The Scattering Waves by Two Spheres in Solid

2013 ◽  
Vol 423-426 ◽  
pp. 1640-1643
Author(s):  
Yan Ru Zhang ◽  
Pei Jun Wei
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Spherical Wave ◽  
Addition Theorem ◽  
Wave Functions ◽  
Interface Condition ◽  
Elastic Sphere ◽  
Numerical Examples ◽  
Transmitted Waves ◽  
Expansion Coefficients

The scattering waves by two elastic spheres in solid are studied. The incident wave, the scattering waves in the host and the transmitted waves in the elastic spheres are all expanded in the series form of spherical wave functions. The total waves are obtained by addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the solid host. The scattering cross section is computed as numerical examples.

The Scattering of Acoustic Wave by a Chain of Elastic Spheres in Liquid

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Yanru Zhang ◽  
Peijun Wei
Keyword(s):  
Acoustic Waves ◽  
Scattering Amplitude ◽  
Spherical Wave ◽  
Addition Theorem ◽  
Interface Condition ◽  
Numerical Examples ◽  
Transmitted Waves ◽  
Scattering Wave ◽  
Expansion Coefficients ◽  
A Chain

The scattering of acoustic waves by a chain of elastic spheres in liquid is studied. The incident wave, the scattering wave in the host, and the transmitted waves (including longitudinal and transverse wave modes) in the elastic spheres are all expanded in the form of a series of spherical wave functions. The total waves are obtained by the addition of all scattered waves from individual elastic sphere. The addition theorem of spherical wave function is used to perform the coordinates transform for the scattering waves from different spheres. The expansion coefficients of scattering waves are determined by the interface condition between the elastic spheres and the liquid host. The scattering cross section and the scattering amplitude in far field are computed as numerical examples. Two cases, steel spheres and lead spheres embedded in water, are considered in the numerical examples.

scholarly journals HIGHER TWIST EFFECTS IN PHOTON–PHOTON COLLISIONS

2008 ◽  
Vol 17 (06) ◽  
pp. 1041-1059 ◽  
Author(s):  
A. I. AHMADOV ◽  
I. BOZTOSUN ◽  
A. SOYLU ◽  
E. A. DADASHOV
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Cross Sections ◽  
Production Cross ◽  
Wave Functions ◽  
Feynman Diagrams ◽  
High Twist ◽  
Higher Twist Effects ◽  
Two Photon ◽  
Pion Wave Function

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT single pseudoscalar and vector mesons inclusive production cross section in two-photon collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, Braun–Filyanov pion wave function, the asymptotic and the Chernyak–Zhitnitsky wave functions are all used in the calculations. For ρ-meson we used the Ball–Braun wave function. The results of the calculations reveal that the high twist cross sections, the ratio R, the dependence transverse momentum pT and the rapidity y of meson in the Φ CLEO (x, Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

An addition theorem for spherical wave functions

1982 ◽  
Vol 35 (11) ◽  
pp. 353-357
Author(s):  
L. Ronchi ◽  
S. Barbarino ◽  
P. Grasso ◽  
G. Guerriera ◽  
F. Musumeci ◽  
...  
Keyword(s):  
Spherical Wave ◽  
Addition Theorem ◽  
Wave Functions

Multiple scattering by a linear array of conducting spheres

1990 ◽  
Vol 68 (10) ◽  
pp. 1157-1165 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Multiple Scattering ◽  
Cross Sections ◽  
Linear Array ◽  
Plane Electromagnetic Wave ◽  
Spherical Wave ◽  
Approximate Solutions ◽  
Addition Theorem ◽  
Wave Functions ◽  
Coordinate Systems ◽  
Conducting Spheres

The problem of multiple scattering of a plane electromagnetic wave incident on N closely spaced perfectly conducting spheres is solved analytically by expanding the incident and scattering fields in terms of an appropriate set of vector spherical wave functions. To impose the boundary conditions, the scattered field from one sphere is expressed in coordinate systems attached to the others by using the translation addition theorem. An approximate solution is obtained to solve for the scattering by N small spheres. Numerical results for the normalized backscattering and bistatic cross sections for systems of spheres show that the agreement between the analytic and approximate solutions is better for larger electrical distances between neighbouring spheres.

