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We investigate a semiclassical momentum density energy functional for atoms and show that it yields the same value as the well-known Thomas-Fermi functional. In fact, we show an explicit relation between the minimizers of the two…

Mathematical Physics · Physics 2013-11-18 Verena von Conta , Heinz Siedentop

The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…

Quantum Physics · Physics 2025-06-26 A. Bagci , P. E. Hoggan

We present a numerical tool for solving the non-relativistic Kohn-Sham problem for spherically-symmetric atoms. It treats the Schr\"{o}dinger equation as an integral equation relying heavily on convolutions. The solver supports different…

Atomic and Molecular Clusters · Physics 2022-07-13 Jānis Užulis , Andris Gulans

The frequency-dependent linear response of a plasma is studied in the finite-temperature Thomas-Fermi approximation, with electron dynamics described using Bloch hydrodynamics. The variational framework of average-atoms in a plasma is used.…

Plasma Physics · Physics 2016-08-31 C. Caizergues , T. Blenski , R. Piron

The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both…

Atomic Physics · Physics 2007-05-23 A. Sarsa , F. J. Galvez , E. Buendia

The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a…

Statistical Mechanics · Physics 2017-09-19 A. R. Fernandes Nt. , L. F. Santos

The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen-like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no…

Mathematical Physics · Physics 2015-05-13 Hakan Ciftci , Richard L. Hall , Nasser Saad

Theoretical approaches to the photoionization of few-electron atoms are discussed. These include nonequilibrium Greens functions and wave function based approaches. In particular, the Multiconfiguration Time-Dependent Hartree-Fock method is…

Atomic Physics · Physics 2015-05-14 M. Bonitz , D. Hochstuhl , S. Bauch , K. Balzer

This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…

Classical Analysis and ODEs · Mathematics 2015-05-26 Mauro Bologna

The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…

Statistical Mechanics · Physics 2014-10-08 Maciej Janowicz , Filip Krzyżewski , Joanna Kaleta , Marian Rusek , Arkadiusz Orłowski

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is…

Nuclear Theory · Physics 2010-12-23 X. Vinas , P. Schuck , M. Farine , M. Centelles

We consider two-dimensional (2D) "artificial atoms" confined by an axially symmetric potential $V(\rho)$. Such configurations arise in circular quantum dots and other systems effectively restricted to a 2D layer. Using the semiclassical…

Mesoscale and Nanoscale Physics · Physics 2014-07-28 Yu. N. Ovchinnikov , Avik Halder , Vitaly V. Kresin

We demonstrate that $V^{N-M}$ approximation is a good starting point for the configuration interaction calculations for many-electron atoms and ions. $N$ is the total number of electrons in the neutral atom, $M$ is the number of valence…

Atomic Physics · Physics 2009-11-11 V. A. Dzuba

The Thomas-Fermi approximation is a powerful method that has been widely used to describe atomic structures, finite nuclei, and nonuniform matter in supernovae and neutron-star crusts. Nonuniform nuclear matter at subnuclear density is…

Nuclear Theory · Physics 2025-08-05 Shuying Li , Hong Shen , Jinniu Hu

The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizs\"acker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.

Mathematical Physics · Physics 2020-10-26 Hongshuo Chen , Rupert L. Frank , Heinz Siedentop

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…

Materials Science · Physics 2009-11-10 Hong Jiang , Weitao Yang

A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…

Chemical Physics · Physics 2024-05-03 Alexander V. Mironenko

We study atoms with N electrons, and nuclear charge Z. It is well known that the cationic regime, Z > N is qualitatively described by Thomas-Fermi theory. The anionic regime, Z < N, on the other hand, is characterized by an instability…

Atomic Physics · Physics 2013-09-13 Gabriel Gil , Augusto Gonzalez

Atom probe tomography (APT) helps elucidate the link between the nanoscale chemical variations and physical properties, but it has limited structural resolution. Field ion microscopy (FIM), a predecessor technique to APT, is capable of…

We compute the isotope shifts of the \emph{total} electron binding energy of neutral atoms and singly charged ions up to element $Z=120$, using relativistic Hartree-Fock method including the Breit interaction. Field shift coefficients are…

Atomic Physics · Physics 2025-07-30 V. A. Dzuba , V. V. Flambaum