Exchange interaction isotropic

The dominating contribution to exchange interaction is isotropic as expressed by the scalar parameter used in (4.80) anisotropic and antisymmetric contributions [87] are mostly ignored. Equation (4.80) can be evaluated in the coupled presenta-... 

The Lines approximation is expected to be quite accurate for the description of the exchange interaction between a strongly axial doublet and an arbitrary isotropic spin. For all other cases, the Lines model [84] is a reasonable approximation. Efficient implementation of the Lines model was done in the program POLY ANISO. 

Let us now consider the metallic regime, following the discussion of [18]. For nuclei coupled to a mobile system of independent electrons by an isotropic exchange interaction of the form A l S, where I is the nuclear spin and S the electron s spin, the Knight shift can be written as... 

Perhaps the most detailed studies of both the isotropic and anisotropic exchange interactions have been made for InP, where the anisotropic (pseudo-dipolar) part of the 31P-115In exchange coupling was shown to reduce the measured 31P second moments from theoretical values calculated from dipolar couplings alone [255, 256]. Double and triple resonance 31P MAS-NMR experiments have also provided much information as a result of the existence of the two nearly identical isotopes of... 

Equation 7.1 utilizes exchange coefficients to predict steady-state BCFs and ATswS, and the model assumptions include a uniform lipid phase enclosed in a non-interactive membrane. The model shows that the magnitude of a BMO s BCF or an SPMD s Ksvj is affected by variations in ku and/or ke, unless both constants rise or fall proportionally. In the case of SPMDs, Huckins et al. (1993,2002a) have shown that the uptake and release process is essentially isotropic for HOCs. When residue exchange is isotropic, AfswS will remain relatively constant even when exposure conditions affect SPMD ku and ke values. This is not always the case for BMOs, yet isotropic exchange is a fundamental assumption of EP theory. 

The coefficients a and b (see Table 3.2) take into account the restrictions in spin dimensionality. For a = b= 1, the Heisenberg model with isotropic exchange interaction and isotropic susceptibility results. The combination of a = 1 and b = 0 yields the strictly anisotropic Ising model, in which the orientation of the spins is restricted to the z-axis. Consequently, the susceptibility is strongly orientation dependent and one needs to differentiate between x" in the direction of the z-axis ( easy axis ) and x perpendicular to z. The molar susceptibilities are then related as... 

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