Long-range asymptotic behaviour of the ground-state electron density in He-like ions as a function of atomic number

Abstract

From the early work of Hoffmann–Ostenhof, the electron density ρ(r) for He-like ions at sufficiently large r has the form Ar n exp(−2 √ 2 Ir) where I is the ionization potential. A derivation of the relation between n and I is briefly presented. The non-relativistic ionization potential I is then calculated quantitatively from diffusion quantum Monte Carlo (DMC) calculations, as is the range of validity of the above asymptotic form for Z 2. The above arguments are valid away from Z = Zc, the critical atomic number 0.911 028 at which the ionization potential I tends to zero. Again analytic theory plus DMC is used at Z = Zc to quantify ρ(r).