Orientational averaging of integrated cross sections in the discrete dipole method

Using the discrete dipole method, exact and approximate analytical solutions for orientation-averaged cross sections for extinction, absorption, and scattering of light are obtained. The analytical solutions can be applied to the calculation of integrated cross sections of fractal clusters formed by primary particles with different optical properties (soot in air and aqueous suspensions of aggregates of polystyrene, gold, and silver nanoparticles). It is shown that two models of aggregates that differ only in trajectories (ballistic or Brownian) of primary particles and intermediate clusters and in average fractal dimensions give close values of averaged extinction cross sections.     

Absorption and scattering properties of arbitrarily shaped particles in the Rayleigh domain: A rapid computational method and a theoretical foundation for the statistical approach

We provide a theoretical foundation for the statistical approach for computing the absorption properties of particles in the Rayleigh domain. We present a general method based on the discrete dipole approximation to compute the absorption and scattering properties of particles in the Rayleigh domain. The method allows to separate the geometrical aspects of a particle from its material properties. Doing the computation of the optical properties of a particle once, provides them for any set of refractive indices, wavelengths and orientations. This allows for fast computations of e.g. absorption spectra of arbitrarily shaped particles. Other practical applications of the method are in the interpretation of atmospheric and radar measurements as well as computations of the scattering matrix of small particles as a function of the scattering angle. In the statistical approach, the optical properties of irregularly shaped particles are represented by the average properties of an ensemble of particles with simple shapes. We show that the absorption cross section of an ensemble of arbitrarily shaped particles with arbitrary orientations can always be uniquely represented by the average absorption cross section of an ensemble of spheroidal particles with the same composition and fixed orientation. This proves for the first time that the statistical approach is generally viable in the Rayleigh domain.     

Optical properties of pigmented coatings taking into account particle interactions

A T-matrix approach is used to obtain the orientation-averaged scattering and absorption cross sections of randomly oriented particle clusters, and the average angular distribution of the radiation scattered by them. The coefficients involved in the expansion of the phase function are obtained from this T-matrix approach, and used in a multiple scattering formalism to characterize the angular distribution of the diffuse radiation propagating through a particulate coating perpendicularly illuminated with collimated visible radiation. Asymmetry between forward and backward propagating diffuse radiation intensities is taken into account by means of this multiple scattering approach, which is based on solving the radiative transfer equation for successive scattering order contributions. A four-flux model is applied to compute the reflectance in terms of wavelength of the incident radiation and particle concentration. An application of the formalism is carried out to predict the optical properties of titanium dioxide pigmented polymer coatings, in terms of the pigment volume fraction and the degree of aggregation.     

General derivation of the total electromagnetic cross sections for an arbitrary particle

This work concerns a common problem in electromagnetic scattering; calculation of the total scattering, extinction, and absorption cross sections for an arbitrary particle. Typical expressions for the cross sections are obtained in terms of the vector spherical wave function expansions for the incident and scattered waves. The unique aspect of this work is that the derivation is carried out specifically without use of the far-field zone approximation. The resulting expressions, valid at any distance, exactly match those obtained from the far-field approximation. This demonstrates that the cross sections are independent of the distance from the particle at which they are calculated as one would expect from energy conservation. Numerical simulations of the near and far-field zone energy flows due to a spherical particle are presented to illustrate several implications of this result.     

随机取向烟尘团簇粒子的光学截面的数值计算

采用蒙特卡罗方法根据团簇—团簇凝聚（CCA）模型对由球形原始微粒凝聚而成的烟尘团簇粒子进行了模拟,利用离散偶极子近似（DDA）方法数值计算了不同原始微粒粒径和数目组成的随机取向的烟尘团簇粒子的总消光截面、吸收截面及散射截面等光学特性参数,研究了原始微粒粒径及数目对随机取向烟尘团簇粒子光学特性的影响。结果表明：当入射波长一定时,随机取向烟尘団簇粒子的光学特性主要取决于原始微粒的粒径和数目;烟尘团簇粒子对不同波段激光的吸收和散射存在差别,这种差别随原始微粒粒径及数目变化而变化。这一工作为研究电磁波在烟尘中的传输特性提供重要参考数据。     

