Isotropic values electron spin resonance

The electron densities for a spin electrons and for spin electrons are always equal in a singlet spin state, but in non-singlet spin states the densities may be different, giving a resultant spin density. If we evaluate the spin density function at the position of certain nuclei, it gives a value proportional to the isotropic hyperfine coupling constant that can be measured from electron spin resonance experiments. 

Fig. 18. The dashed curves represent the axially-symmetric powder pattern for the dangling bond observed at Si-SiOj interfaces (Caplan et al 1979) for several values of isotropic broadening W. The solid curve is the ESR spectrum in a-Si H. [Reprinted by permission of the publisher from Electron spin resonance studies of amorphous silicon, by D.K. Biegelsen, Proceedings of the Electron Resonance Society Symposium, Vol. 3, pp. 85 - 94. Copyright 1981 by Elsevier Science Publishing Co., Inc.]...

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]. 

For nitroxides in dilute liquid solution, the generally anisotropic spin Hamilton operator is simplified tremendously and, if imresolved proton hyperfine couplings are treated as line broadening, only the electron-Zeeman interaction and the hyperfine coupling to the magnetic nucleus (7 = 1) remain [20]. The g- and hyperfine (4-) tensors are averaged to isotropic values due to fast motion of the spin probe and the resonance condition for the irradiated microwave becomes... 

The conditions necessary for observation of proton magnetic resonance spectra in paramagnetic systems are well established (1). Either the electronic spin-lattice relaxation time, T, or a characteristic electronic exchange time, Te, must be short compared with the isotropic hyperfine contact interaction constant, in order for resonances to be observed. Proton resonances in paramagnetic systems are often shifted hundreds of cps from their values in the diamagnetic substances. These isotropic resonance shifts may arise from two causes, the hyperfine contact and pseudocontact interactions. The contact shift arises from the existence of unpaired spin-density at the resonating nucleus and is described by 1 (2) for systems obeying the Curie law. 

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