Experimental study of the spatial distributions of relativistic electron beams reflected and refracted by a thin foil

The ratio of the cross section for inelastic scattering to the total cross section for scattering of a fast electron by a cluster, depending on the number of atoms in the cluster, is shown to be not a monotonic function. This nonmonotonicity is not related to the well-known nonmonotonic dependences determined, for example, by the magic numbers in the shell model of clusters but is of purely quantum origin: the coherence of elastic electron scattering and the incoherence of inelastic one by a multipartice target.     

Electron-cluster interactions

Beam depletion spectroscopy has been used to measure absolute total inelastic electron-sodium cluster collision cross sections in the energy range fromE0.1 toE6 eV. The investigation focused on the closed shell clusters Na₈, Na₂₀, and Na₄₀. The measured cross sections show an increase for the lowest collision energies where electron attachment is the primary scattering channel. The electron attachment cross section can be understood in terms of Langevin scattering, connecting this measurement with the polarizability of the cluster. For energies above the dissociation energy the measured electron-cluster cross section is energy independent, thus defining an electron-cluster interaction range. This interaction range increases with the cluster size.     

Electronic and optical properties of Cu, CuO and Cu2O studied by electron spectroscopy

The electronic and optical properties of Cu, CuO and Cu(2)O were studied by x-ray photoelectron spectroscopy (XPS) and reflection electron energy-loss spectroscopy (REELS). We report detailed Cu 2p, Cu LVV, O 1s and O KLL spectra which are in good agreement with previous results. REELS spectra, recorded for primary energies in the range from 150 to 2000 eV, were corrected for multiple inelastically scattered electrons to determine the effective inelastic scattering cross section. The dielectric functions and optical properties were determined by comparing the experimental inelastic electron scattering cross section with a simulated cross section calculated within the semi-classical dielectric response model in which the only input is Im(-1/ε) by using the QUEELS-ε(k,ω)-REELS software package. By Kramers-Kronig transformation of the determined Im(-1/ε), the real and imaginary parts (ε(1) and ε(2)) of the dielectric function, and the refractive index n and extinction coefficient k were determined for Cu, CuO, and Cu(2)O in the 0-100 eV energy range. Observed differences between Cu, CuO and Cu(2)O are mainly due to modifications of the 3d and O 2p electron configurations.     

Polarisationsmessungen an Elektronenstrahlen nach der Transmission durch magnetisierte Eisenschichten

Magnetized iron foils of a thickness of 500 Å were transmitted by 60 keV electrons. The spin polarization of the electron beam was investigated by Mott scattering after transmission. No polarization effect was found. Since the lowest detectable polarization degree wasP=0·003 the atomic polarization cross section must be assumed to be smaller than 0·8·10^?20cm². This cross section is the sum of the spin exchange cross section and the spin dependent part of the total scattering cross section. If the electron binding energy is neglected, the spin depentend part of the total scattering cross section can be calculated from the theory of Møller scattering. In the case of our conditions-60 keV and an aperture of 10^?3 radian-the calculated cross section is smaller than the experimental upper limit. In further experiments the electron beam was split into the energy spectrum by an electrostatic analyzer placed between the iron foil and the Mott scattering foil. In these measurements only small parts of the energy spectrum were investigated, however, even here no detectable polarization occured.     

二氧化钒纳米点阵红外光学特性研究

针对二氧化钒纳米点阵从半导体到金属的可逆相变,考虑到点阵中各个点之间散射光的交互作用,基于VO2在不同温度和波长下的折射率和消光系数,以及小颗粒的吸收和散射特性,建立了VO2纳米颗粒的数学模型,研究了VO2纳米颗粒的相变光学特性.结果表明,随着波长变化,吸收截面相对散射截面占主导,金属相在980 nm附近出现吸收峰值|随着温度变化,可见光区域的消光系数变化较小,而红外区域较大,其中在近红外区域的消光系数变化最大.在纳米点阵中,消光截面随着颗粒间距变化,当颗粒间距增大时,消光峰值出现红移,且峰值大小也会随之增大|当间距超过一定数值后,峰值反而会逐渐减小.采用多孔氧化铝掩模的方法,通过磁控反应溅射制备VO2纳米点阵,测试结果表明其透过率比薄膜的透过率高.     

