Light scattering theories and computer codes

In aerosol science today light scattering simulations are regarded as an indispensable tool to develop new particle characterization techniques or in solving inverse light scattering problems. Light scattering theories and related computational methods have evolved rapidly during the past decade such that scattering computations for wavelength sized nonspherical scatterers can be easily performed. This significant progress has resulted from rapid advances in computational algorithms developed in this field and from improved computer hardware.In this paper a review of the recent progress of light scattering theories and available computational programs is presented. We will focus on exact theories and will not cover approximate methods such as geometrical optics. Short outlines of the various theories are given alongside with informations on their capabilities and restrictions.     

Multiple scattering of plasmons at rough surfaces

We investigated the polarization and angle dependence of the scattered light intensity of surface plasma oscillations (SPO) propagating along rough silver surfaces. The rough silver films were prepared using the methods of pre-evaporating CaF₂ and silver on heated substrates. The scattered light intensity of both systems is explained by surface scattering effects. Differences of the light intensities between the rough silver films prepared by the two methods mainly were observed in “restlight intensities”, which cannot be described by first-order scattering theories. We explain these differences by higher order scattering effects.     

Eikonal theory of electron- and positron-atom collisions

We review recent developments in the application of eikonal methods to the field of electron and positron collisions with atoms. The foundations of the eikonal approximation are first analyzed within the framework of potential scattering, with particular attention to those aspects of the theory which can be generalized to atomic collision processes. We next discuss various many-body applications of the eikonal method, namely: the Glauber approximation, the eikonal-Born series method, optical model theories, the eikonal distorted wave method and the multistate eikonal approximation. We also analyze eikonal exchange amplitudes. Applications of these methods are then considered, first for the case of elastic scattering and then for various inelastic processes.     

Quantum group symmetries and non-local currents in 2D QFT

We construct and study the implications of some new non-local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions, including the sine-Gordon theory and its generalization to affine Toda theory. These non-local currents provide a non-perturbative formulation of the theories. The symmetry algebras correspond to the quantum affine Kac-Moody algebras. TheS-matrices are completely characterized by these symmetries. FormalS-matrices for the imaginary-coupling affine Toda theories are thereby derived. The application of theseS-matrices to perturbed coset conformal field theory is studied. Non-local charges generating the finite dimensional Quantum Group in the Liouville theory are briefly presented. The formalism based on non-local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in 2d.     

On kinematical constraints in boson-boson systems

We consider the scattering of two bosons with negative parity and spin 0 or 1. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to satisfy partial-wave dispersion relations and therefore provide a suitable basis for data analysis and the construction of effective field theories. Our derivation relies on a decomposition of the various scattering amplitudes into suitable sets of invariant functions. A novel algebra was developed that permits the efficient computation of such functions in terms of computer algebra codes.     

Methods of Quantum Field Theory with Rapidly Increasing Spectral Functions

A review of the methods of constructing the scattering amplitudes and Green functions in the non-renormalizable quantum field theories with rapidly increasing spectral functions is given. Such theories as the theories with the chiral Lagrangians, those which describe the interactions with gravitational fields and the theories of weak interactions can be taken as examples. Three big groups of these methods are presented here. In particular, these are as follows: construction of the scattering amplitude in x-space (the function F(x)), construction of the scattering amplitude in momentum space (the function F˜ (p)) and definition of the scattering amplitudes by solving the appropriate equations (in x- or p-Space). This works was reported at the Second International Symposium on Non-local Quantum Field Theory in 1970 at Azau, USSR.     

Reflection amplitudes of boundary Toda theories and thermodynamic Bethe ansatz

We study the ultraviolet asymptotics in A_n affine Toda theories with integrable boundary actions. The reflection amplitudes of non-affine Toda theories in the presence of conformal boundary actions have been obtained from the quantum mechanical reflections of the wave functional in the Weyl chamber and used for the quantization conditions and ground-state energies. We compare these results with the thermodynamic Bethe ansatz derived from both the bulk and (conjectured) boundary scattering amplitudes. The two independent approaches match very well and provide the non-perturbative checks of the boundary scattering amplitudes for Neumann and (+) boundary conditions.     

