Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

Multiple scattering using the Foldy-Twersky integral equation

The importance of multiple scattering processes for the propagation of ultrasound through dispersions is assessed. Under certain well defined conditions, the Foldy-Twersky integral equation can be used to find a value for the amplitude and complex wavenumber of the multiply scattered plane wave collected by either the receiving or the emitting transducer. Expressions for the amplitude and wavenumber are evaluated in terms of particle number density, wavelength of ultrasound and the forward and backward scattering amplitudes. In the case where the wavelength is much greater than the particle size, explicit expressions for the real and imaginary parts of the wavenumber are provided, in terms of the scattering and absorption cross-sections, as far as terms in the square of the number density of particles.     

Variational calculation of elastic nucleon-deuteron scattering

A previously developed variational principle for three-body scattering is applied to elastic nucleon-deuteron scattering. Separable S-wave potentials are used for both the singlet and triplet channels. The scattering amplitudes obtained agree with previous calculations and are accurate to four places. The three-body wave functions, which are needed for perturbation calculations, are also well converged.     

On two-sided estimates of the particle scattering amplitude by a potential and the amplitudes of multichannel processes

Functions permitting two-sided estimates to be obtained for the real and imaginary parts of the particle scattering amplitude by a nonspherical potential and for the amplitudes of multichannel processes are considered. To diminish the interval between the two estimates it is proposed to use Schwinger iteration of the test functions, whose multiparticle generalization permits estimation of the error in the approximation of P-coupled channels and the approximate assignment of the wave functions and the energy of the internal motion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 78–83, July, 1973.The author is deeply grateful to his colleagues m the Theoretical Physics Laboratory of the Joint Institute of Nuclear Research, Lkhagva Oido-Vyn' and Doctor B. N. Zakhar'ev, for formulating the problem and for useful comments which made this research realizable.     

Influence of stacking sequence on scattering characteristics of the fundamental anti-symmetric Lamb wave at through holes in composite laminates

This paper investigates the scattering characteristics of the fundamental anti-symmetric (A(0)) Lamb wave at through holes in composite laminates. Three-dimensional (3D) finite element (FE) simulations and experimental measurements are used to study the physical phenomenon. Unidirectional, bidirectional, and quasi-isotropic composite laminates are considered in the study. The influence of different hole diameter to wavelength aspect ratios and different stacking sequences on wave scattering characteristics are investigated. The results show that amplitudes and directivity distribution of the scattered Lamb wave depend on these parameters. In the case of quasi-isotropic composite laminates, the scattering directivity patterns are dominated by the fiber orientation of the outer layers and are quite different for composite laminates with the same number of laminae but different stacking sequence. The study provides improved physical insight into the scattering phenomena at through holes in composite laminates, which is essential to develop, validate, and optimize guided wave damage detection and characterization techniques.     

Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spins

In this paper each helicity amplitude of the two-body scattering of particles with arbitrary spins is considered as an element of a special class of Hilbert spacesH ^[u]. This space, which is called reproducing kernel Hilbert space (RKHS) has many special properties that appear to make it a natural space of functions to associate with the scattering helicity amplitudes. Some of the special properties of the RKHS are developed and then used to characterization of reproducing kernel (RK) ofH ^[u] as the solution to certain extremal problems. Then, it was shown that the optimal scattering state from the RKHS of the helicity amplitudes is analogous to the coherent state from the RKHS of the wave functions. The essential characteristic features of the scattering of particles with arbitrary spins in the optimal state dominance limit are established. An important alternative to the partial wave helicity analysis in terms of a fundamental set of optimal states is presented.     

Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces

Abstract

The small-slope approximation (SSA) for wave scattering at the rough interface of two homogeneous half-spaces is developed. This method bridges the gap between two classical approaches to the problem: the method of small perturbations and the Kirchhoff (or quasi-classical) approximation. In contrast to these theories, the SSA is applicable irrespective of the wavelength of radiation, provided that the slopes of roughness are small compared with the angles of incidence and scattering.

The resulting expressions for the SSA are given for the entries of an S-matrix that represents the scattering amplitudes of plane waves of different polarizations interacting with the rough boundary. These formulae are quite general and are valid, in fact, for waves of different origins. Apart from the shape of the boundary, some functions in these formulae are coefficients of the expansion of the S-matrix into a power series in terms of elevations. These roughness independent functions are determined by a specific scattering problem. In this paper they are calculated for the case of electromagnetic scattering at the interface of two dielectric half-spaces. In contrast to an earlier paper by the author, where only the formulae for the reflected field were presented, in this paper both reflected and transmitted fields are considered in detail.

The a priori symmetry relations that this scattering problem should obey (reciprocity and energy conservation) are formulated in terms of the S-matrix.

The statistical moments of scattering amplitudes are directly related to the mean-reflection coefficient and scattering cross sections, which are usually determined experimentally. The corresponding formulae are given here for the case of Gaussian space-homogeneous statistics of roughness.     

