Magnetic hyperfine coupling tensor

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 ... 

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

The hyperfine coupling tensor (A) describes the interaction between the electronic spin density and the nuclear magnetic momentum, and can be split into two terms. The first term, usually referred to as Fermi contact interaction, is an isotropic contribution also known as hyperfine coupling constant (HCC), and is related to the spin density at the corresponding nucleus n by [25]... 

Where (3 is the Bohr magneton, H0 is the applied magnetic field, g is the g-tensor, S is the electron spin, I is the nuclear spin, gn and (3n.are the nuclear splitting factor and the nuclear magneton. The hyperfine coupling tensor A consists of an isotropic contact interaction... 

The third term of the nuclear Hamiltonian contains two contributions. The nuclear Zeeman term couples the magnetic moment of the nucleus to the external magnetic field Bo. Furthermore, there is a term that describes the interaction of the nuclear spin with the internal magnetic hyperfine field. For paramagnetic samples this is often done in terms of the hyperfine coupling tensor, which multiplied by the spin... 

Figure 11. The best fit has been found for 5 = 0.7 0.01 nuns, Aitg =—3.25 0.01 nuns, " =(2.11, 2.19, 2.00), "T/ nMn = (-45, 10, 19) T, tj = 0.74 0.1, D = 7.2 0.5 cm, and EID = 0.16 0.02. The zero-field splitting parameter D = 7.2 0.5 cm is comparable to that found for rabredoxin from Clostridium pasteurianum (D = 7.6cm Surprisingly, the rhombicity parameter E/D = 0.16 0.02 differs somewhat from that of rubre-doxin from C. pasteurianum (E/D = 0.28). The hyperfine coupling tensor has been determined to be A = (-14.5, -9.2, -27.5) T. The anisotropy of the hyperfine conpling tensor is cansed by spin-orbit confribntions to the internal magnetic hyperfine field.

E/Z) = 0.16 0.02 differs somewhat from that of rubredoxin from C. pasteurianum ElD = 0.28). The hyperfine coupling tensor has been determined to be A = (—14.5, —9.2, —27.5)T. The anisotropy of the hyperfine coupling tensor is caused by spin-orbit contributions to the internal magnetic hyperfine field. 

The first-order term with respect to a nuclear magnetic moment I is the hyperfine coupling tensor A, giving the coupling the between the nuclear and electronic magnetic moments. The leading order term (c ) can be evaluated as a simple expectation... 

Fig. 2.6 Angular variation plot (rotation axis perpendicular to the magnetic field) for the ENDOR lines of the malonic acid radical, HC (COOH)2 in a single crystal of mtilonic acid. The fully drawn curves are calculated using the hyperfine coupling tensors obriiined from measurements in three planes, according to the Schonland procedure. The curve at high frequency corresponds to Ha in Table 2.1, while the low-frequency lines are attributed to H-atoms at neighbour molecules. The figure is reproduced from [24] with permission from the American Chemictil Society...

Fig. 3.26 Schematic powder ENDOR spectra of an S = Vi species with axially symmetric g and H hyperfine structure. ENDOR spectra with the magnetic field locked at g and gi, respectively, are single-crystal like due to angular selection. The lines for electronic quantum numbers ms = Vi and -V2 are separated by distances equal to A and Aj, the principal values of the hyperfine coupling tensor as indicated in the figure...

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