ELECTRON-DENSITY NEAR THE NUCLEUS OF A LARGE ATOM

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-->inf inity) by the sum of the squares of all the hydrogenic bound-state fun ctions (with nuclear charge Ze). This density function, which is an im portant limiting function in quantum chemistry, is investigated here i n detail. Several analytic results are found: In particular, the asymp totic expansion for large r is derived and it is shown that the functi on 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.