Polarized electron scattering on spin zero and polarized spin-1/2 targets: Deep inelastic scattering,elastic electron-muon scattering,and elastic electron-nucleon scattering

A covariant formulation is developed and used to derive cross sections for the analysis of experiments in which polarized electrons (muons) are scattered from spin-zero and from polarized spin-1/2 targets. The analysis is based upon the single virtual photon representation of the electromagnetic interaction, initially, neither high-energy nor low-energy approximations are made so that one may derive results in which the orientation of the polarization vectors of the interacting particles changes as a result of the scattering. The general formulation is valid for all polarization configurations for the electron and nucleon in deep inelastic scattering, and for all polarization configurations for the initial and final state particles in elastic scattering. From the general covariant results, specific cross sections are derived for deep inelastic scattering as well as elastic scattering of electrons on muons, nucleons, and spin zero targets. In the latter case, the actual polarization vector for the scattered electron is determined. In the other cases discussed, this vector may be obtained from the cross sections. In addition, a method is presented for defining covariant cross sections, and this method is used to obtain results in the center-of-mass system as well as the laboratory system. Furthermore, explicit cross sections for virtual photon absorption are derived. Finally, in the appendices, an alternative method for the evaluation of traces is given as well as a discussion of the relativistic limit.     

Determination of the absorption and scattering cross sections of zinc phthalocyanine nanoparticles

The real and imaginary parts of the refractive index of thin zinc phthalocyanine films have been measured by two different methods (spectral and ellipsometric). The results obtained have been used to calculate the absorption and scattering cross sections of spherical zinc phthalocyanine nanoparticles in water as functions of their size.     

Positron scattering from alkaline-earth elements

The total (elastic + inelastic) cross sections fore ⁺ impact on alkaline-earth elements from Be to Ra are calculated by employing a complex spherical optical potential. This potential has static, polarization and absorption components. The positron energy range is from a few eV to several thousand eV. We have compared our elastic cross sections for Mg and Ca with the other available results and the agreement is good for energies above 100eV. We have also compared our absorption cross sections withe ⁻ ionization cross sections at high energies where our absorption cross sections are in good accord. We have made Bethe plots fore ⁺ scattering on these elements.     

Light scattering by wavelength-sized particles "dusted" with subwavelength-sized grains

The numerically exact superposition T-matrix method is used to compute the scattering cross sections and the Stokes scattering matrix for polydisperse spherical particles covered with a large number of much smaller grains. We show that the optical effect of the presence of microscopic dust on the surfaces of wavelength-sized, weakly absorbing particles is much less significant than that of a major overall asphericity of the particle shape.     

海洋混合悬浮颗粒对蓝绿激光的散射特性研究

激光在水下的传输很大程度上会受到海水中悬浮颗粒物的影响,而目前对于海洋中悬浮颗粒物光散射的理论研究大多是针对单一成分的悬浮粒子而进行的,但是在真实海洋中悬浮颗粒物都是以多种成分混合的颗粒群形式而存在的,因此研究真实海洋中混合悬浮颗粒物对蓝绿激光的散射特性具有重要意义。该研究选取了对蓝绿激光传输产生较大影响的浮游藻类植物、悬浮泥沙、碎屑、悬浮气泡和矿物质这五种常见的悬浮颗粒物作为研究对象,充分考虑真实海况中这五种悬浮颗粒物的不同混合情况,构建了海水中混合球形悬浮颗粒物对蓝绿激光的散射特性模型。数值计算了海水中五种物质混合的球形悬浮颗粒物对532 nm蓝绿激光的统计平均光散射参量和平均散射相函数,分析不同混合悬浮颗粒物的混合比对平均散射、吸收和消光系数以及单次反照率随着粒子有效半径和粒子数浓度变化的影响,同时分析了不同粒子尺寸下的不同混合比对混合悬浮颗粒物的平均散射相函数随着角度变化的影响。数值结果表明,当悬浮泥沙在整个混合模型中占比越大时,平均散射系数越大,而当悬浮藻类粒子在整个混合模型中占比增大时,平均吸收系数增大,由此可知海洋中对光造成主要影响的五种常见悬浮颗粒物中,悬浮泥沙对光散射作用影响最大,悬浮藻类粒子对光吸收作用影响最大。随着悬浮颗粒物浓度的增大,混合粒子的单次反照率保持不变,由此可知混合悬浮颗粒物的平均光散射参量随着粒子浓度的增长速率是一致的。海洋中混合悬浮颗粒物的平均散射相函数随着粒子的有效半径的增大而增大,散射作用最大的混合比下的悬浮颗粒物其平均散射相函数最大,悬浮颗粒物的前向散射较强。该工作对蓝绿激光在海水中传输、信道建模,水下无线光通信的研究以及激光探测都具有重要的理论指导意义。     

