Kinetic energy and ground-state electron densities as fingerprints of wavefunction entanglement in two-electron spin-compensated atomic models

Abstract

We take as a starting point the ground-state electron density in two-electron model atoms in which Coulomb confinement in the He atom is first replaced by harmonic restoring forces. Switching off electron–electron interactions, one readily constructs a third-order differential equation for the ground-state electron density, as in the recent work of March and Ludena (2004 Phys. Lett. A 330 16). We then switch on two different model interactions, first in the so-called Hookean atom going back to Kestner and Sinanoglu (1962 Phys. Rev. 128 2687), in which e2/r12 is retained as in He, and secondly in the Moshinsky (1968 Am. J. Phys. 36 52) atom in which Kr212/2 is switched on. Some analyticity properties of the low-order linear homogeneous differential equations which result are next studied. He-like atomic ions are then treated in the limit of large atomic number Z. In this latter case, one identifies both the electron–nuclear cusp, or equivalently Kato's theorem, and the corresponding electron–electron cusp in the ground-state spatial wavefunction Ψ(r1, r2). A final comment concerns quantum information and entanglement in relation to the recent work of Amovilli and March (2004 Phys. Rev. A 69 054302).