Enhancement Factors from Pauli Potential

The Weizsacker functional is exact for noninteracting bosons. The correction to the Weizshcker functional then is solely due to the Pauli principle. The Pauli kinetic energy can then be defined as 

Because the Weizsacker kinetic energy functional is a lower bound, the Pauli kinetic energy is always If one differentiates the resulting energy 

Here te(r) is the local Pauli kinetic energy, which is defined as le(r) = [ -y/ l,  

The nonnegativity constraints on the Pauli correction and its potential give stringent constraints on the types of functionals that can be considered. The most popular form for the kinetic energy has attempted to modify the enhancement factors from Thomas-Fermi-based kinetic energy functionals, defining  

The resulting functionals, however, become negative (and even diverge) near the atomic nuclei. This problem is avoided by using so-called reduced gradient approximations, where the Pauli kinetic energy has the form  

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The temperature dependence of the g-factor is shown in fig. 48 (Schlott 1989). For temperatures above 20 K, g T) closely follows the tempeiatuie dependence of the bulk susceptibility. At low temperatures the onset of moment compensation is clearly visible leading to an enhanced temperature-indqrendent Pauli-spin susceptibility. Fig. 48 clearly indicates the power and the potential of magnetic resonance experiments Moment compensation can easily be detected in the local susceptibility of microscopic measurements. It can hardly be detected in bulk measurements due to the contributions from defect states with local moments. 

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