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Asymptotic forms of atomic scattering factors and momentum densities
Author(s) -
Yusaf M. S.,
Lawes G. P.,
March N. H.
Publication year - 1980
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560170503
Subject(s) - thomas–fermi model , coulomb , physics , momentum (technical analysis) , scattering , fourier transform , quantum mechanics , statistical theory , quantum electrodynamics , range (aeronautics) , kinetic energy , density functional theory , connection (principal bundle) , electron , mathematics , statistics , materials science , geometry , finance , economics , composite material
Within the framework of the nonrelativistic Schrödinger equation, the Coulomb field case is used to assess the range of validity of the Thomas–Fermi statistical theory of atoms. In particular, attention is focused on (a) the x‐ray scattering factor, which is the Fourier transform of the electron density; and (b) the momentum density. In each case the predictions of the statistical theory are compared with the exact results for the Coulomb potential. These can conveniently be calculated using earlier work of Fock. Some assessment is also made of the accuracy of the statistical approximation for the kinetic energy density; this is of interest in connection with the density functional approach. Finally, some brief comments are made on the relation between the self‐consistent Thomas–Fermi method and the Hartree theory for atoms.