2,977 research outputs found
On the relation between the Hartree-Fock and Kohn-Sham approaches
We show that the Hartree-Fock (HF) results cannot be reproduced within the
framework of Kohn-Sham (KS) theory because the single-particle densities of
finite systems obtained within the HF calculations are not -representable,
i.e., do not correspond to any ground state of a non-interacting electron
systems in a local external potential. For this reason, the KS theory, which
finds a minimum on a different subset of all densities, can overestimate the
ground state energy, as compared to the HF result. The discrepancy between the
two approaches provides no grounds to assume that either the KS theory or the
density functional theory suffers from internal contradictions.Comment: 7 pages, ReVtex, revised and accepted by Physics Letters
Pairing correlations beyond the mean field
We discuss dynamical pairing correlations in the context of configuration
mixing of projected self-consistent mean-field states, and the origin of a
divergence that might appear when such calculations are done using an energy
functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre
Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at
Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys.
E, in prin
A simple parameter-free one-center model potential for an effective one-electron description of molecular hydrogen
For the description of an H2 molecule an effective one-electron model
potential is proposed which is fully determined by the exact ionization
potential of the H2 molecule. In order to test the model potential and examine
its properties it is employed to determine excitation energies, transition
moments, and oscillator strengths in a range of the internuclear distances, 0.8
< R < 2.5 a.u. In addition, it is used as a description of an H2 target in
calculations of the cross sections for photoionization and for partial
excitation in collisions with singly-charged ions. The comparison of the
results obtained with the model potential with literature data for H2 molecules
yields a good agreement and encourages therefore an extended usage of the
potential in various other applications or in order to consider the importance
of two-electron and anisotropy effects.Comment: 8 pages, 6 figure
Big consequences of small changes (Non-locality and non-linearity of Hartree-Fock equations)
It is demonstrated that non-locality and non-linearity of Hartree-Fock
equations dramatically affect the properties of their solutions that
essentially differ from solutions of Schr?dinger equation with a local
potential. Namely, it acquires extra zeroes, has different coordinate
asymptotic, violates so-called gauge-invariance, has different scattering
phases at zero energy, has in some cases several solutions with the same set of
quantum numbers, usually equivalent expressions of current and Green's
functions became non-equivalent. These features result in a number of
consequences for probabilities of some physical processes, leading e. g. to
extra width of atomic Giant resonances and enhance considerably the ionization
probability of inner atomic electrons by a strong field.Comment: 16 pages, 3 figure
Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation
The radial Schrodinger equation for a spherically symmetric potential can be
regarded as a one dimensional classical harmonic oscillator with a
time-dependent spring constant. For solving classical dynamics problems,
symplectic integrators are well known for their excellent conservation
properties. The class of {\it gradient} symplectic algorithms is particularly
suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for
decomposing time-ordered operators, these algorithms can be easily applied to
the Schrodinger equation. We demonstrate the power of this class of gradient
algorithms by solving the spectrum of highly singular radial potentials using
Killingbeck's method of backward Newton-Ralphson iterations.Comment: 19 pages, 10 figure
Symmetry of the Atomic Electron Density in Hartree, Hartree-Fock, and Density Functional Theory
The density of an atom in a state of well-defined angular momentum has a
specific finite spherical harmonic content, without and with interactions.
Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and
Local Density Approximations, generally violate this feature. We analyze, by
means of perturbation theory, the degree of this violation and show that it is
small. The correct symmetry of the density can be assured by a
constrained-search formulation without significantly altering the calculated
energies. We compare our procedure to the (different) common practice of
spherically averaging the self-consistent potential. Kohn-Sham density
functional theory with the exact exchange-correlation potential has the correct
finite spherical harmonic content in its density; but the corresponding exact
single particle potential and wavefunctions contain an infinite number of
spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic
expansion of Hartree density. Some typos corrected, references adde
The metabolism of homogenates of the mouse epididymis
This study has attempted an evaluation of the in vitro metabolic characteristics of the epididymis of the mouse and a definition of areas for further research pursuant to the elucidation of the role of this organ in the process of sperm maturation and storage. Optimal conditions were ascertained for the manometric measurement of total respiration and for the estimation of glycolytic activity by assay of lactate accumulation and phosphate esterification in fluoride poisoned homogenates. Homogenates of mouse kidney were utilized in all experiments for comparative purposes. The in vitro data presented indicate the epididymis to be predominantly oriented to a glycolytic metabolism. It is suggested that this metabolic orientation when considered with the results of other investigators is compatible with a hypothesis for the secretion of lactic acid by the epididymal epithelium into the lumen of the epididymal canal for spermatozoan utilization.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50125/1/1030660305_ftp.pd
From Microscales to Macroscales in 3D: Selfconsistent Equation of State for Supernova and Neutron Star Models
First results from a fully self-consistent, temperature-dependent equation of
state that spans the whole density range of neutron stars and supernova cores
are presented. The equation of state (EoS) is calculated using a mean-field
Hartree-Fock method in three dimensions (3D). The nuclear interaction is
represented by the phenomenological Skyrme model in this work, but the EoS can
be obtained in our framework for any suitable form of the nucleon-nucleon
effective interaction. The scheme we employ naturally allows effects such as
(i) neutron drip, which results in an external neutron gas, (ii) the variety of
exotic nuclear shapes expected for extremely neutron heavy nuclei, and (iii)
the subsequent dissolution of these nuclei into nuclear matter. In this way,
the equation of state is calculated across phase transitions without recourse
to interpolation techniques between density regimes described by different
physical models. EoS tables are calculated in the wide range of densities,
temperature and proton/neutron ratios on the ORNL NCCS XT3, using up to 2000
processors simultaneously.Comment: 6 pages, 11 figures. Published in conference proceedings Journal of
Physics: Conference Series 46 (2006) 408. Extended version to be submitted to
Phys. Rev.
Density Functional Theory versus the Hartree Fock Method: Comparative Assessment
We compare two different approaches to investigations of many-electron
systems. The first is the Hartree-Fock (HF) method and the second is the
Density Functional Theory (DFT). Overview of the main features and peculiar
properties of the HF method are presented. A way to realize the HF method
within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this
is impossible without including a specific correlation energy, which is defined
by the difference between the sum of the kinetic and exchange energies of a
system considered within KS and HF, respectively. It is the nonlocal exchange
potential entering the HF equations that generates this correlation energy. We
show that the total correlation energy of a finite electron system, which has
to include this correlation energy, cannot be obtained from considerations of
uniform electron systems. The single-particle excitation spectrum of
many-electron systems is related to the eigenvalues of the corresponding KS
equations. We demonstrate that this spectrum does not coincide in general with
the eigenvalues of KS or HF equations.Comment: 16 pages, Revtex, no figure
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