Quantum scattering from classical field theory

We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial-value conditions. The initial-value conditions are such as to make the solution of the classical field equations amenable to numerical methods. We propose a practical procedure for computing classical solutions which contribute to high energy two-particle scattering amplitudes. We consider in this regard the implications of a recent numerical simulation in classical SU(2) Yang-Mills theory for multiparticle scattering in quantum gauge theories and speculate on its generalization to electroweak theory. We also generalize our results to the case of complex trajectories and discuss the prospects for finding a solution to the resulting complex boundary value problem, which would allow the application of our method to any wave packet to coherent state transition. Finally, we discuss the relevance of these results to the issues of baryon number violation and multiparticle scattering at high energies.     

The sigma model (dual) representation for a two-parameter family of integrable quantum field theories

We introduce and study two-parameter families of integrable field theories. The perturbative and non-perturbative methods are used to justify their factorized scattering theory in the form of the direct products of two S-matrices of the sine-Gordon model. The Bethe ansatz technique is applied for the calculation of the observables in the strong coupling region. The results are in the exact agreement with ones following from the sigma model action which is a two-parameter U(1) ⊗ (1) symmetrical deformation of the O(4) non-finear sigma model. The application of the sigma model representation to related perturbed conformal field theories is discussed.     

On some aspects of the definition of scattering states in quantum field theory

The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering states. As the strong limit is not suitable for the definition of scattering states in quantum field theory, some other limiting procedure is needed. Two possibilities are considered, the abelian limit and adiabatic switching. Formulas for the scattering states based on both methods are discussed, and it is found that generally there are significant differences between the two approaches. As an illustration of the applications and the features of these formulas, S-matrix elements and energy corrections in two quantum field theoretical models are calculated using (generalized) old-fashioned perturbation theory. The two methods are found to give equivalent results.     

New collective mode in the fractional quantum Hall liquid

We apply the methods of continuum mechanics to the study of the collective modes of the fractional quantum Hall liquid. Our main result is that at long-wavelength, there are two distinct modes of oscillations, while previous theories predicted only one. The two modes are shown to arise from the internal dynamics of shear stresses created by the Coulomb interaction in the liquid. Our prediction is supported by recent light scattering experiments, which report the observation of two long-wavelength modes in a quantum Hall liquid.     

利用T-matrix计算非球形粒子散射特性的研究

本文用T-matrix方法计算了非球形气溶胶粒子的光学特性,得到了气溶胶粒子的消光截面、散射截面、吸收截面与气溶胶粒子形状的关系,不同形状气溶胶粒子的有着相同的散射相函数和不同的偏振度,非球形气溶胶粒子的散射相函数对其复折射指数的实部和虚部都不太敏感,而偏振相函数对其实部和虚部都比较敏感.此结论为研究大气辐射传输提供了较好的方法,尤其是偏振度与偏振相函数的提出为用偏振的方法进一步的反演气溶胶的光学参数提供了理论基础.     

The influence of different anomalous terms in effective meson lagrangians on baryon resonances

Anomalous actions are responsible for the coupling of ω-mesons in effective meson theories. The influence of two different choices for the anomalous terms on baryon resonances is investigated. It is shown that pion-nucleon scattering does not provide a criterion to prefer one of these two terms.     

A heuristic model approximation for scattering from perfectly conducting one-dimensional random rough surfaces

We propose a model for scattering from one-dimensional, perfectly conducting, slightly rough surfaces. A possible method for solving the scattering equations is examined which, with some assumptions, suggests the final result. The approximation is relatively simple and is comparable in computational effort with most first-order theories. We compare the bistatic scattering cross section for TE waves predicted by the present model for Gaussian randomly rough surfaces with numerical simulations and with some first-order theories. The comparison shows that the model is remarkably accurate for slightly rough surfaces and TE polarization.     

