Hyperfine splitting isotropic contribution

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]... 

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... 

In the general case, both isotropic and anisotropic hyperfine interachons contribute to the experimental spectrum. The whole interaction is therefore dependent once again on orientation and must be expressed by a tensor. The effechve spin Hamiltonian for this more reahstic descriphon of a paramagnehc species in the solid state was given earher in Equahon 1.28. Nevertheless the A tensor may be split into its component isotropic and anisotropic parts as follows ... 

Electron Spin Resonance (ESR) spectroscopy was used to characterize sodium atoms in the highly non-stoichiometric Na Siigg clathrates [28, 88, 89]. In addition to an intense and broad line centered at g = 2.0021 due to the presence of Na clusters, four sharp lines of a hyperfine quadruplet with an isotropic hf splitting of 13.3 mT was observed, corresponding to isolated Na atoms (I = 3/2). From the observed hf splitting value, the spin density in the 3 s orbitals was estimated to be 45 % of one unit spin density [88]. With decreasing x values, the intensity of the cluster line decreases, whereas those of the hyperfine quadruplet lines increased. For the lowest x content, the contribution of the cluster line to the total intensity was very low and a quantitative determination of the residual x content was possible by comparison of the observed intensities with those of standards (diluted solutions of Cr " doped alum). The ultimate e sodium content in Na Siise was found to be close to 0.006, i.e. 35 ppm [89]. 

Combination of isotropy and anisotropy Since any orbital may be considered as a hybrid of suitable combinations of s, p or d orbitals, so also may a hyperfine coupling be divided into a contribution arising from p or d orbitals (anisotropic) and s orbitals (isotropic). In general both isotropic and anisotropic hyperfine couplings occur when one or more nuclei with 1 0 are present in the system. The whole interaction is therefore dependent on orientation and must be expressed by the second rank A tensor as given in Equation [13]. The A tensor may be split into an anisotropic and isotropic part as follows... 

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