Analytical Expressions for Potentials of Neutral Thomas—Fermi—Dirac Atoms and for the Corresponding Atomic Scattering Factors for X Rays and Electrons

Abstract

Approximate analytical expressions for the electrostatic potentials of neutral Thomas—Fermi—Dirac atoms have been obtained by fitting a sum of three exponential terms to the tabulated values by least-squares methods. The six different parameters used for each atom are expressed as functions of the atomic number. The corresponding expressions for the radical electron density, the mean-square radius, the diamagnetic susceptibility, the atomic scattering factors for x rays and the atomic scattering factors for electrons according to the first Born approximation are given. The accuracy of the approximate expressions are discussed in relation to results obtained from the tabulated values of the electrostatic potential and from the corresponding electron density.