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

Abstract

Let \ensuremath{\psi} 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 \ensuremath{\psi}, N+1 with F no larger than 4. Evidence was presented that F=F(N)\ensuremath{\rightarrow}2 as N\ensuremath{\rightarrow}\ensuremath{\infty}. In this paper we show that the same result holds in classical mechanics for a bound system.