Asymptotic form at large r of a third-order linear homogeneous differential equation for the ground-state electron density of the He atom

N. H. March, Á. Nagy, and C. Amovilli
Phys. Rev. A 77, 034501 – Published 6 March 2008

Abstract

In earlier work a linear differential equation satified by the Schwartz ground-state electron density ϱ(r) for (non-relativistic) He-like atomic ions with large atomic number Z has been derived. Here, we utilize the asymptotic expansion at large r given by Amovilli and March for the neutral He atom. We thereby show that a linear differential equation of the same general shape as that satisfied by the Schwartz ϱ(r) again emerges for the neutral He atom itself, in the asymptotic limit of large r. We argue that essential input into the final differential equation for the He ground-state electron density will be the ionization potential plus the atomic polarizability.

  • Received 22 November 2007

DOI:https://doi.org/10.1103/PhysRevA.77.034501

©2008 American Physical Society

Authors & Affiliations

N. H. March1,2, Á. Nagy3, and C. Amovilli4

  • 1Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
  • 2Oxford University, Oxford, England
  • 3Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary
  • 4Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa, Italy

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Vol. 77, Iss. 3 — March 2008

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