Thomas-Fermi statistics

Eq. (2.16) is not an entirely new result. After this work had been concluded and we were looking around in search of bibliographical material, we came upon a paper by Englert and Schwinger [24] dealing with the introduction of quantum corrections to the Thomas-Fermi statistical atom. These authors attain the same result expressed by eq. (2.16) (for... 

It is not absolutely necessary to have accurate interatomic potentials to perform reasonably good calculations because the many collisions involved tend to obscure the details of the interaction. This, together with the fact that accurate potentials are only known for a few systems makes the Thomas-Fermi approach quite attractive. The Thomas-Fermi statistical model assumes that the atomic potential V(r) varies slowly enough within an electron wavelength so that many electrons can be localized within a volume over which the potential changes by a fraction of itself. The electrons can then be treated by statistical mechanics and obey Fermi-Dirac statistics. In this approximation, the potential in the atom is given by ... 

Model potential methods and their utilization in atomic structure calculations are reviewed in [139], main attention being paid to analytic effective model potentials in the Coulomb and non-Coulomb approximations, to effective model potentials based on the Thomas-Fermi statistical model of the atom, as well as employing a self-consistent field core potential. Relativistic effects in model potential calculations are discussed there, too. Paper [140] has examples of numerous model potential calculations of various atomic spectroscopic properties. 

Density-Potential Relation of Thomas-Fermi Statistical Theory... 

Wang et al.s0 have calculated T0, T2, and Tt using good wave-mechanical densities for closed-shell atoms and a selection of their results is recorded in Table 5. The inequality (80) is seen to be fulfilled. Furthermore, since the Thomas-Fermi statistical theory becomes correct for sufficiently large numbers of electrons, it follows that the importance of T% diminishes continually for heavier atoms. 

Fig. 32-1.—The electron distribution function D for the normal rubidium atom, as calculated I, by Hartrec s method of the self-consistent field II, by the screening-constant method and 111, by the Thomas-Fermi statistical method.

The most widely used screening function is that due to Moliere [206] using Thomas-Fermi statistics, which is approximated by... 

For electronic structure calculations there are mainly three exactly solvable models the Thomas-Fermi statistical model, the noninteracting electron model, and the large-dimension model. With the poineering work of Herschbach, it was recognized that the large dimension limit, where the dimensionality of space is treated as a free parameter, is simple, captures the main physics of the system, and is analytically solvable. In the final section we will summarize the main ideas of the large-dimension model for electronic structure problems. 

For electronic structure calculations of atoms and molecules there are three exactly solvable models the Thomas-Fermi statistical model (the limit A —> oo for fixed N/Z, where N is the number of electrons and Z is the nuclear charge) the noninteracting electron model,the limit of infinite nuclear charge (Z —> oo, for fixed N) and the large-dimension model D - oo for fixed N and Z). ... 

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