Truncated expansion of the ground-state energy of a neutral atom in powers of Z-1/3: coefficients of the leading terms
- 28 February 1981
- journal article
- letter
- Published by IOP Publishing in Journal of Physics B: Atomic, Molecular and Optical Physics
- Vol. 14 (4) , L121-L125
- https://doi.org/10.1088/0022-3700/14/4/001
Abstract
Numerical estimates of the ground-state energy E of a neutral atom of atomic number Z have been obtained for a few values of Z ranging from 86 to 290 by performing atomic self-consistent-field calculations, treating exchange exactly, using a statistical approximation for correlation, and neglecting relativistic corrections. These numerical values are used to estimate the coefficients in a truncated expansion of E in powers of Z-13/. Writing E approximately=-(c7Z7/3+c6Z6/3+c5Z5/3+c4Z4/3)Ryd with c7 determined from the Thomas-Fermi model the authors find c6=-1.0 in agreement with the prediction of Scott (and of Lieb (1976) and of Schwinger (1980)), they find c5 approximately=0.55, which is close to the value suggested by March and Plaskett, and they find that c4, if it exists, is near to zero.Keywords
This publication has 8 references indexed in Scilit:
- Thomas-Fermi model: The leading correctionPhysical Review A, 1980
- The Thomas-Fermi theory of atoms, molecules and solidsAdvances in Mathematics, 1977
- The stability of matterReviews of Modern Physics, 1976
- Atomic Self-Consistent-Field Calculations Using Statistical Approximations for Exchange and CorrelationPhysical Review B, 1967
- The relation between the Wentzel-Kramers-Brillouin and the Thomas-Fermi approximationsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1956
- The ‘Boundary effect’ in the Thomas-Fermi model for atomsJournal of Computers in Education, 1955
- LXXXII. The binding energy of the Thomas-Fermi AtomJournal of Computers in Education, 1952
- Note on Exchange Phenomena in the Thomas AtomMathematical Proceedings of the Cambridge Philosophical Society, 1930