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Title: Revised Thomas-Fermi approximation for singular potentials

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 94; Journal Issue: 7; Related Information: CHORUS Timestamp: 2016-08-31 18:10:32; Journal ID: ISSN 2469-9950
American Physical Society
Country of Publication:
United States

Citation Formats

Dufty, James W., and Trickey, S. B. Revised Thomas-Fermi approximation for singular potentials. United States: N. p., 2016. Web. doi:10.1103/PhysRevB.94.075158.
Dufty, James W., & Trickey, S. B. Revised Thomas-Fermi approximation for singular potentials. United States. doi:10.1103/PhysRevB.94.075158.
Dufty, James W., and Trickey, S. B. 2016. "Revised Thomas-Fermi approximation for singular potentials". United States. doi:10.1103/PhysRevB.94.075158.
title = {Revised Thomas-Fermi approximation for singular potentials},
author = {Dufty, James W. and Trickey, S. B.},
abstractNote = {},
doi = {10.1103/PhysRevB.94.075158},
journal = {Physical Review B},
number = 7,
volume = 94,
place = {United States},
year = 2016,
month = 8

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevB.94.075158

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  • Many-body atomic potentials, epsilon, are functions of the nuclear coordinates, and are defined by differences of ground-state energies, E, e.g., epsilon(1,2) = E(1,2)-E(1)-E(2). It is proved that in Thomas--Fermi theory the n-body potential always has the sign (-1)/sup n/ for all coordinates. It is also proved that the remainder in the expansion of the total energy E in terms of the epsilon's, when truncated at the n-body terms, has the sign (-1)/sup n+1/.
  • Both exact and approximate expressions for the elastic differential scattering cross sections were derived for various Thomas-Fermi atomic potentials. The numerical results obtained for the elastic differential scattering cross sections were compared with the corresponding Hartree values.
  • Using the ab initio energy-minimization procedure of Bass, Green, and Wood, two potential parameters, xi and eta are determined, characterizing the independent-particle-model potential of Green, Sellin, and Zachor (GSZ) for atoms and positive ions with 36 less than Z less than or equal to 54. This extends earlier modified-Hartree--Fock (MHF) calculations of Szydlik and Green and of Green, Garvey, and Jackman. It is found that both of the parameters in question display, to a good approximation, a linear dependence on the degree of ionization Z--N for fixed numbers of electrons N. The slopes and y intercepts associated with the linearmore » dependence of xi display marked shell-like behavior, while those associated with eta vary rather smoothly with N. The determinations of total energies are usually within 50 ppm of earlier Hartree--Fock calculations for those cases in which such calculations exist. Using the entire collection of energies and GSZ minimization parameters now available, a modified version of the Thomas--Fermi statistical model (MTF) due to Green, Sellin, and Darewych is reexamined. This model is shown to be capable of yielding the linear Z--N dependence of the GSZ parameters which were found empirically in the MHF work. By numerical adjustment of the coefficients of our MTF model, energies of stable atoms and ions, as well as GSZ potential parameters which are in good agreement with the MHF calculations are obtained. 3 tables, 4 figures. (auth)« less