Zeeman nuclear

Hfi includes a nuclear Zeeman term, a nuclear dipole-dipole term, an electron-nuclear dipole term and a term describing the interaction between the nuclear dipole and the electron orbital motion. 

The electron-electron dipolar term, Ho, equals S1.D.S2. The tensor D is completely anisotropic and only mixes T-states with one another. It is therefore dropped. The nuclear Zeeman term, tlzi =... 

The intensity of a non-degenerate n.m.r. transition between the nuclear Zeeman levels n and m is proportional to the difference in population of levels n and m as given by the Boltzmann distribution. This can be expressed by equation (35). 

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... 

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

The nuclear Zeeman effect is not a very strong interaction as compared to electric quadrupole splitting because of the relatively weak nuclear magneton. A field of B... 

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

Au dissolved in ferromagnetic hosts of Fe, Co, Ni as sources versus Au metal absorber Nuclear Zeeman effect in Au atoms, super-transferred hf fields, // at Au sites... 

HYSCORE spectra of zeaxanthin radicals photo-generated on silica-alumina were taken at two different magnetic fields B0=3450G and B0=3422G, respectively. In order to combine the data from the two spectra, the field correction was applied (Dikanov and Bowman 1998). The correction consists of a set of equations that allow transformation of spectra to a common nuclear Zeeman frequency. The set of new frequencies was added to that of the former spectrum and plotted as the squares of the frequencies v2a and v2p. Examples of these plots can be found in Focsan et al. 2008. 

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)... 

Quadrupole coupling, isomer shift Quadrupole tensor, nuclear Zeeman splitting, g values, coupling constants, relaxation times... 

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

In the first row of (3.1) the terms denote the electron Zeeman (2 EZ), the hf (2 hft), the nuclear Zeeman (XNZ) and the nuclear quadrupole interaction (CXQ) of the central (metal) ion. The second row represents the hf, the nuclear Zeeman and the nuclear quadrupole interactions for sets of magnetically equivalent ligand nuclei. Each particular set is denoted by the index k, the individual nuclei of set k by kx. 

Besides a strongly coupled proton with a nearly isotropic hfc of Ah —20 MHz, two clearly separated nitrogen peaks between 15-26 MHz with unresolved quadrupole and nuclear Zeeman splittings have been observed along all three turning points of the g tensor (Fig. 39b). In the evaluation of the hf data collected in Table 12.1 it is assumed that the two metal-coordinated 14N exhibit roughly axial hfs tensors with the Ajj1 values oriented approximately perpendicular to each other. 

The principle of the ENDOR method is illustrated in Fig. 1. It refers to the most simple spin system with an electron spin S = 1/2 and a nuclear spin I = 1/2 for which an isotropic hf interaction, aiso, is considered. In a steady state ENDOR experiment4, an EPR transition (A, D), called the observer, is partly saturated by microwave radiation of amplitude B while a driving rf field of amplitude B2, called the pump, induces nuclear transitions. At frequencies vj and v2, the rf field tends to equalize the populations within the ms-states. This alters the degree of saturation of the observer so that, in the display of the EPR signal height versus the radio frequency, two ENDOR lines at transition frequencies vj = aiso/2 - vn (A, B) and v2 = ais0/2 + v (C, D) will be observed (v = / NgnBo denotes the nuclear Zeeman frequency for a static field B0). 

H is the total Hamiltonian (in the angular frequency units) and L is the total Liouvillian, divided into three parts describing the nuclear spin system (Lj), the lattice (Ll) and the coupling between the two subsystems (L/l). The symbol x is the density operator for the whole system, expressible as the direct product of the density operators for spin (p) and lattice (a), x = p <8> ci. The Liouvillian (Lj) for the spin system is the commutator with the nuclear Zeeman Hamiltonian (we thus treat the nuclear spin system as an ensemble of non-interacting spins in a magnetic field). Ll will be defined later and Ljl... 

HypB protein, 47 289 HypC protein, 47 289 Hyperfine coupling, 13 149-178 anisotropic, 13 150-161 Hyperfine coupling anisotropic dipolar, 13 150-154 nuclear Zeeman interaction, 13 155 quadrupole interaction, 13 154, 155 factors affecting magnitude of metal influence of charge on metal, 13 169-170 isotropic and anisotropic, 13 166-170 libration, 13 170... 

The nuclear Zeeman term describes the interaction of the nuclear spins with the external magnetic field. Just as the hyperfine splitting, this term is not incorporated in the original purely electronic Breit-Pauli Hamiltonian as presented in Eqs. (59) and (60) but becomes relevant for ESR spectroscopy. 

For high accuracy, it is necessary to add the nuclear-Zeeman and electric-quadrupole terms... 

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