A simple analytical form of the Thomas-Fermi screening function and of Firsov's atomic interaction potential

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Abstract
The Thomas-Fermi screening function ∅(x) is shown to be accurately described by the expression 317 × exp(-6.62x1/4) in the range 0.3 < x < 16. The consequent form of the Thomas-Fermi electron density distribution is derived, and Firsov's atomic interaction potential is shown to have the form E = B exp(-αr1/4), where B and α are constants of known Z dependence and r is the internuclear distance. It is also suggested that a potential of the type E' = A' exp(-k'r1/3) gives a better representation of the interaction potential over a wider range of energies and distances, and explicit values of A' and k' are given for copper-copper interactions. However, the Z dependence of A' and k' is not obvious.