Electron-pair logarithmic convexity and interelectronic moments in atoms: Application to heliumlike ions

Journal Article · Wed Sep 01 04:00:00 EDT 1993 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.48.2457· OSTI ID:6275505

Koga, T; Kasai, Y ^[1]; Dehesa, J S; Angulo, J C ^[2]

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1. Department of Applied Chemistry, Muroran Institute of Technology, Muroran, Hokkaido 050 (Japan)
2. Departamento de Fisica Moderna, Facultad de Ciencias, Universidad de Granada, 18071-Granada (Spain)

The electron-pair function [ital h]([ital u]) of a finite many-electron system is not monotonic, but the related quantity [ital h]([ital u])/[ital u][sup [alpha]], [alpha][gt]0, is not only monotonically decreasing from the origin but also convex for the values [alpha][sub 1] and [alpha][sub 2], respectively, as has been recently found. Here, it is first argued that this quantity is also logarithmically convex for any [alpha][ge][alpha][prime] with [alpha][prime]=max[l brace][minus][ital u][sup 2][ital d2][ln[ital h]([ital u])]/[ital du][sup 2][r brace]. Then this property is used to obtain a general inequality which involves three interelectronic moments [l angle][ital u][sup [ital t]][r angle]. Particular cases of this inequality involve relevant characteristics of the system such as the number of electrons and the total electron-electron repulsion energy. Second, the logarithmic-convexity property of [ital h]([ital u]) as well as the accuracy of this inequality are investigated by the optimum 20-term Hylleraas-type wave functions for two-electron atoms with nuclear charge [ital Z]=1, 2, 3, 5, and 10. It is found that (i) 14[lt][alpha][prime][lt]20 for these atomic cases (we remark that [alpha][prime][much gt][alpha][sub 2][much gt][alpha][sub 1]) and (ii) the accuracy of the inequality which involves moments of contiguous orders oscillates between 62.4% and 96.7% according to the specific He-like atom and the moments involved. Finally, the importance of the logarithmic-convexity effects on the interelectronic moments relative to those coming from other monotonicity properties of [ital h]([ital u])/[ital u][sup [alpha]] are analyzed in the same numerical Hylleraas framework.

• OSTI ID: 6275505
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 48:3; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
CHARGED PARTICLES
COORDINATES
CORRELATION FUNCTIONS
CORRELATIONS
ELECTRON CORRELATION
ELECTRON DENSITY
FUNCTIONS
HYLLERAAS COORDINATES
IONS
MATHEMATICS
MULTICHARGED IONS
NUMERICAL ANALYSIS
WAVE FUNCTIONS