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Interrelations among x‐ray scattering, electron densities, and ionization potentials
Author(s) -
Hyman Arthur S.,
Yaniger Stuart I.,
Liebman Joel F.
Publication year - 1978
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.560140608
Subject(s) - atomic physics , scattering , ionization , electron , physics , virial theorem , thomas–fermi model , formalism (music) , atom (system on chip) , electron scattering , quantum mechanics , ion , musical , art , galaxy , computer science , visual arts , embedded system
From the general formalism of elastic x‐ray scattering and a few meaningful assumptions we have shown that for an atom, ∫ρ 2 d τ is an experimentally measurable quantity related to the intensity scattered by an element. We have labeled this quantity ( p ), the “average electron density.” If ψ obeys the virial theorem, within the Thomas–Fermi approximation we show (within a multiplicative constant) that 〈ρ〉 is a lower bound to (∑ ionization potentials ) 3/2 . Thus, the scattered intensity of x rays is related quantitatively to the energy of the scattering atoms. Inequalities have been developed to express these relationships and have been confirmed for the more exact Hartree–Fock wave functions.