skip to main content

Title: Static dielectric function with exact exchange contribution in the electron liquid

The exchange contribution, Π{sub 1}(k, 0), to the static dielectric function in the electron liquid is evaluated exactly. Expression for it is derived analytically in terms of one quadrature. The expression, as presented in Eq. (3) in the Introduction, turns out to be very simple. A fully explicit expression (with no more integral in it) for Π{sub 1}(k, 0) is further developed in terms of series. Equation (3) is proved to be equal to the expression obtained before under some mathematical assumption by Engel and Vosko [Phys. Rev. B 42, 4940 (1990)], thus in the meanwhile putting the latter on a rigorous basis. The expansions of Π{sub 1}(k, 0) at the wavevectors of k = 0, k = 2k{sub F}, and at limiting large k are derived. The results all verify those obtained by Engel and Vosko.
Authors:
 [1]
  1. Department of Physics, Peking University, Beijing 100871 (China)
Publication Date:
OSTI Identifier:
22479552
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIELECTRIC MATERIALS; ELECTRONS; EQUATIONS; FUNCTIONS; INTEGRALS; LIQUIDS; QUADRATURES