Interrelations among x‐ray scattering, electron densities, and ionization potentials

Abstract

Abstract 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.