Thomas-Fermi atom

N. H. March, Self-consistent Fields in Atoms Hartree and Thomas-Fermi Atoms (Pergamon, Oxford, 1975). 

March, N. H. "Self-Consistent Fields in Atoms. Hartree and Thomas-Fermi Atoms" Pergamon Oxford 1975,131. 

March and Parr also point out as already mentioned above that the interpretation of the result ju=0 for the neutral Thomas-Fermi atom (cf the result for the central field model for molecules in Section 9, where the chemical potential is also zero for neutral molecules) is that the gross trend with Z is juocZ-1/3 at large Z. Of course, such a discussion would have to be refined considerably to reproduce the chemically important periodic effects in p, which will be focused upon below. 

While Eq. (12) represents the correct prediction of the non-relativistic Schro-dinger equation as Z —> oo, in the range of the Periodic Table corrections are needed. One is due to the fact that Eq. (11) near the point atomic nucleus assumed, shows that pit) diverges as r 3/2 and this is due to neglecting density gradients in the Fermi gas model employed. This, as was shown by Scott [12], corrects [13,14] Eq. (12) with a term (1/2)Z2. Earlier Dirac had introduced the exchange energy A into the Thomas-Fermi atom, with the result... 

Equation (5.7) provides a means for calculating stopping cross-sections based on the Thomas-Fermi atom with an accuracy of -20%. The ranges of validity for values of m arc... 

Furthermore, the Thomas-Fermi energy density functional cannot be inserted in the density functional philosophy presented by the mappings (13) and (14) for all p(r) e T>n since the ground-state energies of many Thomas-Fermi atoms and ions" lie below the exact ones. ... 

The last formula is circumvented to the high-density total correlation density approaches rooting at their turn on the Thomas-Fermi atomic theory. Very interesting, the relation (4.477) may be seen as an atomic reflection of the (solid state) high-density regime (r < 1) given by Perdew et al. (Perdew, 1986 Wang Perdew, 1989 Seidl et al., 1999 Perdew et al., 1996) ... 

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