Thomas-Fermi model electron density with correct boundary conditions: Application to atoms and ions

The author proposes an electron density in atoms and ions, which has the Thomas-Fermi-Dirac form in the intermediate region of r, satisfies the Kato condition for small r, and has the correct asymptotic behavior at large values of r, where r is the distance from the nucleus. He also analyzes the perturbation in the density produced by multipolar fields. He uses these densities in the Poisson equation to deduce average values of rm, 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%. He tabulates here the coefficient A in the asymptotic density; radial expectation values (rm) for m = 2, 4, 6; multipolar polarizabilities α1, α2, α3; expectation values left-angle r0 right-angle and left-angle r2 right-angle of the asymptotic electron density; and the van der Waals coefficient C6 for atoms and ions with 2 ≤ Z ≤ 92. Many of the 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