Random phase approximation

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The random phase -approximation ( English random-phase approximation , RPA, dt. Approximately, approximation random phase ') is an approximation method for the treatment of quantum mechanical many-body systems having the Hartree-Fock approximation or, more generally, the mean-field theory generalized and sometimes called dynamic Hartree -Fock approximation is called. The method is used, for example, in nuclear physics to describe collective excitations.

So-called. Bubble diagrams that add up to the RPA.
Solid lines stand for interacting or non-interacting Green functions , dashed lines for two-particle interactions.

RPA is a microscopic method to describe the structure of collective excitation based on 1-particle-1-hole states , which corresponds to a simple diagrammatic approximation (summation of so-called bubble diagrams ).

The method is related to the Tamm-Dancoff approximation (TDA), but differs in that ground-state correlations are also possible.

Special cases are the quasiparticle random-phase approximation (QRPA), relativistic random-phase approximation (RRPA), continuum quasiparticle random-phase approximation (CQRPA), relativistic quasiparticle random-phase approximation (RQRPA).

The method was introduced by David Bohm and David Pines in the 1950s for electron gases and interpreted in 1957 by Keith Brueckner and Murray Gell-Mann as the summation of Feynman diagrams, which was an essential support of the then controversial RPA theory.

Individual evidence

  1. ^ David Bohm, David Pines: A Collective Description of Electron Interactions. I. Magnetic Interactions . In: Physical Review . tape 82 , no. 5 , June 1, 1951, p. 625-634 , doi : 10.1103 / PhysRev.82.625 .
  2. ^ David Pines, David Bohm: A Collective Description of Electron Interactions: II. Collective vs Individual Particle Aspects of the Interactions . In: Physical Review . tape 85 , no. 2 , January 15, 1952, p. 338-353 , doi : 10.1103 / PhysRev.85.338 .
  3. ^ David Bohm, David Pines: A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas . In: Physical Review . tape 92 , no. 3 , November 1, 1953, p. 609-625 , doi : 10.1103 / PhysRev.92.609 .
  4. ^ Murray Gell-Mann, Keith A. Brueckner: Correlation Energy of an Electron Gas at High Density . In: Physical Review . tape 106 , no. 2 , April 15, 1957, p. 364-368 , doi : 10.1103 / PhysRev.106.364 .