Pair-correlation function at zero-interelectronic distance and its coupling-constant average in electron gas

• Published in: Physica. B, Condensed matter Condensed matter, 2002-09, Vol.322 (3), p.419-422
• Main Author: Van Cong, H.
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Density functional theory; Density functional theory, local density approximation; Electron gas; Electron gas, Fermi gas; Electron states; Exact sciences and technology; Fermion systems; Physics; Theories and models of many electron systems
• ISSN: 0921-4526; 1873-2135
• DOI: 10.1016/S0921-4526(02)01311-X

Based on its exact asymptotic forms obtained in the high- and low-density limits, an accurate simple expression for the short-range pair-correlation function at zero-interelectronic distance, G, for the uniform electron gas of any Wigner–Seitz radius in units of the Bohr radius r s and relative spin polarization, ζ, is investigated. Therefore, the coupling-constant average of this pair-correlation function, 〈 G〉, is determined and calculated. We find that for any r s and ζ the maximal relative deviations in absolute values between our numerical results of G and 〈 G〉 and the corresponding ones calculated, using our spin-scaling relation and the accurate formula of G for ζ=0 obtained by Yasuhara (Solid State Commun. 11 (1972) 1481), are equal to 4.51% and 2.41%, while for ζ=1 those between ours and the corresponding ones obtained recently by Gori–Giorgi and Perdew (Phys. Rev. B 64 (2001) 155102) are found to be equal to 77.28% and 20.19%, respectively.