Two-Nucleon Scattering Without Partial Waves Using a Momentum Space Argonne V18 Interaction

We test the operator form of the Fourier transform of the Argonne V18 potential by computing selected scattering observables and all Wolfenstein parameters for a variety of energies. These are compared to the GW-DAC database and to partial wave calculations. We represent the interaction and transition operators as expansions in a spin-momentum basis. In this representation the Lippmann–Schwinger equation becomes a six channel integral equation in two variables. Our calculations use different numbers of spin-momentum basis elements to represent the on- and off-shell transition operators. This is because different numbers of independent spin-momentum basis elements are required to expand the on- and off-shell transition operators. The choice of on and off-shell spin-momentum basis elements is made so that the coefficients of the on-shell spin-momentum basis vectors are simply related to the corresponding off-shell coefficients.     

Scattering Theory for Jacobi Operators with Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators which are short range perturbations of quasi-periodic finite-gap operators. We show existence of transformation operators, investigate their properties, derive the corresponding Gel'fand-Levitan-Marchenko equation, and find minimal scattering data which determine the perturbed operator uniquely. Work supported by the Austrian Science Fund (FWF) under Grant No. P17762, the Austrian Academy of Sciences under DOC-21388, and INTAS Research Network NeCCA 03-51-6637.     

Scattering and absorption by spherical multilayer particles

We present a recursion formalism for the scattering coefficients of multilayered spherical particles which is more treatable for computer programs than the matrixformalism of Bhandari [1]. We computed explicitely the extinction and scattering cross section spectra of different metal coated spheres. Comparison with experimental results is done for gold-silver heterosystems. The spectra are in very good agreement with the experimental data.     

Stationary Scattering Theory for a Charged Particles Transport Problem

We consider a nonautonomous transport problem, the modelization of the charge exchange dynamics in a monoatomic ionized gas, and apply scattering theory to its dynamics. The free dynamics corresponds to the evolution of the total distribution of particles (neutral plus ionized particles) and the perturbed dynamics corresponds to the evolution of the neutral particles, which is the solution of a nonautonomous transport problem. The existence of the time-dependent wave operators was proved by the first author. In the present paper we follow Howland's formalism in constructing a stationary scattering theory for this nonautonomous transport problem by studying the evolution equation. We prove the existence of the wave operators and by using the smooth perturbation technique we obtain the similarity between perturbed and unperturbed operators.     

近距离雾的激光多次散射模拟

为了满足精确快速获取雾的多次散射仿真需求,在近程雷达距离较近情况下,将雷达方程和Mie散射理论相结合,提出一种快速有效的激光多次散射计算方法.首先通过雾滴谱模型建立雾颗粒的几何模型,然后根据Mie散射理论获得的单个粒子的散射函数计算激光在雾模型中单个颗粒的一次散射和二次散射功率密度,结合雷达方程推导出雾的多次等效散射截面和散射系数计算函数.模拟计算表明:雾的激光二次等效散射截面与雾浓度的2/3次方成正比,二次散射系数随能见度增加的衰减比一次散射系数快.     

Universality in Four-Body Scattering

The four-body system is studied in the limit of large two-body scattering length by solving momentum-space integral equations for the transition operators or, alternatively, configuration-space equations for wave function. A number of universal results for atom-trimer and dimer?Cdimer scattering observables are found. We furthermore address the question whether the universal four-body systems contain additional states besides the known two S-wave states.     

General N-Body Theory of Nonrelativistic Quantum Scattering

 The two-Hilbert-space theory of scattering is reviewed with particular reference to its application to nonrelativistic multichannel quantum- mechanical scattering theory. In Part I the abstract assumptions of the theory are collected, transition operators (both on- and off-energy-shell) are defined, the dynamical equations that determine the off-shell transition operators are presented and their real-energy limits examined, and the convergence of sequences of approximate transition operators is established. A section on how to incorporate group symmetries into the formalism reports new work. The material of Part I is relevant to a variety of both classical and quantum scattering systems. In Part II attention is directed specifically to N-body nonrelativistic quantum scattering systems in which the particles interact via short-range pair potentials. A method of constructing approximate transition operators is presented and shown to satisfy all the abstract assumptions of Part I. The dynamical equations that determine the half-on-shell approximate transition operators are shown to be coupled one-dimensional integral equations that have compact kernels and unique solutions when considered as operators on a Hilbert space of H?lder continuous functions. Moreover, the on-shell parts of those approximate transition amplitudes are shown to converge to the exact on-shell amplitudes as the order of the approximation increases. Detailed formulas for the kernels of the integral equations are written down for systems of particles that are distinguishable and for systems containing identical particles. Finally, some important open problems are described. Received July 2, 1999; accepted in final form October 27, 1999     

