Scattering Amplitudes Research Articles

Application of the generalized scattering amplitude in quantum potential scatterings.

The concept of a generalized scattering amplitude is introduced and applied to quantum potential scatterings. After an outgoing spherical wave is factored out from a wave function, the remaining wave envelope is defined as the generalized scattering amplitude. The transformed Schr\odinger equation, in terms of the generalized scattering amplitude, can be solved numerically by using a finite-difference method over the entire scattering domain. Example problems of scatterings by a spherical potential well and the (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,H) static field interaction potential are solved to validate the theoretical formulation and numerical method. The far-field solutions for the ordinary scattering amplitude and differential cross section agree very well with those obtained from the partial-wave analysis. The radial profiles of the generalized scattering amplitude and particle density function over the entire scattering region are also presented, and their properties are discussed. These results demonstrate that the method can be used to yield a complete and accurate solution to scattering problems involving arbitrary interaction potentials.

Tree scattering amplitudes of the spin-4/3 fractional superstring. I. The untwisted sectors.

Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by the spin-4/3 fractional superconformal algebra---a parafermionic algebra studied by Zamolodchikov and Fateev involving chiral spin-4/3 currents on the world-sheet in addition to the stress-energy tensor. Examples of tree scattering amplitudes are calculated in an explicit c=5 representation of this fractional superconformal algebra realized in terms of free bosons on the string world-sheet. The target space of this model is three-dimensional flat Minkowski space-time with a level-2 Kac-Moody so(2,1) internal symmetry, and has bosons and fermions in its spectrum. Its closed string version contains a graviton in its spectrum. Tree-level unitarity (i.e., the no-ghost theorem for space-time bosonic physical states) can be shown for this model. Since the critical central charge of the spin-4/3 fractional superstring theory is 10, this c=5 representation cannot be consistent at the string loop level. The existence of a critical fractional superstring containing a four-dimensional space-time remains an open question.

The Cauchy Data and the Scattering Amplitude

(1994). The Cauchy Data and the Scattering Amplitude. Communications in Partial Differential Equations: Vol. 19, No. 9-10, pp. 1735-1741.

Strong-field cyclotron scattering. I - Scattering amplitudes and natural line width

The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold et al. (1982) and of Sokolov and Ternov (1968), which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson and Lippmann (1949) are not. In addition, it is shown that the Breit-Wigner broadening approximation E tends to E - i(Gamma)/2 is consistent with the perturbation-theoretic order of the calculation, if the former basis states are chosen, but not the latter.

General class of scattering for dyadic elastic waves

Scattering amplitudes for a single object in isolation, multiple-scattering amplitudes for a fixed configuration of spherical scatterers, integral equations, energy theorems, and systems of algebraic equations for single- and multiple-scattering coefficients are given for dyadic elastic incident waves with general polarization vector. Monopole-dipole leading-term approximations for the dyadic scattering amplitudes are derived and the case of two spheres is treated.

DIVERGENCES OF DISCRETE STATES AMPLITUDES AND EFFECTIVE LAGRANGIAN IN 2D STRING THEORY

Scattering amplitudes for discrete states in 2D string theory are considered. Pole divergences of tree-level amplitudes are observed and residues are interpreted as renormalized amplitudes for discrete states. An effective Lagrangian generating renormalized amplitudes for open string is obtained and the corresponding Ward identities are presented. A relation of this Lagrangian with homotopy Lie algebra is discussed.

Fourier Transform of Scattering Amplitude and Channel Transfer Model

The full scattering amplitude is transformed into the explicit Fourier transform. The inverse· transform involves also a Fourier·type integral form. The properties of the new amplitude closely resemble those of the partial wave scattering amplitude, and they also give rise to some physical quantities for the elastic and inelastic scattering cross sections over the entire range of energy. The Fourier·type scattering amplitude is extended to a complex integral, so that the full scattering amplitude is generated from poles of the new scattering amplitude. As an application, a response function is introduced between the s· and f·channel of the 7[+7[- scattering, and the differential cross sections are estimated at the energy region of the p·resonance. It is also shown that the response function is applicable to the evaluation of the p·exchange contribution in the 7[+7[­ scattering as well as in the 7[-P charge exchange scattering. The Fourier transform has contributed to the advancement of science and engi­ neering due to the application~ of its excellent formalism. This expression is formulated in terms of a newly designed variable different from the primary one. It is most applicable to investigate what behaviors give rise to a physical system with respect to the secondary parameter, and what method makes mathematical calcula­ tions easy. The former is seen in a study on the transfer function of an impulse response in the communication system, and the latter is observed in a mathematical calculation on the oscillating system and the electric circuit. The Fourier transform also is very important for the broad application of particle physics. In the scattering theory of particles, the scattering amplitude is divided into discrete partial waves by means of the Legendre polynomial. ; Although this expan­ sion holds a quantum mechanical nature, it has disturbed us because of its discrete property in some practical evaluations. In the high energy scattering, the scattering amplitude has often been expressed in a continuous integral form called impact parameter representation. It may be looked upon as the Laplace-type transform of a scattering amplitude, if we compare it with the formulation described in this article.I)-3) The other continuous spectrum representation was briefly formulated by the present author sixteen years ago. 4

