Thomas-Fermi factor

The exponential term is a Thomas-Fermi screening factor which accounts for the screening by the core electrons. Direct measurement of the ionic character of a bond is a complex operation. In principle, a number of techniques such as X-ray or neutron diffraction, nmr, photoelectron or Mossbauer spectroscopy provide information about electron distribution and charge density in practice the results are usually far from unambiguous. 

The kinetic and exchange energy functionals given by Eqs. (8) and (12), respectively, contain universal terms that just depend upon the one-particle density. In the case of the former, such term is p6/3, the Thomas-Fermi term [22,23] and for the latter, the set p(ri)(4+fc 3, where the first term p4 3 (for k = 0) is the Dirac exchange expression [24]. But in addition, in Eq. (8) we observe the presence of a factor, which we call Fis([p]jr) defined as ... 

The subjects dealt with in these papers have lost none of their interest or attraction for investigators since our conference was held. The real cause of superconduction still remains a mystery. On the other hand, Heisenberg has quite recently found a method, based on the Thomas-Fermi distribution, for calculating the atom form factor for the incoherent radiation, a method which is just as simple as that previously known for the coherent part of the radiation. Many other problems will suggest themselves to the readers of this book. That, indeed, is the object of its publication, and I accordingly welcome the extension of its influence by the present English translation. 

The above form includes also the Thomas-Fermi functional (LDA) for which F(s) = const = 1. Fig. 5 shows the considered enhancement factors GEA2 -... 

This began with a landmark paper by Slater in which he proposed that the effects of exchange in the wave function could be replaced by an exchange potential, proportional to p where p is the electron density function. This followed earlier work by Dirac, in which he showed how to add the exchange energy to the Thomas-Fermi theory of the atom. The exchange potential is also dependent on a factor, cv, which is allowed to vary somewhat from its value in a uniform electron gas. The method is called the Xa method and involves solving a series of one-electron wave equations in a self-consistent manner. 

Slater proposes an effective quantum number n = 3.7, the atomic factor can only be presented in the form of a sum with an infinite number of components. The series may be terminated if the effective quantum number for the N shell is taken as 3.5, 4.0, or 4.5. We calculated values of the atomic factor for the neutral Br atom with different values of n. The most satisfactory agreement with the theoretical form factors, calculated according to the Thomas—Fermi—Dirac model, was obtained at n — 4.5 screening coefficients proposed in [11] were used in the calculations. The equation of the atomic scattering function for the N shell in the case of a spherically symmetrical electron density distribution and n — 4.5 has the following form ... 

The Thomas-Fermi expression underestimates the kinetic energy relative to Hartree-Fock and Kohn-Sham theory [41], To reduce this discrepancy, Waldman and Gordon [41] introduced constant scaling factors that depend only on the atomic number. We use a more dynamic scaling that depends on the local charge density and is thus sensitive to the configuration rf the ions, and approaches the local ionic scaling when the overlap is small ... 

Each of the theoretical charge distributions will give rise to a definite dependence of the atomic form factor F upon its argument s according to equation (5 2). For the Thomas-Fermi distribution, again, an especially simple expression results for F, One finds... 

The nonnegativity constraints on the Pauli correction and its potential give stringent constraints on the types of functionals that can be considered. The most popular form for the kinetic energy has attempted to modify the enhancement factors from Thomas-Fermi-based kinetic energy functionals, defining ... 

The parameter t is expressed in terms of the Thomas-Fermi screening wave number a = /Akp/nao (see also Chapter 9), the spin scaling factor... 

Finally, this section can be closed on a suitable note of uncertainty with two reports. Firstly, the spontaneous-fission half-life of tooFm has recently been measured by Hulet et The value found is 380+60 / s, which is no less than a factor of eight orders of magnitude smaller than predicted, and the authors conclude that The fission barriei calculated from singleparticle effects superimposed on the liquid drop model are not realistic for estimating half-lives . Secondly, Weyer finds that the statistical model of Thomas and Fermi indicates that no nucleus containing more than 300 nucleons can possibly be stable. He does not, however, attempt to treat... 

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