Approximate variational solution of the thomas-fermi-amaldi equation for singly charged negative ions

Abstract

In the present work, approximate analytical solutions of the Thomas-Fermi-Amaldi (TFA) equation are obtained for the singly charged negative ions F−, Cl−, Br−, and I− by making use of an equivalent variational principle. This approach is made possible by the fact that the TFA model for these ions can be expressed by a differential equation of the same form as the one which describes the Thomas-Fermi model for neutral atoms. (Formally, the two differential equations differ only in the definition of the independent variable.) This situation permits one to use the same variational principle in connection with the TFA equation for singly charged negative ions as that used in obtaining an approximate analytical solution of the TF equation for neutral atoms. The approximate solutions obtained for F−, CI−, Br−, and I− have been tested by calculating the diamagnetic susceptibilities of these ions and comparing them (1) with experimental values, (2) with values obtained by Jensen using a variational principle based on the density functional formalism, and (3) with values obtained by the author using a perturbation technique for relating the electron densities in the negative ions to those in neutral atoms.