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.     

Resonant mechanisms of inelastic light scattering by low-dimensional electron gases

The contribution of elementary excitations in low-dimensional electron gases to resonant inelastic light scattering is found to be determined by interband transitions involving states at specific wave vectors. In modulation-doped GaAs/GaAlAs quantum wells, we detect only the single-particle excitations (SPE) at resonances with electron-hole transitions at the Fermi wave vector, and only plasmons at resonances with zone-center excitons. The plasmon cross section is comparable to the SPE when double electronic resonance is achieved by tuning the plasmon energy to a valence subband separation.     

Elastic light scattering by semiconductor quantum dots of arbitrary shape

Elastic light scattering by low-dimensional quantum objects without a change in the frequency is theoretically investigated in terms of the quantum perturbation theory. The differential cross section of resonance light scattering from any excitons in any quantum dots is calculated. It is demonstrated that, when the light wavelengths considerably exceed the quantum-dot size, the polarization and angular distribution of the scattered light do not depend on the shape, the size, or the configuration of quantum dots. In this case, the total light scattering cross section is independent of the quantum-dot size. If the radiative damping of an exciton exceeds the nonradiative damping, the total light scattering cross section at resonance is of the order of the light wavelength squared. The radiative damping associated with the long-range exchange interaction between electrons and holes is calculated for any excitons and any quantum dots.     

Low-energy electron bremsstrahlung from metal clusters

Expressions are derived allowing numerical calculation of the matrix element of the dipole moment between states that belong to a continuous spectrum for the case where a charged particle in an arbitrary orbital state is scattered by a spherically symmetric short-range potential. The calculation scheme is based on expanding a diverging matrix element into a sum of converging integrals. The method is used to study static bremsstrahlung of a slow electron scattered by sodium clusters. The bremsstrahlung cross section is shown to be resonant. The resonances arise at certain energies (depending on a cluster) of an electron having emitted a photon and are due to electron capture on quasi-steady-state levels.     

Comparative analysis of characteristic electron energy loss spectra and inelastic scattering cross-section spectra of Fe

The inelastic electron scattering cross section spectra of Fe have been calculated based on experimental spectra of characteristic reflection electron energy loss as dependences of the product of the inelastic mean free path by the differential inelastic electron scattering cross section on the electron energy loss. It has been shown that the inelastic electron scattering cross-section spectra have certain advantages over the electron energy loss spectra in the analysis of the interaction of electrons with substance. The peaks of energy loss in the spectra of characteristic electron energy loss and inelastic electron scattering cross sections have been determined from the integral and differential spectra. It has been shown that the energy of the bulk plasmon is practically independent of the energy of primary electrons in the characteristic electron energy loss spectra and monotonically increases with increasing energy of primary electrons in the inelastic electron scattering cross-section spectra. The variation in the maximum energy of the inelastic electron scattering cross-section spectra is caused by the redistribution of intensities over the peaks of losses due to various excitations. The inelastic electron scattering cross-section spectra have been analyzed using the decomposition of the spectra into peaks of the energy loss. This method has been used for the quantitative estimation of the contributions from different energy loss processes to the inelastic electron scattering cross-section spectra of Fe and for the determination of the nature of the energy loss peaks.     

Metallic-like droplets produced by irradiating rare-gas clusters with free electron laser pulses

Unlike metallic elements, rare-gas atoms remain non-metallic even if they are condensed. However, once rare-gas clusters are irradiated by extreme ultraviolet free electron laser (EUV-FEL) pulses with slightly higher energy than their ionization potential, they exhibit metallic-like behaviors because the ionization takes place sequentially within the clusters owing to the huge valence electron ionization cross section in the EUV regime. In this work Ar and Xe clusters were produced by pulsed supersonic jets, and the cluster beams were crossed synchronously with focused EUV-FEL beams ejected from the SCSS test accelerator in Japan. We measured time-of-flight (TOF) mass spectra and kinetic energy distribution (KED) of daughter ions produced via Coulomb explosion by using three dimensional (3D) momentum imaging spectrometer. The metallic-like nature is evidenced not only by widely spread charge distributions within the cluster but also by enhanced positive surface charges surrounded by quasi-free electron clouds.     

