Abstract
For a uniform electron gas of density n=+=3/4π=π/192 and spin polarization ζ=(-)/n, we study the Fourier transform ρ(k,,ζ) of the correlation hole, as well as the correlation energy (,ζ)=dk ρ/π. In the high-density (→0) limit, we find a simple scaling relation ρ/π→f(z,ζ), where z=k/, g=[(1+ζ+(1-ζ]/2, and f(z,1)=f(z,0). The function f(z,ζ) is only weakly ζ dependent, and its small-z expansion -3z/+4 √3 /+... is also the exact small-wave-vector (k→0) expansion for any or ζ. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Padé representations for ρ at any k, , or ζ, one within and one beyond the random-phase approximation (RPA). We also show that ρ¯ obeys a generalization of Misawa’s spin-scaling relation for , and that the low-density (→∞) limit of is ∼.
- Received 10 June 1991
DOI:https://doi.org/10.1103/PhysRevB.44.13298
©1991 American Physical Society