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Title: Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories

Abstract

In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential v{sub ee}(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is v{sub ee}(r)=v{sub ee}(0)+{beta}r+O(r{sup 2}), with v{sub ee}(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange v{sub x}(r) and correlation v{sub c}(r) potentials. These functions also approach the nucleus linearly with the linear term of v{sub x}(r) being solely due to the lowest-order correlation kinetic effects, and the linear term of v{sub c}(r) being due solely to themore » higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.« less

Authors:
;  [1];  [2]
  1. Department of Physics, Peking University, Beijing 100871 (China)
  2. (United States)
Publication Date:
OSTI Identifier:
20982314
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032517; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; COULOMB FIELD; COUPLING CONSTANTS; DENSITY FUNCTIONAL METHOD; ELECTRONIC STRUCTURE; ELECTRONS; INTERACTIONS; NUCLEI; PAULI PRINCIPLE; PERTURBATION THEORY; POTENTIALS; SCHROEDINGER EQUATION; SPHERICAL CONFIGURATION; SYMMETRY; WAVE FUNCTIONS

Citation Formats

Qian, Zhixin, Sahni, Viraht, and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.032517.
Qian, Zhixin, Sahni, Viraht, & Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories. United States. doi:10.1103/PHYSREVA.75.032517.
Qian, Zhixin, Sahni, Viraht, and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Thu . "Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories". United States. doi:10.1103/PHYSREVA.75.032517.
@article{osti_20982314,
title = {Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories},
author = {Qian, Zhixin and Sahni, Viraht and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210},
abstractNote = {In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential v{sub ee}(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is v{sub ee}(r)=v{sub ee}(0)+{beta}r+O(r{sup 2}), with v{sub ee}(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange v{sub x}(r) and correlation v{sub c}(r) potentials. These functions also approach the nucleus linearly with the linear term of v{sub x}(r) being solely due to the lowest-order correlation kinetic effects, and the linear term of v{sub c}(r) being due solely to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.},
doi = {10.1103/PHYSREVA.75.032517},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • Local(multiplicative) effective potential energy-theories of electronic structure comprise the transformation of the Schroedinger equation for interacting Fermi systems to model noninteracting Fermi or Bose systems whereby the equivalent density and energy are obtained. By employing the integrated form of the Kato electron-nucleus cusp condition, we prove that the effective electron-interaction potential energy of these model fermions or bosons is finite at a nucleus. The proof is general and valid for arbitrary system whether it be atomic, molecular, or solid state, and for arbitrary state and symmetry. This then provides justification for all prior work in the literature based on themore » assumption of finiteness of this potential energy at a nucleus. We further demonstrate the criticality of the electron-nucleus cusp condition to such theories by an example of the hydrogen molecule. We show thereby that both model system effective electron-interaction potential energies, as determined from densities derived from accurate wave functions, will be singular at the nucleus unless the wave function satisfies the electron-nucleus cusp condition.« less
  • We investigated the excitation of nuclei by longitudinally polarized electrons in view of parity mixtures of nuclear states. The asymmetry in the cross section for the left- and right-polarized electrons is shown to be already very large at low momentum transfer. In many cases the asymmetries caused by parity mixtures and larger by orders of magnitude compared to the contributions expected from weak Z/sup 0/-boson exchange.
  • We construct an effective interaction, which when treated in a relativistic Hartree-Fock approximation, reproduces rather accurately the nucleon self-energy in nuclear matter and the Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations. This effective interaction is constructed by adding Born terms, describing the exchange of pseudoparticles, to the Born terms of the Dirac-Hartree-Fock analysis. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange while exchange of a pseudo-omega with an imaginary coupling constant hasmore » the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation.« less