A Review of Elastic Light Scattering Theories

Mie scattering is an important tool for diagnosing microparticles or aerosol particles in technical or natural environments. Mie theory is restricted to spherical, homogeneous, isotropic and non-magnetic particles in a non-absorbing medium. However, as microparticles are hardly ever spherical or homogeneous, there is much interest in more advanced scattering theories. During recent decades, scattering methods for non-spherical and non-homogeneous particles have been developed and even some computer codes are readily available. Extension of Mie theory covers coated spheres, stratified spheres and clustered spheres. For homogeneous non-spherical particles such as spheroids, ellipsoids and finite cylinders, surface discretization methods have been developed. Scattering by inhomogeneous particles may be computed by volume discretization methods.     

Multiple scattering, optical potential, and N-body approaches to elastic two-fragment collisions

Two-fragment elastic scattering problems are often studied using multiple scattering theories such as those due to Watson along with Feshbach-type optical potentials. These conventional methods are re-examined, rephased, and generalized using the language and techniques of contemporary N-particle scattering theory. A special realization of the latter theory is developed which is especially useful for relating the older and newer methods. This is facilitated by maintaining the same off-shell continuations of the scattering operators in both approaches. In particular, a set of connected-kernel scattering integral equations is introduced which provides a consistent N-particle framework for the calculation of that definition of the optical potential possessing the Feshbach off-shell continuation. These equations exhibit a multiple-scattering substructure and therefore allow the systematic generalization of some of the usual low-order approximations.     

Selected topics in lattice dynamics: a critical review (including breathers)

We present a review of lattice dynamics to provide the underpinnings for the study of nonlinear localized modes, the so-called breathers. After a historical survey we address the following topics: harmonic theories, anharmonic perturbation theory, self-consistent theories, classical simulation techniques, path-integral theories, realistic crystal potentials, and intrinsic localized modes. We discuss both static and dynamic properties of crystals, e.g., neutron and x-ray scattering. We do not consider transport properties. Throughout, our emphasis is on discussing the major advances in the field and citing the appropriate references. Our aim is to achieve clarity and simplicity for readers who wish to move on to the study of breathers. We have made a special effort to set up the language and notation that is generally accepted in the field. In order to acquaint the reader with the techniques used in lattice dynamics we have analyzed a number of key problems in detail including a comparison with the available experimental data.     

A heuristic model approximation for scattering from perfectly conducting one-dimensional random rough surfaces

Abstract

We propose a model for scattering from one-dimensional, perfectly conducting, slightly rough surfaces. A possible method for solving the scattering equations is examined which, with some assumptions, suggests the final result. The approximation is relatively simple and is comparable in computational effort with most first-order theories. We compare the bistatic scattering cross section for TE waves predicted by the present model for Gaussian randomly rough surfaces with numerical simulations and with some first-order theories. The comparison shows that the model is remarkably accurate for slightly rough surfaces and TE polarization.     

Role of spin-flip exchange scattering for hot-electron lifetimes in cobalt

The spin-dependent lifetimes of hot electrons in fcc Co films were studied by spin- and time-resolved two-photon photoemission. Even for excitation energies close to the Fermi level, we find almost identical lifetimes for majority and minority electrons. This result contradicts ab initio theories predicting 5 to 10 times longer lifetimes for the majority electrons in 3d ferromagnets. We provide direct experimental evidence that this discrepancy is caused by the dominance of exchange scattering in inelastic electron decay, in combination with the excitation of secondary electrons. The latter are inherent for all real materials and devices.     

奇异点展开法（SEM）与共振散射理论（RST）之间的联系

近年来,在声散射问题中提出了两种理论:奇异点展开法(SEM)和共振散射理论(RST)。本文建立这两种理论之间的联系,以水中弹性柱和球的散射为例,我们证明RST可以直接从SEM导出,因此两者是等价的。首先从总散射波中分离出刚性背景,然后应用Mittag-Leffler定理将纯弹性散射波展开成严格共振公式。我们特别证明,对于大多数水中实弹性体,再辐射效率和共振宽度近似地正比于相应极点的虚部,这说明共振散射特性可以整个地由复频率极点确定。因此,目前的分析允许对RST有更深的理解。对于水中铝柱和钨碳球的情况,我们用新的共振公式计算了分波形态函数,其结果与严格计算符合良好。