Antiproton-Nucleus Interaction and Coulomb Effect at High Energies

The Coulomb effect in high energy antiproton-nucleus elastic and inelastic scattering from ¹²C and ¹⁶O is studied in the framework of Glauber multiple scattering theory for five kinetic energies ranged from 0.23 to 1.83 GeV. A microscopic shell-model nuclear wave functions, Woods-Saxon single-particle wave functions, and experimental pN amplitudes are used in the calculations. The results show that the Coulomb effect is of paramount importance for filling up the dips of differential cross sections. We claim that the present result for inelastic scattering of antiproton-¹²C is sufficiently reliable to be a guide for measurements in the very near future. We also believe that antiproton nucleus elastic and inelastic scattering may produce new information on both the nuclear structure and the antinucleon-nucleon interaction, in particular the p-neutron interaction.     

Quantum scattering by nonspherical objects

The problem of scattering by spherically asymmetric potentials is considered where angular momentum not only ceases to be a conserved quantity but is also not a convenient basis for the expansion of wave functions and scattering amplitudes. Numerical solutions of the two-dimensional differential equation for the scattering amplitude of a particle and a coupled pair on a semitransparent disc of finite thickness are obtained. The effect of resonant diffraction is shown. A numerical scheme can be used to describe the scattering of a particle by deformed atomic nuclei.     

Recursion relations and scattering amplitudes in the light-front formalism

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends–Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.     

Cross sections for charmonia dissociation in collisions with pions, rhos and kaons

We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π,ρ and K in a potential that is derived from QCD.The reactions are governed by the quark-interchange processes.The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential.The numerical wave functions and cross sections are parametrized.The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms.We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difierence of quark or antiquark masses and of quark-antiquark spatial distributions ofthe two mesons.     

On the Kohn variational principles for three-particle systems

The Kohn-type variational principles are formulated, which can be used for calculating the (2 → 3), (3 → 2), and (3 → 3) scattering amplitudes if the two-particle wave functions are known.     

Submillimeter-wave scattering indicatrices for oversized water drops and ice particles in a cloud

Angular distribution functions for the intensity scattered by oversized water drops and ice particles in the raining clouds are considered in the paper for five wavelength values in the submillimeter (SubMM) wave band. It is shown that the obtained scattering indicatrices may be used to explain the effect of abnormal SubMM backscatter originating in the water-ice phase transition of oversized drops, as well as the effect of small-angle scattering on abnormal backscatter emission.     

Weighted-Residual Methods for the Solution of Two-Particle Lippmann–Schwinger Equation Without Partial-Wave Decomposition

Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves. The aim of the present work is to show that the weighted-residual approach in combination with local basis functions give rise to convenient computational schemes for the solution of the multi-variable integral equations without the partial wave expansion. The weighted-residual approach provides a unifying framework for various variational and degenerate-kernel methods for integral equations of scattering theory. Using a direct-product basis of localized quadratic interpolation polynomials, Galerkin, collocation and Schwinger variational realizations of the weighted-residual approach have been implemented for a model potential. It is demonstrated that, for a given expansion basis, Schwinger variational method exhibits better convergence with basis size than Galerkin and collocation methods. A novel hybrid-collocation method is implemented with promising results as well.     

Solutions of the integral equations for four identical particles

Using the separable representation of the scattering amplitudes for the subsystems 3 + 1 and 2 + 2, the integral equations for four identical particles with a separable two-particle interaction are reduced to a set of single variable integral equations. By solving the equations obtained, the binding energies and wave functions of the low-lying 0⁺ states of the system of four identical bosons, as well as the scattering length of a particle scattered by three bound particles, are calculated. The solution of the set of integral equations, describing the bound state of four nucleons, is performed, approximating the space wave function by a symmetric one, and the binding energy and wave function of the nucleus ⁴He are calculated.     

Elastic scattering of γ-rays from lead for energies from 0.145 to 1.33 MeV

Differential cross sections for elastic scattering of 889 and 1120 keV γ-rays from lead have been measured at angles ranging from 30° to 150°. These results and previously measured differential cross sections at 145, 279, 412, 662 and 1332 keV are compared with theoretical predictions taking into account Rayleigh scattering, nuclear Thomson scattering, and Delbrück scattering. The Rayleigh amplitudes of the K-shell were obtained from the theory of Brown et al., the amplitudes of the other shells from form factors calculated from relativistic HFS wave functions. Discrepancies are found at 145, 889, 1120 and 1332 keV while the experimental data at 279, 412 and 662 keV are in good agreement with the theory. A discussion of possible explanations and consequences is presented.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces - study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Scattering of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces – study with the curvilinear coordinate method

We present a method giving the bi-static scattering coefficient of two-dimensional (2-D) perfectly conducting random rough surface illuminated by a plane wave. The theory is based on Maxwell's equations written in a nonorthogonal coordinate system. This method leads to an eigenvalue system. The scattered field is expanded as a linear combination of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The Monte Carlo technique is applied and the bi-static scattering coefficient is estimated by averaging the scattering amplitudes over several realizations. The random surface is represented by a Gaussian stochastic process. Results are compared to published numerical and experimental data. Comparisons are conclusive.     

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.