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.

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

Wave-number dependence of the static screening function of an interacting electron gas. II. Higher-order exchange and correlation effects

1970 ◽  
Vol 48 (2) ◽  
pp. 167-181 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Density Dependence ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Interpolation Formula ◽  
Higher Order ◽  
Wave Number ◽  
Correlation Effects ◽  
Many Body ◽  
Static Screening

An interpolation formula is suggested for the wave-number and density dependence of the static screening function for an interacting electron gas in its ground state. The approximate screening function simulates a number of properties of the exact screening function which have been established by analysis of its many-body perturbation expansion. The accuracy of the interpolation formula is discussed and is considered to be adequate for practical calculations in the range of intermediate metallic densities.

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 SCREENING FUNCTION OF AN INTERACTING ELECTRON GAS

1966 ◽  
Vol 44 (9) ◽  
pp. 2137-2171 ◽  
Author(s):  
D. J. W. Geldart ◽  
S. H. Vosko
Keyword(s):  
Electron Gas ◽  
Substantial Contribution ◽  
Fundamental Relation ◽  
Many Body ◽  
Screening Constant ◽  
Self Energy ◽  
Self Consistent ◽  
Small Wave ◽  
Many Body Perturbation Theory ◽  
Zero Frequency

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

Wave-number dependence of the static screening function of an interacting electron gas. I. Lowest-order Hartree–Fock corrections

1970 ◽  
Vol 48 (2) ◽  
pp. 155-165 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Coulomb Interaction ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Wave Number ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Static Screening ◽  
Zero Frequency

The lowest-order Hartree–Fock contributions to the zero frequency screening function are examined for an interacting electron gas in its ground state. Computational methods are developed to treat singularities associated with the bare coulomb interaction and vanishing energy denominators of the many-body perturbation expansion. Numerical results are given. The wave-number dependence in the intermediate (k ~ kF) range differs considerably from that of previous estimates.

The description of collective motions in terms of many-body perturbation theory III. The extension of the theory to the non-uniform gas

1958 ◽  
Vol 244 (1237) ◽  
pp. 199-211 ◽  
Keyword(s):  
Correlation Energy ◽  
Electron Gas ◽  
Approximate Expression ◽  
Many Body ◽  
Local Field Correction ◽  
Consistent Field ◽  
Homogeneous Integral Equation ◽  
Collective Motions ◽  
Self Consistent Field ◽  
Many Body Perturbation Theory

The theory previously developed and applied to calculate the correlation energy of a free-electron gas is extended in this paper to calculate the energy of an electron gas in a potential field. Two new features arise: (i) the introduction of a self-consistent field which is a generalization of the ordinary Hartree field; (ii) the occurrence of ‘local field correction’ effects. It is shown that the energy of the gas can be expressed in terms of the eigenvalues of a certain homogeneous integral equation and a stationary principle for these eigenvalues is given. The theory is applied to crystals and an approximate expression for the correlation energy of a metal is derived neglecting Lorentz-Lorenz corrections effects.

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