Abstract

The Laplacian of the spherically averaged charge density ∇2ρ̄(r) has been computed from nonrelativistic SCF wave functions for the neutral atoms from hydrogen to uranium, and the singly positive ions, from helium to barium and lutetium to radium, in order to examine the shell structure. ∇2ρ̄(r) exhibits a number of extremal points and zeros with the absolute value of the function becoming smaller at each successive extremal point. The zeros, in particular the odd numbered zeros, are shown to exhibit good correlation with the Bohr theory of an atom while the extremal points correlate to a lesser extent. At most five shells are seen in the studied atomic cases based on the fact that the odd numbered zeros are the topological feature of ∇2ρ̄(r) most indicative of a shell.

Keywords

Bohr modelIonPhysicsAtomic physicsAtom (system on chip)Effective nuclear chargeLaplace operatorCharge densityCharge (physics)Wave functionAtomic numberQuantum mechanics

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Publication Info

Year
1988
Type
article
Volume
88
Issue
7
Pages
4367-4374
Citations
139
Access
Closed

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Robin P. Sagar, Andrew C. T. Ku, Vedene H. Smith et al. (1988). The Laplacian of the charge density and its relationship to the shell structure of atoms and ions. The Journal of Chemical Physics , 88 (7) , 4367-4374. https://doi.org/10.1063/1.453796

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DOI
10.1063/1.453796