Abstract
The Thomas-Fermi model and the perturbation expansion for ions with nuclear charge and electrons are considered in the limits of large and where the Thomas-Fermi model becomes exact. It is shown that the Baker expansion of the Thomas-Fermi function may be rearranged into , where and the 's are polynomials in . The functions are obtained through a recursive set of differential equations where is known. It is then shown that the function , , which determines the total binding energy by means of in both the Thomas-Fermi theory and the perturbation theory, is given by . The first few coefficients in this series are determined. The function is then computed through numerical integrations of the Thomas-Fermi equation with different initial slopes. The results are tabulated for and analytically continued beyond . Finally the ratio ( being the nuclear-electron attraction energy) is obtained in terms of for both positive and negative ions and found to be in agreement with the corresponding Hartree-Fock ratios. It is an extension of the well-known ratio of for neutral atoms.
- Received 14 April 1980
DOI:https://doi.org/10.1103/PhysRevA.23.408
©1981 American Physical Society