Random phase approximation: Difference between revisions

Revision as of 18:45, 23 November 2023

Revision as of 20:52, 23 November 2023

Line 1:

[[File:Random phase approximation ring diagrams.png|thumb|Bubble diagrams, which result in the RPA when summed up. Solid lines stand for interacting or non-interacting [[Green's function (many-body theory)|Green's functions]], dashed lines for two-particle 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 name="Bohm Pines pp. 625–634">{{cite journal | last1=Bohm | first1=David |author-link= David Bohm| last2=Pines | first2=David |author-link2=David Pines| title=A Collective Description of Electron Interactions. I. Magnetic Interactions | journal=Physical Review | publisher=American Physical Society (APS) | volume=82 | issue=5 | date=1 May 1951 | issn=0031-899X | doi=10.1103/physrev.82.625 | pages=625–634| bibcode=1951PhRv...82..625B }}</ref><ref name="Pines Bohm pp. 338–353">{{cite journal | last1=Pines | first1=David |author-link=David Pines| last2=Bohm | first2=David |author-link2=David Bohm| title=A Collective Description of Electron Interactions: II. CollectivevsIndividual Particle Aspects of the Interactions | journal=Physical Review | publisher=American Physical Society (APS) | volume=85 | issue=2 | date=15 January 1952 | issn=0031-899X | doi=10.1103/physrev.85.338 | pages=338–353| bibcode=1952PhRv...85..338P }}</ref><ref name="Bohm Pines pp. 609–625">{{cite journal | last1=Bohm | first1=David |author-link=David Bohm| last2=Pines | first2=David |author-link2=David Pines| title=A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas | journal=Physical Review | publisher=American Physical Society (APS) | volume=92 | issue=3 | date=1 October 1953 | issn=0031-899X | doi=10.1103/physrev.92.609 | pages=609–625| bibcode=1953PhRv...92..609B }}</ref> For decades physicists had been trying to incorporate the effect of microscopic [[Quantum mechanics|quantum mechanical]] interactions between [[Electron|electronselectron]]s 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. It was further developed to the relativistic form (RRPA) by solving the [[Dirac equation]].<ref>{{Cite journal |last=Deshmukh |first=Pranawa C. |author-link=Pranawachandra Deshmukh |last2=Manson |first2=Steven T. |date=September 2022-09 |title=Photoionization of Atomic Systems Using the Random-Phase Approximation Including Relativistic Interactions |url=https://www.mdpi.com/2218-2004/10/3/71 |journal=Atoms |language=en |volume=10 |issue=3 |pages=71 |doi=10.3390/atoms10030071 |issn=2218-2004 |doi-access=free}}</ref>.

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''_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 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_RPA('''k''', ''ω'').