Some extensions of the born approximation for phase shifts

1963 ◽  
Vol 28 (2) ◽  
pp. 229-239 ◽  
Author(s):  
R. F. Dashen
Keyword(s):  
Born Approximation ◽  
Phase Shifts

A modified Born approximation for singular potentials

1970 ◽  
Vol 48 (5) ◽  
pp. 511-512
Author(s):  
Byung Chan Eu
Keyword(s):  
Cross Sections ◽  
Born Approximation ◽  
Phase Shifts ◽  
Phase Method ◽  
Singular Potentials ◽  
Variable Phase ◽  
Scattering Cross ◽  
Lennard Jones ◽  
Variable Phase Method ◽  
Scattering Cross Sections

The variable-phase method is used to obtain nondiverging Born phase shifts for a singular (Lennard–Jones (12,6)) potential. An exemplary calculation is made for the parameters kσ = 18 and εσ2 = 125, and the agreement between the approximate and exact differential scattering cross sections is fairly good.

Dynamical Scattering in Crystalline Biological Specimens. I. Criteria of Validity for Scattering Approximations

1975 ◽  
Vol 33 ◽  
pp. 192-193
Author(s):  
Robert M. Glaeser ◽  
Bing K. Jap
Keyword(s):  
Biological Sciences ◽  
Electron Microscopy ◽  
Electron Microscope ◽  
Electron Diffraction ◽  
Born Approximation ◽  
Materials Science ◽  
Image Data ◽  
Dynamical Effect ◽  
Crystallographic Structure ◽  
Electron Microscope Image

The dynamical scattering effect, which can be described as the failure of the first Born approximation, is perhaps the most important factor that has prevented the widespread use of electron diffraction intensities for crystallographic structure determination. It would seem to be quite certain that dynamical effects will also interfere with structure analysis based upon electron microscope image data, whenever the dynamical effect seriously perturbs the diffracted wave. While it is normally taken for granted that the dynamical effect must be taken into consideration in materials science applications of electron microscopy, very little attention has been given to this problem in the biological sciences.

Structural studies of small amorphous volumes by electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 122-123
Author(s):  
Pierre Moine
Keyword(s):  
Electron Diffraction ◽  
Born Approximation ◽  
Structural Information ◽  
Fundamental Relation ◽  
X Rays ◽  
Structural Studies ◽  
Diffraction Experiment ◽  
Transmission Electron ◽  
Amorphous Structures ◽  
Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

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