Lindhard-Mermin dielectric function

Several different models for (k,CO) were explored by them, including the (local) Drade model, a hydrodynamic model, and the Lindhard-Mermin dielectric function. At low frequencies, much below the plasma frequency, they found that the imaginary part of the polarizability was actually enhanced, but that at higher frequencies this enhancement was not as pronounced. The enhancement was attributed to the excitation of particle-hole pairs in the metal. 

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... 

In Eq. (5.63), kp is the Fermi wavevector. This dielectric constant can be used in the framework of the specular scattering or semiclassical infinite-barrier (SCIB) model for planar metal surface [88]. Within the framework of such approach, the different descriptions of the metal response discussed so far (local dielectrics, hydrod3mamic dielectric function and Lindhard-Mermin dielectric function) can be compared. This has been done in Ref. [89] for the metal-induced non radiative rate of a molecule close to an Ag surface. The results are summarized in Fig. 5.9. 

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). 

Figure 5.9 Non radiative decay rate Ynr of biacetyl in an ammonia matrix as a function of the metal-molecule distance from a silver surface described through a local, a modified hydrodynamic [Eq. (5.61)] and a modified Lindhard-Mermin [Eq. (5.62)] dielectric constant. The molecular plane is parallel to the metal surface. Reprinted with permission from Ref [89]. Cop5n lght [2003], American Institute of Physics.

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