THOMAS–FERMI MODEL ELECTRON DENSITY WITH CORRECT BOUNDARY CONDITIONS: APPLICATIONS TO ATOMS AND IONS

Abstract

We propose an electron density in atoms and ions, which has the Thomas–Fermi–Dirac form in the intermediate region ofr, satisfies the Kato condition for smallr, and has the correct asymptotic behavior at large values ofr, whereris the distance from the nucleus. We also analyze the perturbation in the density produced by multipolar fields. We use these densities in the Poisson equation to deduce average values ofrm, multipolar polarizabilities, and dispersion coefficients of atoms and ions. The predictions are in good agreement with experimental and other theoretical values, generally within about 20%. We tabulate here the coefficientAin the asymptotic density; radial expectation values 〈rm〉 form= 2, 4, 6; multipolar polarizabilities α1, α2, α3; expectation values 〈r0〉 and 〈r2〉 of the asymptotic electron density; and the van der Waals coefficientC6for atoms and ions with 2 ≤Z≤ 92. Many of our results, particularly the multipolar polarizabilities and the higher order dispersion coefficients, are the only ones available in the literature. The variation of these properties also provides interesting insight into the shell structure of atoms and ions. Overall, the Thomas–Fermi–Dirac model with the correct boundary conditions provides a good global description of atoms and ions.