Thomas-Fermi distance

Z2 are the mass atomic number of the target atom, and is the Thomas-Fermi screening distance given by equation 4 ... 

The universal function x(x) obtained by numerical integration and valid for all neutral atoms decreases monotonically. The electron density is similar for all atoms, except for a different length scale, which is determined by the quantity b and proportional to Z. The density is poorly determined at both small and large values of r. However, since most electrons in complex atoms are at intermediate distances from the nucleus the Thomas-Fermi model is useful for calculating quantities that depend on the average electron density, such as the total energy. The Thomas-Fermi model therefore cannot account for the periodic properties of atoms, but provides a good estimate of initial fields used in more elaborate calculations like those to be discussed in the next section. 

Figure 1 Types of solution of the dimensionless Thomas-Fermi equation (10). Function 4> expresses the potential distribution in the atomic ion as a function of distance from the nucleus.

The first statistical models of these interactions are the well-known Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) theories based on the idea of approximating the behavior of electrons by that of the uniform negatively charged gas. Some authors (Sheldon, 1955 Teller, 1962 Balazs, 1967 Firsov, 1953,1957 Townsend and Handler, 1962 Townsend and Keller, 1963 Goodisman, 1971) proved that these theories provide an adequate description of purely repulsive diatomic interactions. Abraham-son (1963, 1964) and Konowalow et al. (Konowalow, 1969 Konowalow and Zakheim, 1972) extended this region to intermediate internuclear distances, but Gombas (1949) and March (1957) showed that the Abraham-son approach is incorrect, and so the question of how adequately the TFD theory provides diatomic interactions for closed-shell atoms is still open. Here we need to note that until recently, there has existed only work by Sheldon (1955), as far as we know, in which the TFD interaction potential is actually calculated by solving the TFD equation for a series of internuclear distances (see also, Kaplan, 1982). 

Examining (3.30) we see that e is a dimensionless energy unit. Physically, s gives a measure of how energetic the collision is and how close the ion gets to the nucleus of the target atom. For example, the value of the Thomas-Fermi screening distance, aTF, for He on Si is... 

The primary wave function output data from the Herman-Skillman program are the products rR r), which are known as the numerical radial functions. The radial wave function itself can be recovered on division by the radial distance, r, and approximately near the origin by extrapolating to avoid the infinity. There is one other detail. For the purposes of the numerical integration procedure in the Herman-Skillman procedure the radial data are defined on a non-uniform grid, x, known as the Thomas-Fermi mesh (4). These are converted, in the output from hs.exe, to radial arrays specific to each atom, with... 

Thermalization distance, 252, 254-260, 262 electron, 252-259 Thomas-Fermi screening length, 330, 344... 

This leads to a local Fermi wave number, ky(r), given by / k. (r) /2m = L i.(r), and from Lq. (15-4), a local electron density N(r) =/<. (r) /(37c ). This is called the Fermi-Thomas approximation. The essential assumption that is required is that the potential does not vary greatly over the distance corresponding to the electron wavelength. 

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