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Penetration would reduce d. 85 A. This is greatly in excess of any reasonable Thomas-Fermi screening length but is compatible with Newns' results40 if rs is 3-4. The large increase in screening length relative to Thomas-Fermi theory is related to the low electron density near the surface of the metal. Beck and Celli65 also calculated the linear response of a metal to an external charge distribution by a method equivalent to that of Newns,40 with the electrons confined to a half-space by an infinite barrier.

In the simplest such theories, the free-energy density is a function of the local particle density. By requiring that the chemical potential (electrochemical potential, for a system of charged particles) be independent of z, one derives49 an equation for n(z). This approach has been applied to a one-component plasma, with a background step-function density of compensating charge, and gives results which agree well with the results of computer simulation for this problem. For liquid metals, one has to set up density functionals for the electrons and for the particles making up the positive background (ion cores).

68 The Thomas-Fermi response is discussed in detail, as well as the solutions to the relevant equations. Results are compared to those from self-consistent calculations (see below). 65 One can solve the Thomas-Fermi-Dirac equation numerically to obtain the electron density profile for any surface charge density, thus obtaining the capacitance of the metal surface as well as the surface potential. Here, one is not limited to the linearresponse regime. Making the metal one plate of a capacitor representing the interface, one finds that the inverse capacitance of the metal increases as qM becomes negative.

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