scholarly journals HIGHER TWIST EFFECTS IN PROTON-PROTON COLLISIONS

2006 ◽  
Vol 15 (06) ◽  
pp. 1209-1231 ◽  
Author(s):  
A. I. AHMADOV ◽  
I. BOZTOSUN ◽  
R. KH. MURADOV ◽  
A. SOYLU ◽  
E. A. DADASHOV
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Cross Sections ◽  
Production Cross ◽  
Wave Functions ◽  
High Twist ◽  
Proton Proton ◽  
Proton Collisions ◽  
Pion Wave Function ◽  
Proton Proton Collisions

In this article, we investigate the contribution of the high twist Feynman diagrams to the large-pT pion production cross section in proton-proton collisions and we present the general formulae for the high and leading twist differential cross sections. The pion wave function where two non-trivial Gegenbauer coefficients a2 and a4 have been extracted from the CLEO data, two other pion model wave functions, P2, P3, the asymptotic and the Chernyak-Zhitnitsky wave functions are used in the calculations. The results of all the calculations reveal that the high twist cross sections, the ratios R, r, the dependence transverse momentum pT and the rapidity y of pion in the Φ CLEO (x,Q2) wave function case is very close to the Φ asy (x) asymptotic wave function case. It is shown that the high twist contribution to the cross section depends on the choice of the meson wave functions.

The theory of the T + D reaction

1951 ◽  
Vol 204 (1079) ◽  
pp. 503-513 ◽  
Keyword(s):  
Wave Function ◽  
Cross Section ◽  
Logarithmic Derivative ◽  
Coulomb Field ◽  
Absolute Magnitude ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Complex Reaction ◽  
Strong Spin

The energy dependence and absolute magnitude of the cross-section for the T + D reaction are described in terms of the exact wave-functions of the Coulomb field and a complex reaction length defined by the logarithmic derivative of the wave-function on the reaction surface. Previous difficulties in the interpretation of the experiments are largely attributed to the failure of the Wentzel-Kramers-Brillouin approximation. It is sufficient, but not necessary, to assume that the whole cross-section is due to s -waves; but in either case the presence of strong spin-orbit coupling is indicated.

HOW MUCH CAN BE LEARNT ABOUT PION WAVE FUNCTION FROM THE DRELL–YAN PROCESS?

1993 ◽  
Vol 08 (15) ◽  
pp. 2605-2621 ◽  
Author(s):  
SHAHIN S. AGAEV
Keyword(s):  
Wave Function ◽  
Transverse Momentum ◽  
Cross Section ◽  
Production Cross ◽  
Wave Functions ◽  
Feynman Diagrams ◽  
High Twist ◽  
Dilepton Production ◽  
Pion Wave Function ◽  
Order Of Magnitude

Contribution of the high twist Feynman diagrams to the dilepton production cross section in pion–hadron collisions is investigated. In calculations the asymptotic, Chernyak–Zhitnitsky and two other pion model wave functions P2, P3 are used. It is shown that this contribution depends on the choice of wave functions and for large dilepton transverse momentum pT and invariant mass Q in the limit [Formula: see text] exceeds the leading one by an order of magnitude. Perspectives of the Drell–Yan process in the context of the pion wave function investigation are discussed.

MATTER-DENSITY DISTRIBUTION IN THREE-NUCLEON NUCLEI AND THEIR DIFFRACTIVE INTERACTION WITH HEAVY NUCLEI

2009 ◽  
Vol 18 (03) ◽  
pp. 665-674
Author(s):  
YU. A. BEREZHNOY ◽  
V. YU. KORDA ◽  
A. G. GAKH
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Form Factors ◽  
Matter Density ◽  
Wave Functions ◽  
Heavy Nuclei ◽  
Nucleus Scattering

The nonrelativistic wave functions of 3 H and 3 He nuclei have been obtained on the basis of the experimentally measured charge form factors. The differential cross section of the elastic 3 He -nucleus scattering has been calculated with the help of the wave function derived. This cross section agrees with the experimental data on the elastic scattering of 3 He by 90 Zr , 120 Sn , and 208 Pb nuclei at 130 and 217 MeV. The integrated cross sections of various processes of 3 H and 3 He interaction with heavy nuclei have also been calculated.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

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