Proof of a conjecture about atomic and molecular cores related to Scott's correction

Alexei Iantchenko, Elliott Lieb, Heinz Siedentop

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A great deal is known about the ground states of large atoms in the framework of the non-relativistic Schrödinger equation, with fixed (i.e., infinitely massive) nuclei. The leading term, in powers of the nuclear charge Z, is given exactly by Thomas-Fermi theory, as was proved by Lieb and Simon [12]; see [11] for a review. This leading term in the energy is proportional to Z 7/3, with the proportionahty constant depending on the ratio of N/Z, which is assumed to be held fixed as Z → ∞. Here, N is the electron number. Neutrality, i.e., N=Z is not required, even though it is the case of primary physical interest. The characteristic length scale for the electron density (in the sense that all the electrons can be found on this scale in the limit Z → ∞) is Z1/3 The fact that the true quantummechanical electron density, Qd, converges (after suitable scaUng) to the Thomas-Fermi density, QTf, as Z → ∞ with N/Z fixed was proved in [12]. The chemical radius, which is another length altogether, is believed, but not proved, to be order Z0 as Z → ∞.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Pages127-145
Number of pages19
ISBN (Print)3540420835, 9783540222125
DOIs
StatePublished - Jan 1 2005

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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