Note on “The Electron Density in the Thomas-Fermi Theory”

1974 ◽  
Vol 42 (8) ◽  
pp. 698-698
Author(s):  
David R. Harrington
Keyword(s):  
Electron Density ◽  
Fermi Theory ◽  
Thomas Fermi

The Electron Density in the Thomas-Fermi Theory

1973 ◽  
Vol 41 (7) ◽  
pp. 906-909 ◽  
Author(s):  
David R. Harrington
Keyword(s):  
Electron Density ◽  
Fermi Theory ◽  
Thomas Fermi

Statistical theory of electron densities at nonzero temperatures

1992 ◽  
Vol 70 (2) ◽  
pp. 478-481 ◽  
Author(s):  
Gary G. Hoffman ◽  
Robert A. Harris ◽  
Lawrence R. Pratt
Keyword(s):  
Statistical Theory ◽  
Electron Density ◽  
Ground State ◽  
Finite Temperature ◽  
Density Functional ◽  
Plasma Chemistry ◽  
Plasma Simulation ◽  
Fermi Theory ◽  
Electron Densities ◽  
Thomas Fermi

This paper derives the finite temperature optimized Thomas–Fermi theory applicable to the electronic structure of atoms, molecules, and ions under conditions where both the bulk electron density and the electron temperature are substantial. The derivation provides a simple rule for transcribing the finite temperature case from the previous ground-state statistical electron-density functional theories. Keywords: plasma simulation, plasma chemistry, statistical theory of electron densities, Thomas–Fermi theory, optimized Thomas–Fermi theory.

Statistical theory of electron densities: multiple scattering perturbation theory

1991 ◽  
Vol 435 (1894) ◽  
pp. 245-255 ◽  
Keyword(s):  
Perturbation Theory ◽  
Multiple Scattering ◽  
Electron Density ◽  
Energy Scale ◽  
Zero Order ◽  
Fermi Theory ◽  
Electron Densities ◽  
Thomas Fermi ◽  
Order Contribution ◽  
Explicit Formulae

A multiple scattering perturbation theory for electron densities, originally discussed by N. H. March and A. M. Murray, is derived in a new way. The new derivation does not depend on special choices for the origin of the energy scale. Therefore, it clarifies the point that the result of the perturbation calculation, the electron density, should be independent of the energy origin chosen for the purposes of the calculation even though the individual terms of the series do depend on that choice. This point is not evident in the previous derivations. Appreciation of this point permits adoption of an origin of the energy scale which varies with position without any change in form of the perturbation expansion. This extends the original theory beyond the significant limitation that the zero-order result is the uniform density of the free-electron gas. In particular, the energy origin can be chosen so that the zero-order contribution reproduces any physical model electron density. The theory then gives successive corrections and allows investigation of the usefulness of physical models by an analysis of the low-order corrections. These ideas permit a compact new derivation of the Thomas–Fermi theory, a derivation which also produces explicit formulae for corrections of all orders. An especially useful choice for the energy origin yields the optimized Thomas–Fermi theory as the zero-order contribution. Therefore, new results of this development are explicit formulae for the corrections to that simple theory.

Angular terms in the electron density for the phosphine molecule

1956 ◽  
Vol 52 (4) ◽  
pp. 703-711 ◽  
Author(s):  
R. A. Ballinger ◽  
N. H. March
Keyword(s):  
Variational Method ◽  
Charge Density ◽  
Electron Density ◽  
Legendre Polynomials ◽  
Molecular Axis ◽  
Thomas Fermi ◽  
Line Charge ◽  
Density Map ◽  
Circular Line

ABSTRACTAn attempt is made to calculate the first few angular terms in an expansion of the electron density for the phosphine molecule in Legendre polynomials. Such an expansion is appropriate for a model in which the three hydrogen nuclei are smeared to form a circular line charge. The Thomas–Fermi approximation has been used in conjunction with the variational method. The variational density employed includes p and f angular terms. An approximate charge density map is constructed for a plane containing the molecular axis in order to demonstrate the effect of the angular terms.

Thomas-Fermi Theory of an Inhomogeneous Electron Liquid Generalized to Incorporate Density Gradients

1998 ◽  
Vol 36 (2) ◽  
pp. 91-103 ◽  
Author(s):  
C. Amovilli ◽  
N. H. March ◽  
T. G. Schmalz ◽  
D. J. Klein
Keyword(s):  
Density Gradients ◽  
Fermi Theory ◽  
Thomas Fermi

New Thomas-Fermi theory: A test

1982 ◽  
Vol 25 (4) ◽  
pp. 2399-2401 ◽  
Author(s):  
Lester L. DeRaad ◽  
Julian Schwinger
Keyword(s):  
Fermi Theory ◽  
Thomas Fermi

scholarly journals Caloric curve for finite nuclei in Thomas-Fermi theory

1997 ◽  
Vol 55 (4) ◽  
pp. R1641-R1644 ◽  
Author(s):  
J. N. De ◽  
S. Das Gupta ◽  
S. Shlomo ◽  
S. K. Samaddar
Keyword(s):  
Fermi Theory ◽  
Thomas Fermi ◽  
Caloric Curve ◽  
Finite Nuclei
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