Pair-distribution function and its coupling-constant average for the spin-polarized electron gas

1992 ◽  
Vol 46 (20) ◽  
pp. 12947-12954 ◽  
Author(s):  
John P. Perdew ◽  
Yue Wang
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas ◽  
Coupling Constant ◽  
Spin Polarized

scholarly journals Genetic algorithm for the pair distribution function of the electron gas

2011 ◽  
Vol 3 (4) ◽  
pp. 283-289 ◽  
Author(s):  
Fernando Vericat ◽  
César O. Stoico ◽  
C. Manuel Carlevaro ◽  
Danilo G. Renzi
Keyword(s):  
Genetic Algorithm ◽  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas

Spin-Up-Spin-Down Pair Distribution Function at Metallic Densities

1972 ◽  
Vol 50 (15) ◽  
pp. 1756-1763 ◽  
Author(s):  
B. B. J. Hede ◽  
J. P. Carbotte
Keyword(s):  
Distribution Function ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Born Approximation ◽  
Pair Distribution Function ◽  
Short Range ◽  
Electron Gas ◽  
Scattering Effects ◽  
Wide Range ◽  
Short Range Correlations

Correlations in an electron gas are particularly important at metallic densities because the potential energy cannot be ignored in comparison with the kinetic energy; in particular, interactions are not weak as r → 0, so that a simple Born approximation does not hold in this limit. Short-range correlations between oppositely-spinned electrons can be accounted for by an infinite series of particle–particle ladder diagrams. It leads to a Bethe–Goldstone type of equation which can be solved by an angle-averaged approximation. The resultant spin-up-down p.d.f. is positive over a wide range of metallic densities. A further correction by including particle–hole scattering effects changes the previous results only slightly.

THE PAIR DISTRIBUTION FUNCTION OF AN INTERACTING ELECTRON GAS

1967 ◽  
Vol 45 (9) ◽  
pp. 3139-3161 ◽  
Author(s):  
D. J. W. Geldart
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Electron Gas ◽  
Pauli Principle ◽  
Distribution Functions ◽  
Upper And Lower Bounds ◽  
Wave Number ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Simple Class

The pair distribution function, in the limit of zero separation, of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. It is shown that the usual methods for maintaining self-consistency in approximate calculations violate, in general, the nonnegativity of the pair distribution function. In particular, the Pauli principle yields a rigorous sum rule for the parallel spin density fluctuation propagator which is not satisfied. Upper and lower bounds on one-loop and multiloop contributions to the pair distribution functions are given. These bounds are used to discuss correlation corrections. An improved wave-number dependence is given for Hubbard's (1957) approximation to the screening function and numerical results are given for a simple class of exchange corrections.

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