The Hyperfine and Nuclear Quadrupole Coupling Tensors

The Schonland procedure is also applicable for the determination of hyperfine coupling tensors by ESR and ENDOR, for the zero-field splitting tensor (S V2) by ESR, and the nuclear quadrupole couplings for / Vi by ENDOR and ESEEM, discussed in the following sections. 

The Schonland procedure to obtain the hyperfine coupling tensor differs in some details depending on the magnitude of the coupling and on the applied methods, usually ESR or ENDOR. 

Formulae for the yz-, and zx-planes are obtained as in Section 3.3.2 by cyclic permutations of the X, y, and z indices. Thus, to obtain the tensor gA g the separation A between adjacent hyperfine lines and the. g-factor are both measured at each angle 0 in the three planes. The tensor is then obtained by an algebraic procedure [12] using the g-tensor determined from the same set of measurements. The analysis is simpler for isotropic g, see Exercise E3.9. 

This procedure (neglect of nuclear Zeeman term) is sometimes also adopted to obtain hyperfine coupling tensors from ESR measurements of free radicals. The method is, however, not suitable for the analysis of hyperfine structure due to a-H in jr-electron radicals of the type )Cc-H at X-band, and other cases where the anisotropic hyperfine coupling and the nuclear Zeeman energy are of comparable magnitudes, as discussed for case 3 below. 

The static magnetic field is normally constant or nearly so during the measurements. The tensor can then be obtained by a Schonland type fit. After 

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The analysis in Chapter 3 shows that fittings to the quantities G and P as a function of crystal orientation with respect to the magnetic field according to the Schonland method yield the elements of the hyperfine and nuclear quadrupole coupling tensors. A simple method therefore involves separate measurements of G and P from the observed ENDOR frequencies. 

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