Electron density near the nucleus of a large atom

The density of electrons on a distance scale l/Z near the nucleus of a large atom with nuclear charge Ze is given (asymptotically as Z→∞) 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 r^-3/2 for large r; this behavior coincides with the Thomas-Fermi density for small r. Shell structure is visible, but barely so.