Absorption of electromagnetic radiation by a cylindrical metal particle

The cross section of the absorption of electromagnetic radiation by a cylindrical metal particle is calculated. The calculation is performed in the low-frequency limit, in which the contribution of eddy currents to the absorption dominates, and for comparatively small particles (with radii of ≈10 nm), which allows us to neglect the skin effect. The case when the mean free path of electrons in the metal bulk substantially exceeds the radius of the cylindrical particle is considered in detail. The specific absorption cross sections for spherical and cylindrical particles are compared.     

Inversion of absorption and scattering at plasmon resonance in nanoparticles with a metallic sheath

Numerical simulation of the optical properties of spherical nanostructures comprising an absorbing (amplifying) insulating core and a metallic sheath is carried out under the conditions of plasmon resonance. A decrease in the absorption by the core is shown to increase the cross sections of absorption and scattering by the nanostructure in the plasmon resonance spectral range. If the core exhibits amplification, an extra resonance arises, causing a change in the dependence of the absorption cross section on the amplification factor. Conditions for such a resonance to appear are considered.     

Determining polarizability tensors for an arbitrary small electromagnetic scatterer

In this paper, we present a method to retrieve tensor polarizabilities of general bi-anisotropic particles from their far-field responses to plane-wave illuminations. The necessary number of probing excitations and the directions where the scattered fields need to be calculated or measured have been found. When implemented numerically, the method does not require any spherical harmonic expansion nor direct calculation of dipole moments, but only calculations of co- and cross-polarized scattering cross sections for a number of plane-wave excitations. With this simple approach, the polarizabilities can be found also from experimentally measured cross sections. The method is exemplified considering two bi-anisotropic particles, a reciprocal omega particle and a non-reciprocal particle containing a ferrite inclusion coupled to metal strips.     

Analytical description of the electrodynamic properties of metallic photonic crystals

A method of approximate calculation of the interaction inverse matrix in the method of discrete dipoles is proposed. The knowledge of this matrix makes it possible to determine the optical response of a system to the action of an electromagnetic wave with an arbitrary shape, which can be represented as a combination of vector spherical wave functions. The number of calculation operations of the matrix in the proposed method is considerably smaller than in the case of its direct calculation. In the case of a change in the refractive index of scattering particles, two methods of approximate calculation of the interaction inverse matrix are also proposed. This makes it possible to calculate the optical response of systems with new characteristics without direct solving equations of a system with a large dimension. The accuracy of the methods is numerically determined for particles with spherical and cubic shapes. It is shown that the methods are computationally efficient and can be used to calculate the values of polarization vectors inside particles and extinction and absorption cross sections of systems.     

Test of effective cluster interactions by pion scattering

The superposition of effective interactions is studied by a cluster approach to the pion-nucleus potential with particular emphasis on the treatment of the Pauli principle between the clusters. The model is based on the formalism of Kerman, McManus, and Thaler and constructs the pion-nucleus interaction by a superposition procedure of pion-cluster interactions in the framework of the fish-bone model. The second-order contribution due to excitations of the relative motion between the clusters has been taken into account as well as true absorption. A test calculation of ^+_20 scattering with the cluster approach reproduces the gross structure of the differential elastic cross section and the total non-elastic cross section of conventional calculations quite well. Furthermore, it is confirmed that the three-body Pauli interaction is negligible also in the case of a realistic and rather complicated pion-nucleus interaction thus justifying the usual folding approach. The rotational bands contribute about 10% to the cross sections.     

