Fe nuclear parameters, and then applies the general theory of hyperfine interactions given in Chapter 3 to the specific case of this isotope. 

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