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The Schwinger quantum correction to the classic Thomas-Fermi atom is directly derived by solving for the latter without recourse to a modeling after the harmonic oscillator potential and without solving for the particle density.

Quantum Physics · Physics 2007-06-13 Edouard B. Manoukian , Parut Bantitadawit

We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the…

Classical Analysis and ODEs · Mathematics 2020-11-20 Ronald E. Mickens , Isom H. Herron

We propose a simple approach for studying systems of compressed matter based on the Thomas-Fermi statistical model of single atom. The central point of our work is the development of the concept of ``statistical ionization'' by compression;…

Statistical Mechanics · Physics 2007-05-23 L. Delle Site

In order to obtain a reasonably accurate and easily implemented approach to many-electron calculations, we will develop a new Density Functional Theory (DFT). Specifically, we derive an approximation to electron density, the first term of…

Materials Science · Physics 2010-04-23 Gregory C. Dente

This article concerns the description of the electron sea of an atomic ion with the Thomas-Fermi model. The normalized ion radius $X$, ionization potential $b$ and electronic binding energy $B$ of the Thomas-Fermi ion are functions of the…

Quantum Physics · Physics 2014-02-11 Herbert E. Müller

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z goes to infinity, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an…

Atomic and Molecular Clusters · Physics 2009-11-13 Donghyung Lee , Kieron Burke , Lucian A. Constantin , John P. Perdew

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

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the Thomas-Fermi approach. The Thomas-Fermi solutions statisfy the stability condition against scaling. We apply the…

Nuclear Theory · Physics 2010-12-23 S. K. Patra , M. Centelles , X. Vinas , M. Del Estal

We present an alternative scheme for calculating the unrestricted Hartree-Fock equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity and…

Other Condensed Matter · Physics 2009-06-16 Mitiyasu Miyasita , Katsuhiko Higuchi , Masahiko Higuchi

The semi-classical approach leading to the Thomas-Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of…

Materials Science · Physics 2016-09-06 Eyal Segev , Doron Gazit

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

We present a high-precision solution of Dirac equation by numerically solving the minmax two-center Dirac equation with the finite element method (FEM). The minmax FEM provide a highly accurate benchmark result for systems with light or…

Quantum Physics · Physics 2024-11-22 Ossama Kullie

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

The properties of warm dilute alpha-nucleon matter are studied in a variational approach in the Thomas-Fermi approximation starting from an effective two-body nucleon-nucleon interaction. The equation of state, symmetry energy,…

Nuclear Theory · Physics 2015-03-19 S. K. Samaddar , J. N. De

In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation is a nonlinear singular ordinary differential equation (ODE)…

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic…

Soft Condensed Matter · Physics 2010-01-28 Claudia Eberlein , Stefano Giovanazzi , Duncan H J O'Dell

In this work we calculate the equation of state of nuclear matter for different proton fractions at zero and finite temperature within the Thomas Fermi approach considering three different parameter sets: the well-known NL3 and TM1 and a…

Nuclear Theory · Physics 2011-04-12 S. S. Avancini , M. E. Bracco , M. Chiapparini , D. P. Menezes

The scattering of neutral particles by an atomic nucleus can lead to electronic ionisation and excitation through a process known as the Migdal effect. We revisit and improve upon previous calculations of the Migdal effect, using the…

High Energy Physics - Phenomenology · Physics 2023-03-01 Peter Cox , Matthew J. Dolan , Christopher McCabe , Harry M. Quiney

We study the static linear response in spherical Thomas-Fermi systems deriving a simple diferen- tial equation for general multipolar moments and associated polarizabilities. We test the equation on sodium clusters between 20 and 100 atoms…

Atomic and Molecular Clusters · Physics 2014-06-17 D. I. Palade , V. Baran

In this paper, we introduce a novel analytical solution to Tolman-Oppenheimer-Volkoff (TOV) equation, which is ultimately a hydrostatic equilibrium equation derived from the general relativity in the framework of relativistic isothermal…

General Relativity and Quantum Cosmology · Physics 2017-05-01 A. S. Saad , M. I. Nouh , A. A. Shaker , T. M. Kamel