Determination via classical mechanics of the maximum number of electrons in an atomic bound state

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Abstract
Let ψ be any normalizable energy eigenfunction for N electrons in an atom having Z protons in a fixed pointlike nucleus. Recently, it has been shown with use of quantum mechanics [Phys. Rev. Lett. 53, 907 (1984)] that, for the state ψ, NF no larger than 4. Evidence was presented that F=F(N)→2 as N→∞. In this paper we show that the same result holds in classical mechanics for a bound system.

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