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→ ∞) 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.
Unable to display preview. Download preview PDF.
- G. Zhislin, Tr. Mosk. Mat. Obshch. 9, 81 (1960).Google Scholar
- E. H. Lieb, Phys. Rev. A 29, 3018 (1984).Google Scholar
- E. H. Lieb, Rev. Mod. Phys. 53, 603 (1981); 54, 311 (E) (1982).Google Scholar
- J. M. C. Scott, Philos. Mag. 43, 859 (1952).Google Scholar
- A. Iantchenko, E. H. Lieb, and H. Siedentop, J. Reine Angew. Math. (to be published).Google Scholar
- A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions ( McGraw-Hill, New York, 1953 ).Google Scholar
- F. W. J. Giver, SIAM J. Math. 5, 19 (1974).Google Scholar