Nonrelativistic exchange-energy density and exchange potential in the lowest order of the 1/Z expansion for ten-electron atomic ions - art. no. 062512

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 fir st-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. Th is latter quantity is known analytically from the study of March and Santam aria [Phys. Rev. A 38, 5002 (1988)]. Here epsilon (x)(r) is calculated anal ytically, and presented graphically for Z=92 in this large-Z limit. The Sla ter approximation to the exchange potential V-x(r), namely, V-Sla(r)=2 epsi lon (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 functiona l differentiation of the resultant exchange energy, and is expressed in ter ms of electron and kinetic-energy densities. Numerical calculations, based on V-Sla(r) plus approximate corrections, are also presented.