Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.     

The fixed scatterer approximation and nucleon deuteron scattering

A method of solving the Schroedinger Equation for the scattering from two fixed local potentials is presented. The solutions are used within the framework of the fixed scatterer approximation to perform model calculations of N-D scattering using both effective range theory potentials and a “semi-realistic” potential with a strong repulsive core. For smooth potentials approximate solutions to the fixed scatterer problem are proposed and found to be quite accurate.Other procedures for calculating elastic scattering were compared with the exact fixed scatterer approximation. The results show that the neglect of longitudinal momentum transfer in the Glauber multiple diffraction theory is a severe effect except in the forward direction. For small angle scattering the Glauber prediction for the double scattering amplitude is quite accurate, and does not depend strongly upon either the extent of potential overlap, or the ratio $\text{V}\text{E}$. Comparisons with the Agassi and Gal results for nonoverlapping potentials indicate that the effects of potential overlap are important, at least for the lowest partial waves. Conclusions about the overall importance of off-energy shell effects in nucleon-deuteron scattering, and about the interference of these effects with the determination of the correlation structure of nuclei are not free from ambiguities.     

Calculation analyzing power in the elastic scattering of protons on <Superscript>15</Superscript>C and <Superscript>15</Superscript>N nuclei in the diffraction theory

Shell-model wave functions are used to calculate the vector analyzing power in the elastic scattering of 0.2, 0.6, and 1 GeV protons on ¹⁵C and ¹⁵N nuclei within the Glauber diffraction theory. Single and double collisions are allowed for upon the decomposition of multiple scattering. It is shown that the number of oscillations and the amplitude of the analyzing power increase with rising energy in the same angular range.     

Calculations of the Mie scattering coefficients for multilayered particles with large size parameters

The calculation procedure for the scattering coefficients appearing in the Mie theory is discussed for a case of multilayered particles with a large size parameter. There are two different aspects to the problem. The first aspect concerns a case where the imaginary part of the size parameters remains small. Shown here is the possibility for avoiding the canonical recommendations which prescribe using both upward and downward recursions for different types of Bessel functions. We have justified the procedure based on the upward recursions only where results are as stable as those in the canonical one. The second aspect concerns the case with a large imaginary part of the size parameter. The calculation procedure for a multilayered particle fails in such a case because of 0/0-type uncertainty. However, this problem can be overcome by using the proper asymptotic relations at crucial points. The numerical results are demonstrated for spherical and cylindrical multilayered particles.     

Effect of the shell structure of nuclei on p 15C and p 15N scattering within diffraction theory

The differential cross sections for elastic proton scattering on ¹⁵C and ¹⁵N nuclei at energies of 150 and 800 MeV were calculated within the diffraction theory of Glauber multiple scattering. Shellmodel wave functions were used in these calculations, and particular attention was given to analyzing the sensitivity of the calculated features to distinctions between the shell structure of the ¹⁵C nucleus and the shell structure of the ¹⁵N nucleus. The calculations were performed in the approximation of double scattering. The multiple-scattering operator was written in a form that permits taking into account collisions with nucleons belonging to different shells. It is shown that the difference in structure between the two nuclei in question leads to substantial distinctions between the differential cross sections for scattering at an energy of 800 MeV and scattering angles larger than 25°.     

Effective scattering area of a reflector antenna with a dielectric radome

We propose a technique for exact calculation of the effective scattering area (ESA) of a two-dimensional, parabolic-reflector antenna with a dielectric radome. This technique is based on an iterative approach in which the general problem is reduced to a successive solution of the diffraction problem for separately the antenna and its radome. These two problems are formulated in terms of Fredholm integral equations of the first and second kinds, and are solved numerically. Convergence of the iterative procedure is studied. We numerically calculate the ESA of an antenna having a cylindrical radome and fed from an open-ended planar waveguide. The obtained ESAs of the antenna and the antenna-radome system are compared with the results of calculations based on the physical-optics approximation. 5th Central Testing Institute of the Ministry of Defense of the Russian Federation, Voronezh, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 879–885, September, 1999.     

The determination of the nuclear charge distribution of 208Pb from elastic electron scattering and muonic X-rays

An iterative procedure is presented for determining a static nuclear charge distribution from experimental electron scattering cross sections and muonie atom X-ray transition energies. The errors and error correlations implied by the independent statistical errors in the experimental data are expressed in coordinate space, and kernels are derived which specify the linear constraints imposed on the charge density by the experimental data. Pseudo-experimental data for ²⁰⁸Pb, generated from a known charge distribution, are used to demonstrate the validity of the procedure. A detailed analysis of experimental data for ²⁰⁸Pb is presented, utilizing electron scattering data at five different energies and six muonic energy levels. The theoretical implications of this work concerning quantum density fluctuations and the possible existence of a central depression are discussed.     

Nucleon recoil for low-energy antikaon-deuteron scattering

The effect of the nucleon recoil for antikaon-deuteron scattering is studied in the framework of effective field theory. In particular, we performed a calculation of the nucleon recoil effect for the double scattering process. It is shown that the leading correction to the static term that emerges at order ξ ^1/2, where ξ?=?m _K /M _N , vanishes due to a complete cancellation of individually large terms. The resulting recoil effect for the double scattering process is found to be of order of 10–15% compared to the static term. We also developed a method to include the nucleon recoil effect in the calculation of the multiple scattering diagrams.     

Influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media

Monte Carlo algorithm and Stokes-Mueller formalism are used to simulate the propagation behavior of polarized light in turbid media. The influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media is discussed. Single and double scattering photons form the major part of backscattered polarization patterns, while multiple scattering photons present more likely as background. Further quantitative analyses show that single scattering approximation and double scattering approximation are quite accurate when discussing the polarization patterns near the incident point.     

From scattering singularities to the partition of a horseshoe

In a chaotic scattering system there are two different approaches to construct a symbolic dynamics. One comes from the branching tree obtained from a scattering function. The other comes from a Markov partition based on the line of primary homoclinic tangencies in the Poincare map taken in the interaction region. In general the two results only coincide for a complete horseshoe. We show how to make a different choice for the partition in the internal Poincare section based on scattering behavior and not on homoclinic tangencies. Then the corresponding symbolic dynamics coincides also for the incomplete case with the one obtained naturally from the scattering functions. The scattering based partition lines of the horseshoe are constructed by an iterative procedure. (c) 1999 American Institute of Physics.     

Anomalous elastic scattering of X-ray emission by an atom with open shells

In the nonrelativistic approximation for one-electron wave functions, the differential cross section for anomalous scattering of linearly polarized X-ray emission by a sodium atom near the ionization threshold of the 1s ² shell is studied. The analysis takes into account the many-body effects of relaxation of atomic shells in the field of a deep vacancy, multiplet splitting, and the double excitation/ionization processes. The theoretical results obtained for the anomalous-dispersion scattering region are predictive.     

Structure of 6Li from high-energy proton scattering

The elastic and inelastic (2.189 MeV level) scattering of 1 GeV protons from ⁶Li is predicted using Glauber multiple-scattering theory in conjunction with an α-d cluster model capable of fitting quantitatively a large number of measured form factors, in particular the most recent high-momentum-transfer electron scattering data. The predictions, especially in the inelastic channel, are quite sensitive to the parameters of the model. A valuable opportunity is thus provided via experiments well within the capabilities of LAMPF for comparison of structure information obtained from proton scattering with that from other sources in the case of a “test” nucleus whose properties are relatively well determined and unambiguous. Moreover, proton scattering goes beyond electron scattering in possibly providing information about the effective real part of the proton-deuteron cluster amplitude, and thus indirectly about D-state effects in the deuteron cluster.     

二维高斯波束对多层球粒子电磁散射的解析解

基于矢量波函数在球和柱坐标系中表达式之间的转换关系,提出了一种求解球坐标系中二维高斯波束波形因子的方法,得到了二维高斯波束波形因子在球坐标系中的解析公式.结合广义米理论推导了在轴二维高斯波束入射多层球粒子的电磁散射的解析解,并对散射强度随散射角的分布进行了数值模拟,结果与平面波入射情况进行了比较. 关键词： 矢量波函数 波形因子 电磁散射 广义米理论     

Large corrections to high-pT hadron-hadron scattering in QCD

We have computed the first non-trivial QCD corrections to the quark-quark scattering process which contributes to the production of hadrons at large p_T in hadron-hadron collisions. Using quark distribution functions defined in deep inelastic scattering and fragmentation functions defined in one particle inclusive e⁺e^? annihilation, we find that the corrections are large. This implies that QCD perturbation theory may not be reliable for large-p_T haron physics.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Real and virtual photon contributions to inelasticep scattering

We investigate direct and resolved photon contributions to hardep scattering at high energies. Some terms of the direct contribution are already included in the resolved photon one, described in terms of the photon structure functions. A suitable subtraction mechanism has to be found in order to avoid double counting. Inelasticep scattering requires the knowledge of photon structure functions over a wide range in photon virtuality, in particular from approximately zero up to almost 10⁵ GeV² at HERA. We analyse the real and virtual photon structure function and we comment on the structure of the photon in the intermediate region of low virtuality. We finally describe howep cross sections can be obtained as functions of the virtuality of the exchanged photon.     

Analysis of elastic and inelastic hadron scattering on 6,7Li nuclei within diffraction theory

Within Glauber-Sitenko multiple-scattering theory, the differential cross sections for elastic and inelastic proton, positive-pion, and positive-kaon scattering on ^6,7Li nuclei are calculated at incident-hadron energies ranging between 0.143 and 1.0 GeV. The ⁶Li and ⁷Li wave functions are taken in, respectively, the α2N and the αt clustermodel. The resulting cross sections are investigated as functions of the scattered-particle energy, parameters of the model wave functions, and various scattering multiplicities. It is concluded that a partial filling of the diffraction minimum in the cross section is due to the D-wave contribution to the wave function for the ⁶Li target nucleus.     

Noniterative analytical formula for inverse scattering of multiply scattering point targets

This paper derives, in the exact framework of multiple scattering theory for point targets, a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via, e.g., time-reversal multiple signal classification or another approach. The new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper [A. J. Devaney, E. A. Marengo, and F. K. Gruber, "Time-reversal-based imaging and inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 118, 3129-3138 (2005)]. The two methods (noniterative versus iterative) are comparatively investigated with two numerical examples.