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Asymptotic neutrality of large ions. (English) Zbl 0695.60098

Let \[ H_{NZ}=\sum^{N}_{k=1}(-\Delta_{x_ k}-Z| x_ k|^{-1})+\sum_{1\leq j<k}| x_ j-x_ k|^{-1}, \] acting on functions \(\psi (x_ 1,...,x_ N)\in L^ 2({\mathbb{R}}^{3N})\) with suitable antisymmetry restrictions. For fixed N and Z, let E(N,Z) be the infimum of the spectrum of \(H_{NZ}\). If Z is held fixed and N grows, then E(N,Z) becomes constant once N exceeds a critical number N(Z). Physically, N(Z) is the maximum number of electrons in a stable ion with nuclear charge Z. The result of this paper is that \(N(Z)=Z+O(Z^ c)\) for a particular \(c<1\).
Reviewer: C.L.Fefferman

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
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