Simple Non-Linear Klein–Gordon Equations in Two Space Dimensions,with Long-Range Scattering

We establish that solutions, to the most simple non-linear Klein–Gordon (NLKG) equations in two space dimensions with mass resonance, exhibits long-range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that the modified wave operators can be chosen such that they linearize the non-linear representation of the Poincaré group defined by the NLKG.      

Efimov Physics in Four-Boson Scattering

Four-boson system is studied in the limit of large two-boson scattering length by solving momentum-space integral equations for the four-particle transition operators. A number of universal results for atom-trimer scattering observables is found.     

散射相函数的高阶光学参量研究

漫反射光谱技术被广泛应用于无创测量生物组织光学性质。当光源与探测器很近时,仅仅依靠吸收系数μ_a和约化散射系数μ′_s不能准确描述光源附近光的传播状态。而二阶光学参量γ的引入改善了近光源光的传播状态的描述。本文将生物组织的散射等效成特定球形颗粒的散射,基于Mie散射理论,计算了与散射相函数p(θ)有关的单粒子和多分散系粒子的二阶光学参量γ,研究了γ随尺度参数α和相对折射率m的变化规律,描述了γ与组织结构参量之间的联系,并阐述了γ对粒子特征的表征能力。研究表明,参量γ对尺度参数α小于2的微粒尺寸的改变是敏感的,并呈二次函数关系,其系数与相对折射率呈线性关系;对于相对折射率和尺度参数都不相同的两个粒子,他们的各向异性因子g相同时,二阶光学参量γ却不同,粒子越大,γ表征粒子特征的能力越强。这对于无创探究组织微观形态具有深远的意义。     

均匀椭球粒子对拉盖尔-高斯光束的散射特性研究

基于广义Mie理论, 研究了椭球粒子对在轴入射的拉盖尔-高斯光束的散射特性. 通过局域近似法求解椭球坐标系中的波束因子, 计算得到了波束因子之间满足的普遍关系. 对散射强度随椭球粒子不同尺寸参数和扁圆程度的变化特性进行了数值计算, 并针对不同拓扑荷时的散射强度进行了对比分析. 结果表明: 当椭球粒子尺寸在与入射光波长可比拟的范围内变化时, 散射强度随尺寸参数的增大而增大, 随椭球长短轴之比和拓扑荷的增大而减小. 本文的理论研究能够为拉盖尔-高斯光束在粒径测量、大气激光通信、 大气遥感等领域的应用提供更准确的粒子模型和参考价值. 关键词： 椭球粒子 拉盖尔-高斯光束 波束因子 散射强度     

On the Inverse Scattering Problem for Jacobi Matrices¶with the Spectrum on an Interval, a Finite System¶of Intervals or a Cantor Set of Positive Length

When solving the inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential, one gets reflection coefficients s _± and invertible operators , where is the Hankel operator related to the symbol s _±. The Marchenko–Faddeev theorem [8] (in the continuous case, for the discrete case see [4, 6]), guarantees the uniqueness of the solution of the inverse scattering problem. In this article we ask the following natural question – can one find a precise condition guaranteeing that the inverse scattering problem is uniquely solvable and that operators are invertible? Can one claim that uniqueness implies invertibility or vise versa? Moreover, we are interested here not only in the case of decreasing potential but also in the case of asymptotically almost periodic potentials. So we merge here two mostly developed cases of the inverse problem for Sturm–Liouville operators: the inverse problem with (almost) periodic potential and the inverse problem with the fast decreasing potential. Received: 7 September 2001 / Accepted: 3 December 2001     

周期结构声散射系数的无网格数值计算方法

将无网格思想引入周期结构声散射系数的数值计算,提出两种无网格数值计算模型:边界无网格模型(Boundary Meshless Model,BMM)及无网格平面波分解模型(Meshless Plane Wave Decomposition Model,MPDM),两种模型均可对任意形状周期结构的声散射系数进行计算,其中BMM适用于尺寸有限大的周期结构,而MPDM适用于尺寸无限大的周期结构.详细介绍两种无网格数值计算模型的推导过程,利用两种模型对正弦型周期结构的散射系数进行计算,并与测量实验结果进行对比分析,结果显示两种模型都具有良好的准确性,但BMM相比于MPDM误差更小.最后对两种模型的特点和适用性进行分析.     

