Scattering theory for the Dirac equation of Hartree type and the semirelativistic Hartree equation

2012 ◽  
Vol 75 (8) ◽  
pp. 3531-3542 ◽  
Author(s):  
Makoto Nakamura ◽  
Kimitoshi Tsutaya
Keyword(s):  
Dirac Equation ◽  
Scattering Theory ◽  
Hartree Equation

scholarly journals Scattering theory for the Dirac equation with a non-local term

2009 ◽  
Vol 139 (4) ◽  
pp. 867-878 ◽  
Author(s):  
Shuji Machihara ◽  
Kimitoshi Tsutaya
Keyword(s):  
Dirac Equation ◽  
Initial Data ◽  
Sobolev Spaces ◽  
Scattering Theory ◽  
Scattering Problem ◽  
Small Initial Data ◽  
Non Local ◽  
Scattering Operators ◽  
Local Term

Consider a scattering problem for the Dirac equation with a non-local term including the Hartree type, say the cubic convolution term. We show the existence of scattering operators for small initial data in the subcritical and critical Sobolev spaces.

Relativistic Multiple Scattering Theory for Space Filling Potentials

1991 ◽  
Vol 253 ◽  
Author(s):  
Xindong Wang ◽  
X. -G. Zhang ◽  
W. H. Butler ◽  
B. N. Harmon ◽  
G. M. Stocks
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Secular Equation ◽  
Basis Functions ◽  
Full Potential ◽  
Space Filling ◽  
Multiple Scattering Theory ◽  
The Relationship

ABSTRACTWe derive a relativistic full potential multiple scattering theory (MST) in direct analog to the non-relativistic full potential MST[1, 2]. The secular equation is derived fromi the Lippmann-Schwinger equation by expanding the wave function in terms of cell basis functions which are locally exact solutions of the Dirac equation. The relationship between this theory and currently widely used relativistic munffin-tin MST is also discussed.

On the Scattering Theory of the Dirac Equation

1950 ◽  
Vol 80 (2) ◽  
pp. 261-268 ◽  
Author(s):  
George Parzen
Keyword(s):  
Dirac Equation ◽  
Scattering Theory

scholarly journals Scattering Theory for the Hartree Equation

1998 ◽  
Vol 29 (5) ◽  
pp. 1256-1267 ◽  
Author(s):  
Nakao Hayashi ◽  
Pavel I. Naumkin ◽  
Tohru Ozawa
Keyword(s):  
Scattering Theory ◽  
Hartree Equation

scholarly journals Scattering theory for the Dirac equation of Hartree type in 2+1 dimensions

2009 ◽  
Vol 71 (12) ◽  
pp. e2437-e2441 ◽  
Author(s):  
Shuji Machihara ◽  
Kimitoshi Tsutaya
Keyword(s):  
Dirac Equation ◽  
Scattering Theory

Southern Hemisphere Seti Survey: Five Years of Project Meta II

1997 ◽  
Vol 161 ◽  
pp. 611-621
Author(s):  
Guillermo A. Lemarchand ◽  
Fernando R. Colomb ◽  
E. Eduardo Hurrell ◽  
Juan Carlos Olalde
Keyword(s):  
Southern Hemisphere ◽  
Scattering Theory ◽  
Galactic Plane ◽  
Narrow Band ◽  
Neutral Hydrogen ◽  
Sky Survey ◽  
Inertial Frames ◽  
Interstellar Scattering ◽  
Extraterrestrial Origin ◽  
Spectral Channels

AbstractProject META II, a full sky survey for artificial narrow-band signals, has been conducted from one of the two 30-m radiotelescopes of the Instituto Argentino de Radioastronomía (IAR). The search was performed near the 1420 Mhz line of neutral hydrogen, using a 8.4 million channels Fourier spectrometer of 0.05 Hz resolution and 400 kHz instantaneous bandwidth. The observing frequency was corrected both for motions with respect to three astronomical inertial frames, and for the effect of Earths rotation, which provides a characteristic changing signature for narrow-band signals of extraterrestrial origin. Among the 2 × 1013spectral channels analyzed, 29 extra-statistical narrow-band events were found, exceeding the average threshold of 1.7 × 10−23Wm−2. The strongest signals that survive culling for terrestrial interference lie in or near the galactic plane. A description of the project META II observing scheme and results is made as well as the possible interpretation of the results using the Cordes-Lazio-Sagan model based in interstellar scattering theory.

Dynamical Scattering in Electron Diffraction of wet Protein Crystals

1980 ◽  
Vol 38 ◽  
pp. 42-43
Author(s):  
B. B. Chang ◽  
D. F. Parsons
Keyword(s):  
Electron Diffraction ◽  
Scattering Theory ◽  
Protein Crystals ◽  
Electron Diffraction Data ◽  
Specimen Thickness ◽  
Major Question ◽  
X Ray ◽  
Scattering Effects ◽  
Diffraction Patterns ◽  
Acceleration Voltage

The significance of dynamical scattering effects remains the major question in the structural analysis by electron diffraction of protein crystals preserved in the hydrated state. In the few cases (single layers of purple membrane and 400-600 Å thick catalase crystals examined at 100 kV acceleration voltage) where electron-diffraction patterns were used quantitatively, dynamical scattering effects were considered unimportant on the basis of a comparison with x-ray intensities. The kinematical treatment is usually justified by the thinness of the crystal. A theoretical investigation by Ho et al. using Cowley-Moodie multislice formulation of dynamical scattering theory and cytochrome b5as the test object2 suggests that kinematical analysis of electron diffraction data with 100-keV electrons would not likely be valid for specimen thickness of 300 Å or more. We have chosen to work with electron diffraction patterns obtained from actual wet protein crystals (rat hemoglobin crystals of thickness range 1000 to 2500 Å) at 200 and 1000 kV and to analyze these for dynamical effects.

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