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The effects of various external probes on a gas of interacting electrons confined to a foil are examined in an approximation for the response functions which reduces to the random-phase approximation for a bulk sample. Some band effects are included in a phenomenological manner. Surface corrections to the bulk properties are found which cannot be obtained in a wave-number-independent treatment nor in the Born approximation. The momentum dependence of the surface plasmon's resonant frequency is found and the response of the system to fast incident electrons and electromagnetic radiation is calculated.
P. A. Fedders (Tue,) studied this question.