Differential equation for ground-state electron density of He-like ions for large atomic number

An explicit differential equation satisfied by the ground-state electron density of He-like ions is constructed for large atomic number Z. As in the authorsʹ earlier work on the Hookean atom, the result is a linear third-order homogeneous differential equation. The first-order interacting density matrix is then written in terms of the ground-state electron density. A functional for the correlation kinetic energy is thereby exhibited in the large Z limit for these two-electron ions.