r- and p-space electron densities and related kinetic and exchange energies in terms of s states alone for the leading term in the 1/Z expansion for nonrelativistic closed-shell atomic ions - art. no. 062501

As a step towards constructing nonlocal energy density functionals, the lea ding term in the so-called 1/Z expansion for closed-shell atomic ions is th e focus here. This term is characterized by the properties of the bare Coul omb potential (-Ze(2)/r), and for an arbitrary number of closed shells it i s known that partial derivative rho (r)partial derivativer = -(2Z/a(0))rho (s)(r), where rho (r) is the ground-state electron density while rho (s)(r) is the s-state (l = 0) contribution to rho (r). Here, the kinetic-energy d ensity t(r) is also derived as a double integral in terms of rho (s)(r) and Z. Although the exchange energy density epsilon (x)(r) is more complex tha n t(r), a proof is given that. in the Coulomb limit system, epsilon (x) is indeed also determined by s-state properties alone. The same is shown to be true for the momentum density n(p). which here is obtained explicitly for an arbitrary number of closed shells. Finally, numerical results are presen ted that include (a) ten-electron atomic ions (K+L shells), (b) the limit a s the number of closed shells tends to infinity, where an appeal is made to the analytical r-space study of Heilmann and Lieb [Phys. Rev. A 52, 3628 ( 1995)], and (c) momentum density and Compton line shape for an arbitrary nu mber of closed shells.