Fourier Transform of Scattering Amplitude and Channel Transfer Model

Fourier Transform of Scattering Amplitude and Channel Transfer Model

Symmetry properties of scattering amplitudes and applications to inverse problems

For the transformations of the potential q → q ∘ L, where L is one of the following transformations: rotation, scaling, or translation, the corresponding transformation of the scattering amplitude is given. A necessary and sufficient condition on the scattering amplitude for the scatterer to be spherically symmetric is derived as an application of the above results.

Errata: The Scattering Amplitudes and Cross Sections in the Theory of Thermoelasticity

Errata: The Scattering Amplitudes and Cross Sections in the Theory of Thermoelasticity

On systematic errors in distance estimates of the Virgo cluster and the intrinsic scatter in the Tully-Fisher relation

view Abstract Citations (23) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On Systematic Errors in Distance Estimates of the Virgo Cluster and the Intrinsic Scatter in the Tully-Fisher Relation Burstein, David ; Raychaudhury, Somak Abstract Recent estimates of the amplitude of scatter in the Tully-Fisher relation and the related question of distance to the Virgo cluster are critically examined. The scatter of 0.7 mag in the Tully-Fisher relation found by Kraan-Korteweg, Cameron, and Tammann is found to be primarily observational in origin, the combination of line-of-sight effects within their 121 galaxy sample and the use of older, poorly determined magnitudes. The true scatter in the Tully-Fisher relation is less than 0.4 mag, as found by Pierce and Tully. The assumptions that both Pierce and Tully and Kraan-Korteweg, Cameron, and Tammann used in their separate determinations of the distance to the Virgo cluster are applied to the same combined sample of 131 galaxies, defined to be consistent with the formalism of Kraan-Korteweg, Cameron, and Tammann. The use of different subsets of calibrator galaxies by the two studies permits both distance estimates to be consistent with these data, despite differing in predicted distance modulus by 0.6 mag! In the absence of a general agreement on inclination corrections to magnitudes, diameters, and rotation velocities, the choice of calibrator galaxies and the distances to them and the reliability of observed data, no agreement can be reached on the distance of the Virgo cluster as derived from the Tully-Fisher relation for spiral galaxies. Publication: The Astrophysical Journal Pub Date: August 1989 DOI: 10.1086/167680 Bibcode: 1989ApJ...343...18B Keywords: Astrometry; Distance; Virgo Galactic Cluster; Calibrating; Computational Astrophysics; Cosmology; Error Analysis; Magnitude; Astrophysics; COSMOLOGY; GALAXIES: CLUSTERING; GALAXIES: DISTANCES full text sources ADS | data products SIMBAD (16) NED (16)

Application of chiral bag model to pion photoproduction.

Scattering amplitudes for the pion photoproductions have been derived on the chiral bag model by taking into account pion cloud effects, pion-pole term, and antiquark propagation. The differential cross section for $^{13}\mathrm{C}$(\ensuremath{\gamma},${\ensuremath{\pi}}^{+}$${)}^{13}$B has also been calculated.

Multiloop amplitudes for the bosonic string in the operator formalism

Scattering amplitudes for the bosonic closed string theory are computed at arbitrary genus in the operator formalism. The equivalence with the formulas provided by the Polyakov approach (in the critical dimension d=26) is demonstrated. A discussion about the residual U(1) × U(1) symmetry of the torus is given.

Some physical factors influencing the accuracy of convolution scatter correction in SPECT

In these techniques scatter correction in the projection relies on filter functions, QF, evaluated by Fourier transforms, from measured scatter functions, Qp, obtained from point spread functions. The spatial resolution has a marginal effect on Qp. Thus a single QF can be used in the scatter correction of SPECT measurements. However, it is necessary to examine the details of the shape of point spread functions during evaluation of Qp. QF is completely described by scatter amplitude AF, slope BF and filter sum SF. SF is obtained by summation of the values of QF occupying a 31*31 pixels matrix. Regardless of differences in amplitude and slope, two filter functions are shown to be equivalent in terms of scatter correction ability, whenever their sums are equal. On the basis of filter sum, the observed small influence of ellipticity on QF implies that an average function can be used in scatter correcting SPECT measurements conducted with elliptic objects. Scatter correction by convolution may be severely hampered by photon statistics when SPECT imaging is done with low-energy photons. Whenever superficial and inner radioactive distributions coexist the observed reduction of SF close to the phantom surface indicates that scatter correction of such distributions has to rely on two distinct filter functions. Corrections based on a surface function produce accurate results in the superficial region, while the central distributions are substantially overestimated.

