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A model anisotropic system, suggestive of the graphite structure, is investigated: It consists of a series of equally spaced parallel planes. A finite two-dimensional density of electrons in each plane is allowed to move freely in the plane, but tunneling between planes does not take place. The dielectric screening of a point charge is evaluated exactly in the random-phase approximation. For realistic electron densities and interlayer separations the screened potential drops off very rapidly both in the plane of the charge and perpendicular to it. The induced charge density is determined, and validity of the Thomas-Fermi approximation is discussed.
Visscher et al. (Thu,) studied this question.