Scattering from a rough layer of a random medium

This paper deals with scattering from a random-medium layer with rough boundaries. The fluctuations of the surface heights and medium permittivity are assumed to be small and smooth. All random quantities are assumed to be stationary and independent of each other. After the introduction of approximate boundary conditions, the system of partial differential equations is transformed into an integral equation where the fluctuations of the problem are represented as a zero-mean random operator. Employing smoothing, integral equations for the coherent fields are obtained. Use of the Helmholtz operator leads to solution for the coherent propagation constant while the boundary operators lead to coherent Fresnel coefficients. The characteristics of the results are illustrated by considering several examples.     

The Phase of the Scattering Operator from the Geometry of Certain Infinite-Dimensional Groups

We revisit the computation of the phase of the Dirac fermion scattering operator in external gauge fields. The computation is through a parallel transport along the path of time evolution operators. The novelty of the present paper compared with the earlier geometric approach by Langmann and Mickelsson (J Math Phys 37(8):3933–3953, 1996) is that we can avoid the somewhat arbitrary choice in the regularization of the time evolution for intermediate times using a natural choice of the connection form on the space of appropriate unitary operators.     

Formulas for q-Spherical Functions Using Inverse Scattering Theory of Reflectionless Jacobi Operators

We study the spectral problem associated to a Ruijsenaars-type (q-)difference version of the one-dimensional Schrödinger operator with Pöschl-Teller potential. The eigenfunctions are constructed explicitly with the aid of the inverse scattering theory of reflectionless Jacobi operators. As a result, we arrive at combinatorial formulas for basic hypergeometric deformations of zonal spherical functions on odd-dimensional hyperboloids and spheres.     

Scattering differentiates Alzheimer disease in vitro

The molecular bases of Alzheimer disease and related neurodegenerative disorders are becoming better understood, but the means for definitive diagnosis and monitoring in vivo remain lacking. Near-infrared optical spectroscopy offers a potential solution. We acquired transmission and reflectance spectra of thin brain tissue slabs, from which we calculated wavelength-dependent absorption and reduced scattering coefficients from 470-1000 nm. The reduced scattering coefficients in the near infrared clearly differentiated Alzheimer from control specimens. Diffuse reflectance spectra of gross brain tissue in vitro confirmed this observation. These results suggest a means for diagnosing and monitoring Alzheimer disease in vivo, using near-infrared optical spectroscopy.     

Scattering of electrons with formyl radical

A detailed theoretical study is carried out for electron interactions with formyl radical (HCO) with incident energies ranging from 0.01 to 5000 eV. This wide range of energy has allowed us to investigate a variety of processes and report data on vertical electronic excitation energies, dissociative electron attachment (DEA) and total cross-section along with scattering rate coefficients. We observed Ramsaur–Townsend minimum at 0.59 and 0.74 eV using DZP and cc-pDVZ basis sets, respectively. HCO has large number of low-lying excited states and the present study finds an overall good agreement with earlier reported data. In order to compute total cross-section, we have employed ab initio R-matrix method (0.01 to ～ 20 eV) and the spherical complex optical potential method (～ 10 to 5000 eV) employing static-exchange plus polarisation potential. The R-matrix calculations are performed using a close coupling method with the aid of 21 target states, 1191 configuration state functions and 195 channels. The DEA cross-sections of fragmentation of H^?, excitation cross- sections and scattering rate coefficients are reported for the first time. Total cross section presented here will provide a reference data set over an extensive impact energy range.     

Scattering of a TM plane wave from periodic random surfaces

This paper deals with the scattering of a TM plane wave from conductive periodic random surfaces. By means of the stochastic functional approach, the scattered field is expressed in terms of a harmonic series representation, in which the coefficients are homogeneous random functions and are given by Wiener-Hermite expansions. An approximate solution for the Wiener kernels is obtained up to the second order. Several anomalies appear in the angular distribution of the incoherent scattering because of combinations of scattering due to surface randomness and diffraction due to surface periodicity. These are incoherent Wood's anomalies associated with guided surface waves propagating along the surface, enhanced backscattering and diffracted backscattering enhancement. The physical reasons for these anomalies and numerical results are discussed.