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In the RPA, electrons 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 name="Ehrenreich Cohen pp. 786–790">{{cite journal | last1=Ehrenreich | first1=H. | last2=Cohen | first2=M. H. | title=Self-Consistent Field Approach to the Many-Electron Problem | journal=Physical Review | publisher=American Physical Society (APS) | volume=115 | issue=4 | date=15 August 1959 | issn=0031-899X | doi=10.1103/physrev.115.786 | pages=786–790| bibcode=1959PhRv..115..786E }}</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
The RPA was criticized in the late 1950s for overcounting the degrees of freedom and the call for justification led to intense work among theoretical physicists. In a seminal paper [[Murray Gell-Mann]] and [[Keith Brueckner]] showed that the RPA can be derived from a summation of leading-order chain [[Feynman diagram]]s in a dense electron gas.<ref name="Gell-Mann Brueckner pp. 364–368">{{cite journal | last1=Gell-Mann | first1=Murray | last2=Brueckner | first2=Keith A. | title=Correlation Energy of an Electron Gas at High Density | journal=Physical Review | publisher=American Physical Society (APS) | volume=106 | issue=2 | date=15 April 1957 | issn=0031-899X | doi=10.1103/physrev.106.364 | pages=364–368| bibcode=1957PhRv..106..364G | s2cid=120701027 | url=https://authors.library.caltech.edu/3713/1/GELpr57b.pdf }}</ref>
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