Screening function Lindhard

An especially useful approximation for the Thomas-Fermi potential has been developed by Lindhard and co-workers where the screening function is assumed to have the form ... 

Here Jk = F( k ) is the Lindhard screening function [26, 34]. Note that noncollinear or incommensurate spin states then correspond to a minimum ofV(k). 

Lindhard and coworkers proposed two somewhat simpler and more approximative Thomas-Fermi screening functions given by... 

Fig. 6. A comparison of the screening functions F(r)/t(.(r) for the Coulomb (dash-dotted line), Bohr (solid line), Moli re (dashed line), and Ziegler-Biersack-Lindhard (dotted line) potentials.

A special limit of the Lindhard response function is known as the Thomas-Fermi screening. This is based on the limit of the Lindhard function for k kp. Consistent with our earlier remarks, this corresponds to electron-hole excitations with small total momentum relative to the Fermi momentum. In this case, expanding the occupation numbers n(k k/2) through their definition in Eq. (2.106) about k = 0, we obtain to first order in k... 

In 1965 Lindhard demonstrated that a charged particle moving closely parallel to an atomic row in a crystal experiences a continuum ("string ) potential made up from he atomic potentials in the row. The two dimensional potential, Vr(p) Is cylindrically symmetric and is function only of p, the distance from the row. For any atomic screened Coulomb potential... 

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