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Related papers: A new look at Thomas-Fermi Theory

200 papers

We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.

Mathematical Physics · Physics 2008-05-28 Francisco M. Fernandez

By extrapolating the energies of non-relativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row, even as…

Materials Science · Physics 2015-05-19 Lucian A. Constantin , John C. Snyder , John P. Perdew , Kieron Burke

We briefly review the Thomas-Fermi statistical model of atoms in the classical non-relativistic formulation and in the generalised finite-nucleus relativistic formulation. We then discuss the classical generalisation of the model to finite…

Astrophysics · Physics 2017-08-23 G. Bertone , R. Ruffini

We analyze the range of validity of Thomas Fermi theory for describing charge density modulations induced by external potentials in neutral graphene. We compare exact results obtained from a tight-binding calculation with those of linear…

Mesoscale and Nanoscale Physics · Physics 2010-09-07 L. Brey , H. A. Fertig

We study the non-uniform nuclear matter using the self-consistent Thomas--Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped…

Nuclear Theory · Physics 2014-06-11 Z. W. Zhang , H. Shen

An approximate analytical solution of the Thomas-Fermi equation for neutral atoms is obtained, using the Ritz variational method, which reproduces accurately the numerical solution, in the range $0\leq x\leq50$, and its derivative at $x=0$.…

Atomic Physics · Physics 2011-05-13 M. Oulne

Thomas-Fermi model is applied to describe some basic properties of a negative hydrogen ion in a strong electric field. The equilibrium ionic size, energy and polarizability of the ion are calculated. Collective modes of the dipole…

Materials Science · Physics 2013-02-25 Yuri Kornyushin

We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we…

Statistical Mechanics · Physics 2007-05-23 Jeng-Da Chai , John D. Weeks

We demonstrate that the charge distributions in Hubbard-model representations of transition metal oxide heterojucntions can be described by a Thomas-Fermi theory in which the energy is approximated as the sum of the electrostatic energy and…

Strongly Correlated Electrons · Physics 2009-11-13 Wei-Cheng Lee , A. H. MacDonald

The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, that there is a specific semiclassical limit in which…

Mathematical Physics · Physics 2022-02-14 Kieron Burke

The self-consistent Thomas-Fermi approximation is an essential method for studying the non-uniform nuclear matter with relativistic mean-field theory. In this method, the nucleon distribution in the Wigner-Seitz cell is obtained…

Nuclear Theory · Physics 2015-12-15 Zhao-wen Zhang , Hong Shen

Density functional theory for a simple model of dendrimers is proposed. The theory is based on fundamental measure theory which accounts for the hard-sphere repulsion of the segments and on the Wertheim first-order perturbation theory for…

Soft Condensed Matter · Physics 2012-11-12 Alexandr Malijevsky

We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density…

Nuclear Theory · Physics 2009-02-05 Anirban Bhattacharyya , T. Papenbrock

Nuclear density functional theory (DFT) is the only microscopic, global approach to the structure of atomic nuclei. It is used in numerous applications, from determining the limits of stability to gaining a deep understanding of the…

Nuclear Theory · Physics 2015-02-06 Nicolas Schunck , Jordan D. McDonnell , Jason Sarich , Stefan M. Wild , Dave Higdon

Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…

Classical Analysis and ODEs · Mathematics 2007-05-23 Allan Pinkus

We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation…

Mathematical Physics · Physics 2021-01-19 Heinz Siedentop

The exact form of the kinetic energy functional has remained elusive in orbital-free models of density functional theory (DFT). This has been the main stumbling block for the development of a general-purpose framework on this basis. Here,…

Mesoscale and Nanoscale Physics · Physics 2020-01-06 Thomas Pope , Werner Hofer

By incorporating the zero-point energy contribution we derive simple and accurate extensions of the usual Thomas-Fermi (TF) expressions for the ground-state properties of trapped Bose-Einstein condensates that remain valid for an arbitrary…

Other Condensed Matter · Physics 2016-08-14 A. Muñoz Mateo , V. Delgado

The calculations in Thomas-Fermi approximation show that in a gravitational field each cell of ultra dense matter inside celestial bodies obtains a very small positive electric charge. A celestial body is electrically neutral as a whole,…

Astrophysics · Physics 2007-05-23 B. V. Vasiliev

A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…

Other Condensed Matter · Physics 2007-05-23 R. J. Magyar , K. Burke