Two approximate screening functions for the neutral Thomas-Fermi atom

Abstract

In the Thomas-Fermi model for the atom or ion, the electric potential $\varphi$ and electron density $n$ are both expressed in terms of a screening number $\chi$ and the radius $x$. The second order differential equation for the screening function $\chi (x)$ cannot be solved in closed form. Two approximate formulas for the screening function of the neutral atom are proposed: the first formula is analytically simple, the second formula has the roles of dependent and independent variable interchanged. Both formulas reproduce the true screening function very accurately.

arXiv comment8 pages, 1 eps figure