Electron densities of the He-like sequence of atomic ions, and associated physical properties

Motivated by the studies of Baker et al. [J.D. Baker, D.E. Freund, R.N. Hill, J.D. Morgan III, Phys. Rev. A 41 (1990) 1247] and of Li and Shakeshaft [T. Li, R. Shakeshaft, Phys. Rev. A 71 (2005) 052505] on the stability of two electrons and an arbitrary positive charge, we here use the Chandrasekhar three-parameter variational wave function to present analytical ground-state electron densities for the He-like sequence of atomic ions. This input is then used to calculate: (i) kinetic energy densities with correlation, (ii) the single-particle von Weizsäcker counterparts of (i), (iii) the electrostatic potentials at the atomic nuclei, and (iv) ground-state energy differences between the lightest members of the He series. We stress that (ii)–(iv) above are calculated solely from knowledge of the analytical ground-state densities.