金纳米环结构的光学性质研究

采用离散偶极子近似方法(DDA)研究了两种不同形状的金纳米环结构的消光光谱及其近电场分布, 研究了等离子体消光峰的红移、蓝移现象及消光系数与结构参数之间的关系, 并与盘状的金纳米结构进行了比较. 在等离子体共振峰波长入射时, 金纳米环结构比金纳米盘结构产生更大的局域增强电场分布, 横截面为圆形的金纳米环结构比横截面为矩形的结构具有更大的局域增强电场分布, 更适合作为表面增强拉曼散射的衬底. 关键词： 离散偶极子近似 金纳米环 金纳米盘 光学性质     

Multiple scattering of light transmission in a smoke layer

The visibility in a fire scene decreases because of the existence of smoke produced by the flammable materials. With the growth of smoke concentration, the relationship between light and smoke becomes complicated due to the multiple scattering. In this paper, the radiative transfer equation (RTE) that considers the multiple scattering was applied to calculate the light transmission in a smoke layer. As input parameters of RTE, the single scattering albedo, asymmetry parameter and extinction cross section of single smoke agglomerate were calculated by the discrete dipole approximation (DDA) method. The effects of smoke agglomerate diameter, number density of smoke layer, and the incident light wavelength were considered. The results show that the light transmitted flux decreases with the growth of smoke diameter and number density, and increases with the growth of wavelength. The smoke diameter is dominant among the three parameters, and the light transmitted flux tends to be stable when the wavelength reaches a certain value.     

Coupling to the elastic channel in electron impact spectroscopy: A simple second born model and its application to excitation of the 61P1 state of mercury and to the excitation of molecules

The matrix element in the infinite channel close coupling approximation responsible for coupling to the elastic channel in electron impact inelastic encounters is investigated. The contribution from the imaginary part of the energy denominator in the elastic coupling matrix element for dipole allowed transitions is shown to yield large angle differential cross sections in good agreement with experiment. This coupling mechanism predicts that the shape of the inelastic differential cross section will be dominated by the shape of the elastic cross section in the large angle high energy limit. In fact the coupling matrix element exhibits a dependence on incident energy, k², and momentum transfer, K, of the form 1/kK² which is in agreement with the theoretical predictions of Huo and means that in the limit of high incident energy the non-first-Born elastic coupling will dominate the angular dependence of the inelastic differential cross section at large scattering angles. In the case of molecular electron impact spectra it is shown that the analog of the Massey—Moore coherence features depending on the symmetry of the states involved in the excitation process will also occur in the coupling contribution. It is suggested that this new mechanism for producing coherent features in inelastic differential cross sections may be the explanation of the coherent features observed experimentally by Karle and Swick.It can be concluded on the basis of the results obtained here that the coupling to the elastic cross section provided by the imaginary contribution from the second Born energy denominator is sufficient to explain presently available experimental data on the large angle differential cross section and spin polarization. The simple coupling model was found to be inadequate to explain the small angle differential cross section in the range 10° < θ < 30° even at incident energies as high as 400 eV. The calculations also showed significant differences between first and second Born calculations at zero scattering angle. No conclusion can be drawn about this observation as all the omitted terms should make significant contributions in the small angle region. It is important to again emphasize that the large angle scattering even in the limit of high incident electron energy will be completely dominated by the coupling to the elastic channel^{7, 11}. On the basis of this work it appears that the coherent structure in the large angle inelastic differential cross section observed by Swick and Karle^{12, 13} at incident electron energies in the keV region may well be due to coupling to the elastic channel.     

The integrated extinction for broadband scattering of acoustic waves

In this paper, physical bounds on scattering of acoustic waves over a frequency interval are discussed based on the holomorphic properties of the scattering amplitude in the forward direction. The result is given by a dispersion relation for the extinction cross section which yields an upper bound on the product of the extinction cross section and the associated bandwidth of any frequency interval. The upper bound is shown to depend only on the geometry and the material properties of the scatterer in the static or low-frequency limit. The results are exemplified by permeable and impermeable scatterers with homogeneous and isotropic material properties.     

