2013/09/15 by Herbert E. Müller, Müller, Herbert E.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1309.3786
8 pages, 1 eps figure
arxiv created 2014/02/06 · arxiv updated 2014/02/07
In the Thomas-Fermi model for the atom or ion, the electric potential ϕ and electron density n are both expressed in terms of a screening number χ and the radius x. The second order differential equation for the screening function χ(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.