Anomalous diffraction approximation for light scattering cross section: Case of ordered clusters of non-absorbent spheres

The anomalous diffraction (AD) method has proved to be an adequate approximation of the exact method (GMM code computed by Xu) to obtain the scattering cross section for aggregates whose primary particle size parameter is greater than 2. Indeed, the error of this approximated method is less than approximately 10% when the primary particles are in SiO₂.However, this method is strongly related to the aggregate morphology since it includes in its formulation the concept of chord length. We initially studied the chord distribution for various aggregates, and then we reformulated the anomalous diffraction method, to approximate the scattering cross section, now completely analytically. This new expression is entitled ADr with the r for rapid because this one is at least a hundred times faster than the standard AD method.     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering

Using total light scattering technique to measure the particle size distribution has advantages of simplicity in measurement principle and convenience in the optical arrangement. However, the calculation of extinction efficiency based on Mie theory for a spherical particle is expensive in both time and resources. Thus, a simple but accurate approximation formula for the exact extinction efficiency may be very desirable. The accuracy and limitations of using the anomalous diffraction approximation (ADA) method for calculating the extinction efficiency of a spherical particle are investigated. Meanwhile, the monomodal and bimodal particle size distributions of spherical particles are retrieved using the genetic algorithm in the dependent model. Furthermore, the spheroidal model in the retrieval of non-spherical particle size distribution is also discussed, which verifies the non-sphericity has a significant effect on the retrieval of particle size distribution compared with the assumed homogeneous isotropic sphere. Both numerical computer simulations and experimental results illustrate that the ADA can be successfully applied to retrieve the particle size distributions for spherical and spheroidal particles with high stability even in the presence of random noise. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.     

Anomalous polarization effects during light scattering in random media

The dependence of the intensity of light backscattered from a layer of a randomly inhomogeneous medium on the polarization of incident light and the size of scatterers has been investigated. The results of numerical simulation have demonstrated that the direction of rotation of the plane of polarization is different in systems with small- and large-scale inhomogeneities. It is shown for the first time that the dependence of the sign of the residual circular polarization on the size of scatterers can be observed in systems described by the Henyey-Greenstein phase function used in simulating biological tissues. A similar anomalous polarization effect, which consists in changing the direction of rotation of the plane of polarization of backscattered light with an increase in the scattering angle, is revealed in studying the coherent backscattering component. These polarization effects are observed in light backscattering from optically active media.     

Elastic scattering cross section of photons by water: limits for the free atom approximation

Several papers can be found in the literature in which elastic and inelastic experimental scattering cross sections of photons by water with energies in the keV range are measured. Usually, the authors use some kind of normalization with theoretical values, because of the difficulties in obtaining some parameters necessary to obtain absolute cross sections from the measurements. A reasonable range of momentum transfer has been covered, but nevertheless, inconsistencies and gaps still remain. In this work, we address the problem performing absolute cross section measurements in the high momentum transfer region (0.33 Å^?1 ≤ x ≤ 4.5 Å^?1), where no structure effects can be observed. We compare the results with theory to validate it in an intermediary region (0.33 Å^?1 ≤ x ≤ 1.72 Å^?1) and then use the experimental values to normalize data in the low‐energy region (0.078 Å^?1 ≤ x ≤ 1.72 Å^?1) to obtain the experimental cross section in that region. From the comparison, we concluded that for momentum transfers, x between 0.7 and 4.5 Å^?1 the scattering can be considered as being due to free atoms in free molecules. Therefore, the scattering cross sections may be considered as a sum of those from free atoms. Theoretically, the scattering cross sections can be obtained from the form factors as well as from the second‐order perturbation theory (S‐matrix) because there is no significant difference between both. On the other hand, for x ≤ 0.7 Å^?1, interference between the photon‐scattered amplitudes due to liquid structure generates oscillations in the cross section values. Copyright © 2014 John Wiley & Sons, Ltd.     

