Electron density near the nucleus of a large atom

Ole J. Heilmann, Elliott H. Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter


The density of electrons on a distance scale l/Z near the nucleus of a large atom with nuclear charge Ze is given (asymptotically as Z→∞) by the sum of the squares of all the hydrogenic bound-state functions (with nuclear charge Ze). This density function, which is an important limiting function in quantum chemistry, is investigated here in detail. Several analytic results are found: In particular, the asymptotic expansion for large r is derived and it is shown that the function falls off as r-3/2 for large r; this behavior coincides with the Thomas-Fermi density for small r. Shell structure is visible, but barely so.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Number of pages6
ISBN (Print)3540420835, 9783540222125
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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