THEORY OF BRILLOUIN SCATTERING FROM A PERIODICALLY CORRUGATED SURFACE OF AN OPAQUE SOLID

1993 ◽  
Vol 07 (05) ◽  
pp. 291-297 ◽  
Author(s):  
L. GIOVANNINI ◽  
F. NIZZOLI ◽  
A. M. MARVIN
Keyword(s):  
Rayleigh Wave ◽  
Elasticity Theory ◽  
Cross Section ◽  
Acoustic Phonon ◽  
Flat Surface ◽  
Brillouin Scattering ◽  
Normal Modes ◽  
Corrugated Surface ◽  
Discrete And Continuous Spectra ◽  
The Continuum

We calculate, in the small corrugation limit, the surface-acoustic phonon normal modes and the Brillouin scattering ripple cross-section for a grating on the Si(001) surface. Both the discrete and continuous spectra of acoustic modes have been studied within the elasticity theory. In the continuum the Rayleigh wave becomes a resonance and hybridizes with the longitudinal pseudo-mode of the flat surface, giving rise to a gap. The theory explains quantitatively recent experimental results.

Quasi-static modes of oscillation of a cold toroidal plasma

1975 ◽  
Vol 14 (1) ◽  
pp. 25-37 ◽  
Author(s):  
John D. Love
Keyword(s):  
Dispersion Relation ◽  
Cross Section ◽  
Normal Modes ◽  
Toroidal Plasma ◽  
Cylindrical Plasma ◽  
Aspect Ratios ◽  
Plasma Ring ◽  
Toroidal Geometry

The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.

A GTO basis set calculation of properties of the continuum. Photoionization and resonances of He

1992 ◽  
Vol 70 (2) ◽  
pp. 513-519 ◽  
Author(s):  
Roberto Moccia ◽  
Pietro Spizzo
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Photoionization Cross Section ◽  
Basis Set ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Continuum States ◽  
K Matrix ◽  
The Continuum ◽  
Autoionizing States

By using the K-matrix technique for the continuum states that was previously employed with particularly diffuse L2 basis sets, it is shown that GTO bases are also capable of yielding accurate values for the properties belonging to the electronic continuum. The method has been tested for helium and proved of satisfactory accuracy also for the analysis of the autoionizing states. The results include the phase shifts of the continuum states of the 1Seand 1P° manifolds, the properties of the lowest resonances of these symmetries, the ground state photoionization cross section, and the S contribution to the 1s2p1P° photoionization cross section. The results obtained suggest that the proposed technique should be useful for computing molecular differential photoionization cross sections by exploiting the widely used codes that employ GTO bases. Keywords: photoionization, Gaussian basis sets, helium, autoionizing states.

An Algorithm for the Description of White and Characteristic Tube Spectra (11 ≤ Z ≤ 83, 10keV ≤ Eo ≤ 50keV)

1991 ◽  
Vol 35 (B) ◽  
pp. 721-726 ◽  
Author(s):  
H. Ebel ◽  
H. Wiederschwinger ◽  
J. Wernisch ◽  
P.A. Pella
Keyword(s):  
Kinetic Energy ◽  
Cross Section ◽  
Atomic Number ◽  
Solid Angle ◽  
Electron Interaction ◽  
X Rays ◽  
X Ray ◽  
The Cross ◽  
Spectral Responses ◽  
The Continuum

Kramers described the cross section of electron interaction with target atoms of atomic number Z bywhere Eo is the kinetic energy of impinging electrons, and E o S) the energy of x-ray photons of the continuum, Smith et al modified this equation, introducing an exponent x, so thatWe applied the cross-section σS, E to the evaluation of experimental results. The evaluation of the measured spectral responses of the x-ray signals nE was performed bywhere f(deff) describes the absorption of x-rays of energy E in the target, RE accounts for backscattering of electrons, DE quantifies the efficiency of x-ray detection within the solid angle Ω.

Discrete versus continuum relaxation modes of a hard sphere gas

1984 ◽  
Vol 62 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Bernard Shizgal
Keyword(s):  
Discrete Spectrum ◽  
Cross Section ◽  
Cross Sections ◽  
Hard Sphere ◽  
Expansion Method ◽  
Gas Mixture ◽  
Discrete Ordinate Method ◽  
Discrete Ordinate ◽  
Relaxation Modes ◽  
The Continuum

The nature of the discrete spectrum of the linear Boltzmann collision operators for a simple gas and for a gas mixture is studied numerically with a discrete ordinate method. The discrete ordinate method is found to give a large number of discrete eigenvalues whereas the expansion method with Burnett functions yields only a few converged eigenvalues. The hard sphere cross section is used in the present paper although the methods employed are readily applicable to other cross sections. The approach of the eigenvalues to the continuum boundary is studied in detail and a comparison with a previous asymptotic Wentzell–Kramers–Brillouin (WKB) analysis yields excellent agreement.

Space-eigenvalue problems in the kinetic theory of gases

1970 ◽  
Vol 42 (1) ◽  
pp. 85-95 ◽  
Author(s):  
M. M. R. Williams ◽  
J. Spain
Keyword(s):  
Asymptotic Distribution ◽  
Cross Section ◽  
Hard Sphere ◽  
Eigenvalue Problems ◽  
Linear Boltzmann Equation ◽  
Hard Sphere Model ◽  
Kinetic Theory Of Gases ◽  
Sphere Model ◽  
Scattering Kernel ◽  
The Continuum

The existence of elementary, exponential solutions of the linear Boltzmann equation for gases is examined. Using the hard-sphere model of scattering, it is found that, in problems involving velocity perturbations, there are no discrete non-zero eigenvalues. Thus the relaxation to the asymptotic distribution is non-exponential and is described by the continuum eigenfunctions. For temperature perturbations, however, we find two non-zero discrete eigenvalues whose values are ±0·975 in units of the minimum scattering cross-section. Relaxation to the asymptotic distribution is therefore exponential, although still very rapid.The conclusions stated above are based upon a truncation of the scattering kernel and a subsequent numerical solution of the resulting integral equations.

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