Atomic Form Factor Calculations of S-states of Helium

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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The atomic form factor and the X-ray dispersion corrections as tensor quantities: comparisons between theory and experiment

Radiation Physics and Chemistry ◽

10.1016/s0969-806x(99)00288-1 ◽

1999 ◽

Vol 56 (1-2) ◽

pp. 61-83

Author(s):

D.C. Creagh

Keyword(s):

Form Factor ◽

X Ray ◽

Atomic Form Factor ◽

Theory And Experiment

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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

International Journal of Modern Physics B ◽

10.1142/s0217979204023933 ◽

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).

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Determination of Atomic Form Factor of Silicon by Means of Coherent Bremsstrahlung of 1.2-GeV Electrons

Physical Review Letters ◽

10.1103/physrevlett.60.2292 ◽

1988 ◽

Vol 60 (22) ◽

pp. 2292-2294 ◽

Cited By ~ 8

Author(s):

I. Endo ◽

M. Harada ◽

K. Kitamura ◽

T. Monaka ◽

Y. Sumi ◽

...

Keyword(s):

Form Factor ◽

Coherent Bremsstrahlung ◽

Atomic Form Factor

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The Experimental Value of f(220) for Copper

Australian Journal of Physics ◽

10.1071/ph840651 ◽

1984 ◽

Vol 37 (6) ◽

pp. 651 ◽

Cited By ~ 2

Author(s):

JK Mackenzie ◽

A McL Mathieson

Keyword(s):

Form Factor ◽

Electron Diffraction ◽

The Other ◽

Critical Voltage ◽

Diffraction Measurement ◽

X Ray ◽

A Value ◽

Atomic Form Factor ◽

Ray Methods ◽

Electron Diffraction Measurement

The value of the atomic form factor, /(220), for copper has been determined in recent years by a variety of methods. All the dynamical methods agree on a value in the region of 16'70-16�75. These methods include two X-ray methods, one involving measurement of intensity profiles and the other of Pendellosung beats, and also an electron diffraction measurement using a critical voltage procedure. By contrast, two recent kinematical measurements using y rays both report a distinctly different value of about 16�45. One of these determinations has already been re-examined by the present authors and the iscrepancy removed by an appropriate extrapolation to zero extinction.

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

Journal of Plasma Physics ◽

10.1017/s0022377818000661 ◽

2018 ◽

Vol 84 (3) ◽

Cited By ~ 1

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.

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