Electron density near the nucleus of a large atom.

Abstract

The density of electrons on a distance scale 1/Z near the nucleus of a large atom with nuclear charge Ze is given (asymptotically as Z\ensuremath{\rightarrow}\ensuremath{\infty}) by the sum of the squares of all the hydrogenic bound-state functions (with nuclear charge Ze). This density function, which is an important limiting function in quantum chemistry, is investigated here in detail. Several analytic results are found: In particular, the asymptotic expansion for large r is derived and it is shown that the function falls off as ${\mathit{r}}^{\mathrm{\ensuremath{-}}3/2}$ for large r; this behavior coincides with the Thomas-Fermi density for small r. ``Shell structure'' is visible, but barely so.