Nonrelativistic exchange-energy density and exchange potential in the lowest order of the 1/Z expansion for ten-electron atomic ions
Nonrelativistic exchange-energy density and exchange potential in the lowest order of the 1/Z expansion for ten-electron atomic ions
Faculty of Sciences. Physics

article

2000
Lancaster, Pa
, 2000

Physics

Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015

62(2000)
:6
, p. 1-8

1094-1622

1050-2947

1050-2947

062512

E-only publicatie

English (eng)

University of Antwerp

The Dirac exchange energy E-x has a density epsilon (x)(r) in a spherically symmetric ten-electron atomic ion that is determined by the idempotent first-order density matrix (1 DM). In turn, this 1 DM has as its leading term in the 1/Z expansion, with Z the atomic number, the bare Coulomb result. This latter quantity is known analytically from the study of March and Santamaria [Phys. Rev. A 38, 5002 (1988)]. Here epsilon (x)(r) is calculated analytically, and presented graphically for Z=92 in this large-Z limit. The Slater approximation to the exchange potential V-x(r), namely, V-Sla(r)=2 epsilon (x)(r)/rho (r) with rho (r) the ground-state electron density, is also plotted for Z=92. In the large-Z limit, V-x(r) can be obtained by functional differentiation of the resultant exchange energy, and is expressed in terms of electron and kinetic-energy densities. Numerical calculations, based on V-Sla(r) plus approximate corrections, are also presented.

https://repository.uantwerpen.be/docman/irua/47e2d9/6085.pdf

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