On Singularities of Scattering Amplitudes through a Convex Triangular Obstacle in Scattering Theory

A triangular grating is characterized by three parameters like period, groove depth and angle. A smooth convex triangular obstacle, forming a part of the said grating, is considered herewith for finding the Scattering amplitudes through the illuminated faced of the obstacle. Complex Fourier double transforms of the concerning wave functions has been determined for finding the Scattering amplitudes, allowing thereby the wave number to become unlimitedly large. It has been further justified that the singularities of the Scattering amplitudes occur when the concerning surface harmonics behave like distributions. In particular, the Scattering amplitudes have been determined when the Fourier transforms of the concerning wave functions behave like Dirac distributions. Finally, the expressions of relative powers of the groove fields have been determined in terms of the wedge parameters.

The Scattering Amplitudes and Cross Sections in the Theory of Thermoelasticity

A plane thermoelastic wave, propagating in an isotropic and homogeneous, medium in the absence of body forces and heat sources, is scattered by a smooth, convex and bounded three-dimensional body. The body could be a rigid scatterer at constant temperature, a rigid scatterer at thermal insulation, a cavity at constant temperature, or a cavity at thermal insulation, while in all cases the Kupradze’s radiation conditions are assumed to hold at infinity. The second law of thermodynamics imposes an attenuation of the elastothermal and the thermoelastic waves, which is reflected upon the lack of symmetry of the unified differential operator governing the Biot theory of dynamic thermoelasticity. Normalized spherical scattering amplitudes are introduced for the displacement as well as the temperature field, via asymptotic analysis of appropriate integral representations. With the exception of the scattering amplitudes corresponding to the transverse elastic waves, all the other scattering amplitudes involve attenuation factors. The classical definition of the scattering cross section reduces, in practice, the thermoelastic scattering process to a consideration of the transverse incident and the transverse scattered wave alone. However, more detailed analysis demands the introduction of local units for measuring the energies carried by the elastothermal and the thermoelastic waves, which give rise to five types of scattering cross sections. They measure the total energy for each type of wave, scattered by the body, by the standards of the corresponding incident wave in the forward direction. Throughout this work the thermoelastic coupling is indicated by the well known dimensionless constant $\varepsilon $. The corresponding scattering theory for the classical dynamic elasticity is recovered in the limiting case as $\varepsilon \to 0 + $.

Complex-Frequency Poles of the Acoustic Scattering Amplitude, and Their Ringing

An elastic body immersed in a fluid will ring when isoni- fied by sound whose frequency is the same as one of the resonances of that body. Correspondence has been established between these normal mode resonances of the body and the individual circumferential waves predicted by creeping wave theory. Insonifying the target by a rela- tively long sinusoidal wave train, with a narrow spectrum centered around, or away from, a selected resonance frequency, results in a series of superimposed responses consisting of the specular reflection and succession of creeping waves arriving after repeated circumnavi- gations of the body which, at resonance only, add in phase to generate the ringing response. Echoes from spherical targets are analyzed in this fashion and are also associated with the resonance poles in the complex frequency plane, obtained by us in the form of contour plots.

Elastic scattering of alpha particles and the phase of the nucleon-nucleon scattering amplitude.

Glauber theory can describe elastic scattering of alpha particles by He-4, He-3, H-2, and H-1 at 7 GeV/c if the phase of the nucleon-nucleon elastic-scattering amplitude varies with momentum transfer. The phase variation leads to diffraction patterns differing markedly from those typical of constant-phase calculations and greatly affects the magnitudes of the intensities. These changes are mainly due to changes in the interference between amplitudes for different orders of multiple scattering and to a decrease in their moduli.

Temperature dependence of mobility in scattering on point defects

Scattering amplitude in the field of a short-range force center is calculated using factorization of the potential. The results obtained are used to study the temperature dependence of charge-carrier mobility in the random field of chaotically distributed structural point defects.

One-Dimensional Model of Nucleus-Nucleus Collision with Zero-Range Force: Exact Scattering Amplitude and Equivalent Local Potential

One-Dimensional Model of Nucleus-Nucleus Collision with Zero-Range Force: Exact Scattering Amplitude and Equivalent Local Potential