类胡萝卜素的分子光谱研究

类胡萝卜素是含有9个CC共轭双键的短链多烯类生物分子. 特殊的分子结构, 使其不仅在光采集, 光防护, 防癌, 抗癌等生物学领域有重要应用, 而且在分子导线, 光开关, 滤光器等光电器件研制中也有重要的非生物学应用. 本文对它的分子光谱进行研究和总结, 结果表明, 类胡萝卜素具有宽带荧光, 将其用于荧光增强受激拉曼散射可以获得宽带受激拉曼散射; 电子能隙随温度降低而收缩, 电子吸收光谱红移, 这特性使它能研制优质半导体元件; 极大的拉曼活性和三阶非线性系数, CC键基频拉曼散射截面可以比普通分子大10个数量级, 和频、倍频拉曼散射强度也很高, 低温下与基频强度比可达0.5. 类胡萝卜素分子的这些光谱特性对多烯类分子结构、性能研究及其在非生物学中的应用有重要参数价值.     

Generalization of the optical theorem for an arbitrary multipole in the presence of a transparent half-space

The optical theorem is generalized to the case of excitation of a local inhomogeneity introduced in a transparent substrate by a multipole of arbitrary order. It is shown that, to calculate the generalized extinction cross section, it is sufficient to calculate the derivatives of the scattered field at a single point by adding a constant and a definite integral. Apart from general scientific interest, the proposed generalization makes it possible to calculate the absorption cross section by subtracting the scattering cross section from the extinction cross section. The latter fact is important, because the scattered field in the far zone contains no Sommerfeld integrals. In addition, the proposed generalization allows one to test computer modules for the case where a lossless inhomogeneity is considered.     

基于Mie散射理论的C@H_2O复合粒子散射特性研究

大气中大量存在的复合粒子会对激光传输效率产生很大影响。由于空气中水蒸气含量较高,以C作为凝结核外层包裹以水的核壳结构微粒对光传输具有明显的散射效应。本文应用Mie散射理论对C@H_2O核壳结构微粒的散射特性进行了理论分析和数值计算,首先给出了不同入射波长、核粒子半径以及水膜厚度条件下散射强度分布变化曲线;其次给出了不同入射波长、核粒子半径以及水膜厚度条件下偏振变化情况;最后讨论了光学截面与粒子半径之间的关系。结果表明各参数对前向散射强度影响较大,入射波长越大散射强度越弱,C核半径增大粒子的前向散射增强,水膜厚度增大粒子的前向散射增强,而后向散射无明显影响;入射波长较大时,粒子在多个角度出现线偏振光,入射波长增大、碳核半径变大、水膜厚度增大,偏振度峰值都会增多;随着入射波长的增大,散射截面最大峰值位置向着半径增大的方向移动,并伴随一定的振荡现象,散射和消光截面在碳核半径为0.1μm左右达到最大值。     

Compton and double-compton scattering processes at colliding electron-photon beams

Radiative corrections to the Compton scattering cross section are calculated in the leading and next-to-leading logarithmic approximations in the case of colliding high-energy photon-electron beams. Radiative corrections to the double-Compton scattering cross section in the same experimental setup are calculated in the leading logarithmic approximation. We consider the case where no pairs are created in the final state. We show that the differential cross section can be written in the form of the Drell-Yan process cross section. Numerical values of the K-factor and the leading-order distribution on the scattered electron energy fraction and scattering angle are presented.     

Resonance Compton scattering in an external magnetic field

The scattering of a photon by an electron in an external magnetic field under resonant conditions, when the photon energy is close to the splittings between the Landau levels, is investigated. Formulas are obtained for the cross section of the process taking account of the polarization of the electron. For external fields ～10¹² G the resonant Compton cross section is several orders of magnitude greater than the Thompson cross section, and the width of the resonance is tens of electron volts.