Random phase approximation: Difference between revisions

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[[File:Random phase approximation ring diagrams.png|thumb|400px|Ring diagrams that are summed up in order to obtain the RPA approximation. Above bold lines stand for interacting Green functions, non-bold lines stand for non-interaction Green function, and dashed lines stand for two-body interactions.]]

The '''random phase approximation''' ('''RPA''') is an approximation method in [[condensed matter physics]] and in [[nuclear physics]]. It was first introduced by [[David Bohm]] and [[David Pines]] as an important result in a series of seminal papers of 1952 and 1953.<ref>D. Bohm and D. Pines: ''A Collective Description of Electron Interactions. I. Magnetic Interactions'', Phys. Rev. '''82''', 625–634 (1951) ([http://prola.aps.org/abstract/PR/v82/i5/p625_1 abstract])</ref><ref>D. Pines and D. Bohm: ''A Collective Description of Electron Interactions: II. Collective vs Individual Particle Aspects of the Interactions'', Phys. Rev. '''85''', 338–353 (1952) ([http://prola.aps.org/abstract/PR/v85/i2/p338_1 abstract])</ref><ref>D. Bohm and D. Pines: ''A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas'', Phys. Rev. '''92''', 609–625 (1953) ([http://prola.aps.org/abstract/PR/v92/i3/p609_1 abstract])</ref> For decades physicists had been trying to incorporate the effect of microscopic quantum mechanical interactions between electrons in the theory of matter. Bohm and Pines' RPA accounts for the weak screened Coulomb interaction, and is commonly used for describing the dynamic linear electronic response of electron systems.

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''_ext('''r''') and a screening potential ''V''_sc('''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