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In the RPA, [[electron]]s are assumed to respond only to the [[total electric potential]] ''V''('''r''') which is the sum of the external perturbing potential ''V''<sub>ext</sub>('''r''') and a screening potential ''V''<sub>sc</sub>('''r'''). The external perturbing potential is assumed to oscillate at a single frequency ω, so that the model yields via a [[self-consistent field]] (SCF) method <ref>H. Ehrenreich and M. H. Cohen, [http://dx.doi.org/10.1103/PhysRev.115.786 Phys. Rev. '''115''', 786 (1959)]</ref> a
dynamic [[dielectric]] function denoted by ε<sub>RPA</sub>('''k''', ω).
The contribution to the [[dielectric function]] from the total electric potential is assumed to ''average out'', so that only the potential at wave vector '''k''' contributes. This is what is meant by the random phase approximation. The resulting dielectric function, also called the ''[[Lindhard theory|Lindhard dielectric function]]'',<ref>J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. '''28''', 8 (1954)</ref><ref>N. W. Ashcroft and N. D. Mermin, ''Solid State Physics'' (Thomson Learning, Toronto, 1976)</ref> correctly predicts a number of properties of the electron gas, including [[plasmon]]s.<ref>G. D. Mahan, ''Many-Particle Physics'', 2nd ed. (Plenum Press, New York, 1990)</ref>
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