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Title
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Towards a differential equation for the nonrelativistic ground-state electron density of the He-like sequence of atomic ions
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Author
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Abstract
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| The early study of Schwartz [Ann. Phys. (N.Y.) 6, 156 (1959)] led to an explicit expression for the ground-state electron density rho(r) of He-like atomic ions with nuclear charge Ze in the limit of large Z. Much later, Gal, March, and Nagy [Chem. Phys. Lett. 305, 429 (1999)] derived a third-order linear homogeneous differential equation satisfied by the Schwartz limiting density. Our aim here has been to solve a still correlated model more closely related to the He atom itself. Motivated by semiclassical studies (as by Handke [Phys. Rev. A 50, R3561 (1994)]), we have solved a fully quantal model in which the Coulomb repulsion energy e(2)/r(12) of the two electrons at separation r(12) is expanded in a one-center form about the atomic nucleus and only the s-wave term is retained. From the resulting analytical ground-state density, a differential equation has been derived, which is contrasted with that satisfied by the large-Z limiting form of Schwartz. Suggestions are finally made as to the way the density of the He atomic ion series may be characterized, the ionization potential I(Z) being proposed as crucial input data. |
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Language
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English
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Source (journal)
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Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015
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Publication
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Lancaster, Pa
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2005
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ISSN
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1094-1622
[online]
1050-2947
[print]
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DOI
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10.1103/PHYSREVA.71.042501
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Volume/pages
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71
:4
(2005)
, p. 042501,1-042501,5
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Article Reference
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042501
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ISI
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000228752700058
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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