椭圆截面非球形颗粒群的多重光散射

尽管非球形下一些特殊形状颗粒的单散射已被得到,球形多颗粒系（颗粒群）的多重散射也被研究,但至今仍未得到非球形颗粒群的多重散射.文中建立了一类椭圆截面非球形颗粒模型,求得其散射相位函数,借助于辐射传播方程,考虑形状及大小分布,得到了该类颗粒群的多重光散射.在两种特例情况下的结果能与已有的结果符合较好,说明了方法的可靠性.计算分析表明：非球形颗粒群的多重散射光强角分布要比球形颗粒平坦.椭圆截面颗粒的粒度或形状参数越大,多重散射光越集中于小的散射角;粒度分布或形状分布越宽,多重散射光强的角分布越平坦.随着光学厚 关键词： 多重光散射 颗粒 非球形 椭圆截面     

Steady-state differential cross section for elastic scattering

Lower limits are found on the differential cross section for elastic scattering and on its derivatives with respect to the momentum transfer t at t = 0 at high energies on the basis of completely general considerations. The results are expressed in terms of the measurable total cross sections.Translated from Izvestiya VUZ. Fizika, No. 4, pp. 103–108, April, 1970.     

On the Thomson cross section of light scattering by a moving particle

The Thomson cross section of light scattering is calculated for a moving particle within classical electrodynamics.     

Anomalous diffraction of light with geometrical path statistics of rays and a Gaussian ray approximation

The anomalous-diffraction theory (ADT) of extinction of light by soft particles is shown to be determined by a statistical distribution of the geometrical paths of individual rays inside the particles. Light extinction depends on the mean and the mean-squared geometrical paths of the rays. Analytical formulas for optical efficiencies from a Gaussian distribution of the geometrical paths of rays are derived. This Gaussian ray approximation reduces to the exact ADT in the intermediate case of light scattering for an arbitrary soft particle and describes well the extinction of light from a system of randomly oriented and (or) polydisperse particles. The implications for probing of the sizes and shapes of particles by light extinction are discussed.     

Relationship between the cross section for deep-inelastic scattering and the cross section for inclusive annihilation

Arguments have been presented that suggest that available experimental data on the structure functions for the processes ep → eX and e ⁺ e ^? → p( $\bar p$ )X do not confirm the so-called reciprocity relation, which was obtained in the leading-logarithm approximation of perturbation theory. It has also been shown that the asymptotic relationship between the above processes that was obtained on the basis of more general considerations is compatible with existing data.     

随机表面散射光场的格林函数法与基尔霍夫近似的比较

从简谐光波满足的亥姆霍兹方程出发，将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组，并对其进行数值求解，实现了光场的数值计算. 同时，由透射光场的格林函数积分得出了基尔霍夫近似下光场的表达式. 通过类比推导夫琅和费面上散斑场自相关函数的方法，提出了产生随机表面及其导数的傅里叶变换方法. 在此基础上，对采用基尔霍夫近似进行自仿射分形随机表面的散射光场数值计算的精确程度进行了研究. 发现在随机表面粗糙度比较小时，基尔霍夫近似的精度比较高；在粗糙度相同的情况下，表面的分形 关键词： 格林函数积分 基尔霍夫近似 自仿射分形随机表面     

The reaction cross section for low-energy pion-nucleus scattering

It is shown that for low pion energies it is possible to calculate the pion absorption part of the pion-nucleus reaction cross section from a detailed knowledge of the imaginary part of the pion-nucleus optical potential. Such calculations provide tests of various theories of low-energy pion-nucleus dynamics.     

Temperature effect for an inelastic neutrino scattering cross section

The influence of temperature on inelastic neutrino scattering on hot nuclei is studied with the ⁵⁴Fe nucleus as an example. The strength distribution of charge-neutral Gamov-Teller transitions in ⁵⁴Fe at finite temperature is calculated within the framework of a random phase approximation using the thermo field dynamics formalism. It is shown that for neutrino energies lower than the energy of the Gamov-Teller resonance, the inelastic scattering cross section depends substantially on temperature.