Asymptotic form at largerof a third-order linear homogeneous differential equation for the ground-state electron density of the He atom

Abstract

In earlier work a linear differential equation satified by the Schwartz ground-state electron density $\ensuremath{\varrho}(r)$ for (non-relativistic) He-like atomic ions with large atomic number $Z$ has been derived. Here, we utilize the asymptotic expansion at large $r$ given by Amovilli and March for the neutral He atom. We thereby show that a linear differential equation of the same general shape as that satisfied by the Schwartz $\ensuremath{\varrho}(r)$ again emerges for the neutral He atom itself, in the asymptotic limit of large $r$. We argue that essential input into the final differential equation for the He ground-state electron density will be the ionization potential plus the atomic polarizability.