Analytical Expressions for the Hartree—Fock Potential of Neutral Atoms and for the Corresponding Scattering Factors for X Rays and Electrons

Approximate analytical expressions for the Hartree—Fock potential of neutral atoms to Z=36 have been obtained by fitting the radial electron density with an analytical expression by least squares. The expression for the radial density corresponds to the following form of the screening factor: $$\frac{Z_p\mathrm{(r)}}{Z}={\displaystyle \sum _{\text{i=1}}^2}{}^a{\gamma }_i\exp {\mathrm{(-}}^a{\lambda }_i\mathrm{r)+r}{\displaystyle \sum _{\text{j=1}}^m}{}^b{\gamma }_j\exp {\mathrm{(-}}^b{\lambda }_j\mathrm{r),}$$ where m=2 for Z=2 to Z=18 and m=3 for Z=19 to Z=36. The corresponding expressions for the mean radius, the mean square radius, the diamagnetic susceptibility, and the atomic scattering factors for x rays, and for electrons according to the first Born approximation are given. The accuracy of the approximate expressions is discussed in relation to results obtained by numerical calculations from the Hartree—Fock wavefunctions for the atoms.