Hyperfine structure, nuclear

The spatial localization of H atoms in H2 and HD crystals found from analysis of the hyperfine structure of the EPR spectrum, is caused by the interaction of the uncoupled electron with the matrix protons [Miyazaki 1991 Miyazaki et al. 1991]. The mean distance between an H atom and protons of the nearest molecules was inferred from the ratio of line intensities for the allowed (without change in the nuclear spin projections. Am = 0) and forbidden (Am = 1) transitions. It equals 3.6-4.0 A and 2.3 A for the H2 and HD crystals respectively. It follows from comparison of these distances with the parameters of the hep lattice of H2 that the H atoms in the H2 crystal replace the molecules in the lattice nodes, while in the HD crystal they occupy the octahedral positions. 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

Wolfgang Pauli (1900-1958 Nobel Prize 1945), at the age of 24, formulated the exclusion principle, which became famous as the Pauli principle. Accordingly, all electrons in an atom differ from each other, none are the same. His theoretical considerations led him to the existence of so-called nuclear spins, which also explained the hyperfine structures of spectral lines. His hypothesis was later unambiguously confirmed. As each element has its own... 

The spectra discussed in Chapter 4 were analyzed by neglecting the effects of nuclear quadrupole coupling on the nuclear hyperfine structure. Presented here is the way such effects may be incorporated into the spectra using perturbation theory. 

Here, the directions are defined in Fig. 6. In natural N02 the 170 content is quite small so the only observable hyperfine structure will be due to HN, which has a nuclear spin of one. Recent experiments, however, have been carried out using N02 enriched in 170 (34-) Molecular orbital calculations indicate that c2 is reasonably large, i.e., the unpaired electron is expected to have considerable nitrogen p2 character. 

By far the most important influence of a nuclear spin on the EPR spectrum is through the interaction between the electron spin S and the nuclear spin I. Usually, at X-band frequencies this interaction is weaker, by an order of magnitude or more, than the electronic Zeeman interaction, and so it introduces small changes in the EPR spectrum known as hyperfine structure. As a first orientation to these patterns, note that just like the electron spin S, also the nuclear spin / has a multiplicity ... 

Abragam, A. and Pryce, M.H.L. 1951. Theory of the nuclear hyperfine structure of paramagnetic resonance spectra in crystals. Proceedings of the Royal Society of London A 205 135-153. 

Hyperfine structure arises through the interaction of the electron spin with a nuclear spin. Consider first the interaction of the electron spin with a single magnetic nucleus of spin , In an applied magnetic field the nuclear spin angular momentum vector, of magnitude (/ / -f l)]l/2, precesses around the direction of the field in an exactly analogous way to that of the electron spin. The orientations that the nuclear spin can take up are those for which the spin in the z-direction, M, has components of ... 

Fig. 3. (a) Partially resolved nuclear hyperfine structure in the p.SR spectrum for Mu in GaAs in an applied field of 0.3 T. The structure occurs in the line corresponding to 0 = 90° and Ms = —1/2. (b) Theoretical frequency spectrum obtained by exact diagonalization of the spin Hamiltonian using the nuclear hyperfine and electric quadrupole parameters in Table I for the nearest-neighbor Ga and As on the Mu symmetry axis. Both Ga isotopes, 69Ga and 71Ga, were taken into account. From Kiefl et al. (1987). 

The most convincing evidence for the BC model of Mu in III-V materials comes from the nuclear hyperfine structure in GaAs. The hyperfine parameters for the nearest-neighbor Ga and As on the Mu symmetry axis and the corresponding s and p densities are given in Table I. One finds a total spin density on the As(Ga) of 0.45 (0.38) with the ratio of p to 5 density of 23 (4) respectively. The fact that 83% of the spin density is on the two nearest-neighbor nuclei on the Mu symmetry axis agrees with the expectations of the BC model. From the ratios of p to s one can estimate that the As and Ga are displaced 0.65 (17) A and 0.14(6) A, respectively, away from the bond center. The uncertainties of these estimates were calculated from spin polarization effects, which are not known accurately, and they do not reflect any systematic uncertainties in the approximation. These displacements imply an increase in the Ga—As bond of about 32 (7)%, which is similar to calculated lattice distortions for Mu in diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987) and Si (Estreicher, 1987). 

In the ESR spectra of adsorbed oxovanadium(IV) ions on minerals, Information on the nature of the adsorbed species is obtained from the g-values and V hyperfine coupling constants, but ligand hyperfine structure is seldom, if ever, observed. With ENDOR much smaller hyperfine splittings can be observed than with ESR and it is possible to measure hyperfine coupling from nuclear spins in... 

Moseley s law spect The law that the square-root of the frequency of an x-ray spectral line belonging to a particular series is proportional to the difference between the atomic number and a constant which depends only on the series. mOz-lez, 10 Mossbauer spectroscopy spect The study of Mossbauer spectra, for example, for nuclear hyperfine structure, chemical shifts, and chemical analysis. mus,bau-3r spek tras ko pe ... 

ESR methods unambiguously establishes the presence of species bearing unpaired electrons (ion-radicals and radicals). The ESR spectrum quantitatively characterizes the distribution of electron density within the paramagnetic particle by a hyperfine structure of ESR spectra. This establishes the nature and electronic configuration of the particle. A review by Davies (2001) is highly recommended as a guide to current practice for ESR spectroscopic studies (this quotation is from the title of the review). The ESR method dominates in ion-radical studies. Its modern modifications, namely, ENDOR and electron-nuclear-nuclear triple resonance (TRIPLE) and special methods to observe ion-radicals by swiftness or stealth are described in special literatures (Moebius and Biehl 1979, Kurreck et al. 1988, Werst and Trifunac 1998). 

The electron magnetic moment may also interact with the local magnetic fields of the nuclear dipole moments of nuclei around it. A single electron centered on a nucleus of spin I will experience 2/ -f 1 different local magnetic fields due to the 27 - - 1 different orientations of the nuclear spin I in the external magnetic field. This interaction, which is of the order of 10 cm. i, causes a hyperfine structure in the EPR spectrum. This structure is further discussed and illustrated in Section III,B. 

The phenomenon of NQR is the origin of hyperfine structure in microwave rotational spectra (see Section 2.04.2.1), as well as in electron and nuclear paramagnetic resonance. 

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