Ground-state energy of any atom
- 14 May 1978
- journal article
- Published by IOP Publishing in Journal of Physics B: Atomic and Molecular Physics
- Vol. 11 (9) , 1515-1520
- https://doi.org/10.1088/0022-3700/11/9/007
Abstract
An extremely simplified version of the atomic shell model is used to obtain an explicit parameter-free approximation to the ground-state energy Etot(Z) of any atom. The resultant values of Etot(Z) agree to within a few per cent with those obtained from Hartree-Fock calculations for any Z in the interval Z=2 to Z=102, the agreement being of the order of 0.5% or better for Z>45. This is an order of magnitude better than Thomas-Fermi (TF) theory in this range. For Z to infinity , where TF theory becomes exact (Lieb-Simon theorem), we find (rij-1)/(rj-1) to 2/7, which is the exact TF value, and Etot approximately -CZ7/3 with C=0.74, which is within 4% or Cexact=0.77.Keywords
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