Electron density near the nucleus of a large atom

  • Ole J. Heilmann
  • Elliott H. Lieb


The density of electrons on a distance scale 1/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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ole J. Heilmann
    • 1
  • Elliott H. Lieb
    • 2
  1. 1.Chemistry Laboratory 3, H.C. Orsted InstituteUniversity of CopenhagenCopenhagenDenmark
  2. 2.Departments of Physics and MathematicsPrinceton UniversityPrincetonUSA

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