Electrons Lindhard dielectric function

Kliewer, K. L, and Fuchs, R. (1969] Lindhard dielectric functions with a finite electron lifetime, Phys. Rev., 181, 552-558. 

Fermi level that is, we must have k — k/2 < fcp and k + k/2 > kp (or vice versa), since otherwise the occupation numbers are either both 0 or both 1. These considerations indicate that the contributions to the integral will come from electron-hole excitations with total momentum k. At T = 0, the integral over k in the Lindhard dielectric function can be evaluated to yield... 

In the examples presented here, the extension to the Lindhard RPA [23] suggested by Mermin [24] is used for the bulk dielectric function. This allows one to use non-zero values of the electron gas damping, keeping the number of electrons in the system constant. We want to emphasize that this description incorporates both single-particle excitations (creation of electron-hole pairs) and collective excitations (bulk and surface plasmons). 

When the molecule is close to the metal, the spatially inhomogeneous field can carry the needed momentum. To take into account these electron-hole pair excitations and, more generally, to improve the description of the q-dependence of the dielectric constant, one can use a modified Lindhard-Mermin electric permittivity [84, 85], The Lindhard-Mermin dielectric function is the Lindhard function... 

We wish to derive the Lindhard dielectric response function for the free-electron gas, using perturbation theory. The charge density is defined in terms of the single-particle wavefunctions as... 

In this equation, n is the conduction electron density, Ep the Fermi energy and kp the radius of the Fermi sphere. e(Q) given by (4.159) is also known as the Lindhard dielectric constant [4.69]. For Q 0, the quantity in the square brackets is equal to 1 and e(Q) then reduces to the Thomas-Fermi dielectric function [4.69],... 

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