Special features of absorption of electromagnetic radiation by a cylindrical particle

The cross section of electromagnetic radiation absorption by a cylindrical metal particle was calculated. No limitations were imposed on the relation between the electron mean free path and the particle size. Specific absorption cross sections of cylindrical and spherical particles are compared. The results of the numerical calculation are presented graphically.     

CDCC Approaches and Roles of Closed Channels in d-Nucleus Reactions

The effect of deuteron breakup in d-nucleus reaction is treated with the continuum discretized coupled channels (CDCC) approach, and the effects on the total reaction cross sections and elastic scattering angular distributions are studied by comparing the calculations of CDCC and spherical optical model with our global deuteron optical potential [Phys. Rev. C 73 (2006) 054605] below 200 MeV, for target nuclei ranging from ¹²C to ²⁰⁸Pb. The contributions from the closed channels to the total reaction and breakup cross sections, and angular distributions of elastic scattering are also seriously discussed.     

MENDF—一个计算200 MeV以下裂变核数据的程序(英文)

基于球型光学模型、 预平衡发射和Hauser-Feshbach统计等理论, 编制了MENDF（Medium Energy Nuclear Data for Fission）程序, 该程序适用于裂变核在入射粒子能量低于200 MeV的中低能区的全套核数据计算。 对于中子和质子在200 MeV以下诱发的核反应, 其全截面、 反应截面、 弹性散射微分截面、 裂变截面和裂变中子谱、 5种发射粒子的单举截面和相应的能谱等理论计算值与相应的实验值基本符合。 MENDF在我国已被广泛用于核数据计算及建立中能核数据库。Based on the spherical optical model, pre equilibrium and Hauser Feshbach statistical theory, the code MENDF (Medium Energy Nuclear Data for Fission) is written to calculate a complete set of nuclear data for fission nuclei in the medium low energy region (≤200 MeV). For neutron and proton induced reactions below 200 MeV, the total cross sections, reaction cross sections, elastic scattering differential cross sections, fission cross section, energy spectra of fission neutron and five kinds of emitting particles, etc. are calculated by MENDF. The calculated data generally agree with their corresponding experimental data. MENDF is widely used for nuclear data calculation and to establish ENDF 6 formatted files for the medium low energy region in China.     

Diffraction scattering of Λ 3 H and Λ 6 He hypernuclei on nuclei with allowance for edge diffuseness, the structure of hypernuclei, and multiple-scattering effects

General formulas for the amplitudes of the diffraction scattering of two-and three-cluster loosely bound nuclei on spherical nuclei for an arbitrary dependence of the profile functions on the impact parameter are represented in a form that is convenient for calculations. The differential cross sections for the elastic scattering of _Λ ³ H and _Λ ⁶ He hypernuclei and the total cross sections are obtained with allowance for the diffuseness of the target-nucleus edge, the binding energy of incident hypernuclei, the ranges of nuclear forces between the clusters in the hypernuclei, and multiple (double and triple) scattering. Changes in the behavior of the cross sections in response to a transition from the two-cluster to the three-cluster model of the aforementioned nuclei are revealed.     

The pion optical potential and its application to reaction processes

The gross features of the pion-nucleus interaction are studied within the framework of an optical potential approach. The optical potential is determined by a systematic analysis of the data on pionic atoms and elastic scattering. It is then decomposed into quasi-free and absorption terms through theoretical consideration of the reactive content. A method of calculating the absorption cross section using the optical potential with the above decomposition is proposed. It takes into account not only direct absorption from the elastic channel but also the absorption after the quasi-free processes. The calculated absorption cross sections are in reasonable agreement with the observed ones. The cross sections for inelastic, single-charge-exchange and double-charge-exchange processes are calculated as an extended application of the method. The results are consistent with the available data. Inclusive spectra of pions and protons are also considered in this approach. An application to the (γ, π) reaction is briefly discussed.