THE THOMAS–FERMI–GOMBÁS ATOM MODELS IN WHICH THE ELECTRONS ARE GROUPED INTO n- AND nl-SHELLS AND A CALCULATION OF THE ATOMIC FORM FACTOR

2004 ◽  
Vol 18 (03) ◽  
pp. 409-419
Author(s):  
V. F. TARASOV
Keyword(s):  
Form Factor ◽  
Kinetic Energy ◽  
Total Energy ◽  
Hypergeometric Functions ◽  
Fermi Theory ◽  
Thomas Fermi ◽  
Atomic Form Factor ◽  
First Time ◽  
Analytical Expressions ◽  
Gradient Correction

This article, considers in detail P. Gombás's idea of grouping electrons into n- and nl-shells in the Thomas–Fermi theory of free atoms briefly, the TFG n- and TFG nl-models respectively). Using these models, exact analytical expressions for the total energy E and the atomic form factor F(κ) are obtained. All integrals of the TFG nl-model are computed by means of the hypergeometric functions 2F1(x), 3F2(x), F2(x,y) and FA(x1,…,x6) for the first time. In particular, Weizsäcker's gradient correction to the kinetic energy of the nl-th shell [Formula: see text] generates a new numerical triangle [Formula: see text] with coefficients bw=n+2l(n-l-1).

RELATIVISTIC CORRECTIONS OF THE α2-ORDER FOR THE TOTAL ENERGY AND THE MINIMUM PRESSURE IN THE THOMAS–FERMI THEORY

2002 ◽  
Vol 16 (23n24) ◽  
pp. 901-906 ◽  
Author(s):  
V. F. TARASOV
Keyword(s):  
Kinetic Energy ◽  
Total Energy ◽  
Electron Gas ◽  
Degenerate Electron ◽  
Fermi Theory ◽  
Minimum Pressure ◽  
Thomas Fermi ◽  
Relativistic Corrections ◽  
Relativistic Kinetic Energy ◽  
Degenerate Electron Gas

The total relativistic kinetic energy of the Thomas–Fermi atom is Ekr = Ek + Er, where Ek = κk ∫ ρ5/3dv and Er = -κr ∫ ρ7/3dv + o(α2), [Formula: see text]. The minimum pressure of a relativistic degenerate electron gas is [Formula: see text]. In just the same way, the cases x = pμ / mc = 1 and x > 1 are explicitly considered.

Gradient correction in Thomas-Fermi theory

1986 ◽  
Vol 34 (6) ◽  
pp. 4575-4585 ◽  
Author(s):  
Weitao Yang
Keyword(s):  
Fermi Theory ◽  
Thomas Fermi ◽  
Gradient Correction

Eikonal-Glauber Thomas–Fermi model for atomic collisions with many-electron atoms for plasma applications

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
Myoung-Jae Lee ◽  
Young-Dae Jung
Keyword(s):  
Form Factor ◽  
Phase Shift ◽  
Momentum Transfer ◽  
Cross Section ◽  
Atomic Charge ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Scattering Phase ◽  
Effective Atomic Charge ◽  
Atomic Form Factor

We have derived the universal eikonal-Glauber Thomas–Fermi model for atomic collision cross-sections with many-electron atoms, such as iron and tungsten atoms, including the influence of atomic screening in fusion devices and plasma technologies. The eikonal-Glauber method is employed to obtain the analytic expressions for the effective atomic charge, the scattering phase shift and the atomic cross-section in terms of the atomic form factor and the Mott–Massey screening parameter. The result shows that the effective atomic charge would be the same as the case of the net nuclear charge for the large momentum transfer domain and becomes zero without momentum transfer due to the influence of bound atomic electrons. It is shown that the eikonal scattering phase shift and the total eikonal-Glauber scattering cross-section increase with increasing charge number$Z$of the nucleus of the target atom. It is also found that the charge dependence of the total eikonal-Glauber scattering cross-section decreases with an increase of the scaled collision energy since the atomic form factor is small for large collision energies.

The Elastic Scattering of Low Energy Electrons in Thomas-Fermi Theory

1971 ◽  
Vol 26 (6) ◽  
pp. 1054-1057 ◽  
Author(s):  
T. Tietz
Keyword(s):  
Elastic Scattering ◽  
Total Cross Section ◽  
Cross Section ◽  
Scattering Length ◽  
Low Energy ◽  
Fermi Theory ◽  
Thomas Fermi ◽  
Low Energy Electrons ◽  
Analytical Expressions

Abstract A detailed study has been made of the elastic scattering of lew-energy electrons in Thomas-Fermi Theory. The analytical expressions which have been obtained for the scattering length a and the total cross section o are illustrated numerically.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

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