Title
Towards a differential equation for the nonrelativistic ground-state electron density of the He-like sequence of atomic ions
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Lancaster, Pa ,
Subject
Physics
Source (journal)
Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015
Volume/pages
71(2005) :4 , p. 042501,1-042501,5
ISSN
1094-1622
1050-2947
Article Reference
042501
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/ea5a59/2240.pdf
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