Simple algorithm for quantitative analysis of reflection electron energy loss spectra (REELS)

A detailed comparison of two different physical approaches for quantitative analysis of reflection electron energy loss spectra (REELS) is presented. The Tougaard–Chorkendorff (TC) algorithm [S. Tougaard, I. Chorkendorff, Phys. Rev. B35 (1987) 6570] is analyzed theoretically and applied to experimental spectra of four elemental solids (Si, Cu, Ag, and Au). A closed expression is derived for the quantity retrieved by the TC-algorithm, the so-called “effective” cross section, which was originally only given as a recursive procedure. Single scattering loss distributions are derived from the experimental spectra using the bivariate reversal method [W.S.M. Werner, Phys. Rev. B74 (2006) 075421]. The latter agree satisfactorily with density functional theory (DFT) calculations and other data found in the literature. Using these single scattering loss distributions, the TC “effective” cross section can be perfectly reproduced if the fact is taken into account that the effective cross section is not a single scattering loss distribution and is governed to a significant extent by elastic scattering. On the basis of the above results, a dramatically simplified deconvolution scheme for quantitative analysis of REELS is developed.     

Elastic neutron scattering measurements on239Pu in the energy range between 0.19 and 0.38 MeV

Five neutron scattering angular distributions of²³⁹Pu were measured in the primary neutron energy range between 0.19 and 0.38 MeV. The absolute cross section results are presented in the form of coefficients of Legendre polynomial expansions. Integrated scattering cross sections are also given. Cross section calculations using a central optical model were made and their results were compared with the experimental values.     

The total reaction cross section for α-induced deuteron break-up in the energy range 20–28 MeV

Alpha-particle spectra resulting from the bombardment of douterons with α-particles have been measured at energies of 20.4, 24.2 and 28.1 MeV for all kinematically possible scattering angles θ_1ab > 5°. Angular distributions for the break-up cross section have been obtained by integration over the α-particle energy. The total reaction cross section is computed by extrapolating the angular distributions to 0°. The results are compared with predictions calculated from α-d phase shifts and Faddeev theory.     

The elastic scattering of low energy electrons from Xenon

Calculations are presented of angular distributions for electrons elastically scattered from xenon in the energy range 5.5 to 10 eV. The potential describing the xenon atom is determined by the X_α-approximation. The relative dependence with energy of the differential cross section at 30° scattering angle has been calculated in the range 30 to 200 eV. The theoretical results are in very good agreement with experimental data.     

Monte Carlo方法计算低能电子作用下固体背散射电子发射及空间分布

应用Monte Carlo方法,对能量E₀≤5keV低能电子作用下固体Al、Cu、Ag、Au的背散射电子发射及表面空间分布作了计算.模型应用Mott散射截面及修正的Bethe方程分别描述低能电子在固体中的弹性和非弹性散射.计算了背散射电子能量分布、表面空间分布、深度分布和角分布规律及特征,还计算分析了背散射电子角分布与深度分布、表面空间分布及能量分布之间的关系,系统地描述了背散射电子的发射及分布规律.     

Proton-nucleus inelastic cross section at ultra high energy

Energy dependence of proton-nucleus reaction cross section at very high energy is discussed. It is stressed that depending on the gluon distribution near the nuclear surface, proton-nucleous total cross section increases much more rapidly compared to the usual Glauber independent nucleon estimate. The recent observation of smaller X _max than the expected value at UHECR domain can be an indication for such a mechanism.     

Monte Carlo方法模拟低能电子在多元介质中散射——基于平均散射截面方法

应用基于平均散射截面低能电子在多元介质中散射Monte Carlo方法,模拟E≤5eV低能电子在多种多元介质中散射。计算了电子背散射系数,背散射电子能谱、角分布,入射电子、背散射电子在介质中的作用范围、沉积能分布,并与确定散射中心方法的结果比较。两种方法计算结果广泛一致,进一步证明基于平均散射截面方法的有效性和可靠性。入射电子能量较低,介质平均原子序数较大时,计算的背散射电子角分析不服从余弦分布律。     

Separation of angular and energy relaxations of nonequilibrium electrons in a solid

We demonstrate that the collision integral of the kinetic equation for the interaction of hot electrons with phonons can be split into substantially different parts that correspond to elastic and inelastic collisions. In particular, this applies to electrons with energies of about 1 eV that propagate in semiconductors. The difference in the characteristic energy and momentum relaxation times makes it possible to separate the angular and energy relaxation processes. If the differential cross section of elastic scattering depends, not on the scattering angle, but on the directions of incident and scattered electrons (which is observed, e.g., for the interaction of an electron with piezoelectric lattice vibrations in A^IIIB^V compounds), the Laplacian in the equation that describes the spatial and energy distributions of electrons can be replaced by an elliptical operator; i.e., the electron diffusion turns out to be anisotropic.     

Spectral power determinations of compressibility and density variations in model media and calf liver using ultrasound

A model of scattering is used to relate average differential scattering cross section and power spectra of scattering medium variations. The model expresses the average differential scattering cross section as a sum of the power spectrum of medium compressibility variations, the power spectrum of density variations weighted by the square of the cosine of the scattering angle, and the cross-power spectrum of compressibility and density variations weighted by twice the cosine of the scattering angle. Known values of the average differential scattering cross section at a minimum of three different scattering angles and temporal frequencies corresponding to the same spatial frequency are used to calculate each of the three power spectra. Since noise and statistical fluctuations are present in actual measurements of average differential scattering cross section, the calculations of power spectra are obtained from an overdetermined set of equations to which a solution is found by using a singular value decomposition. Data derived from a model for scattering from a cloud of correlated particles are employed to show the influence of additive noise. Calculations are also made from measurements of scattering from three suspensions of particles that have a different average radius in each suspension but are similarly modeled by scattering from a cloud. Additionally, the calculations are applied to measurements of average differential scattering cross section of calf liver. The results show that determination of the power spectra of scattering medium variations can be made under practical conditions, and also imply that density variations contribute significantly to scattering by calf liver.     

电子垂直入射电离氦原子碰撞机理的理论研究

用3C模型和修正后的3C模型在低能、两个出射电子等能分享几何条件下,对电子垂直入射碰撞电离氦原子的三重微分散射截面进行了理论计算,并把计算结果与实验测量结果进行了比较,系统研究了(e,2e)反应中各种屏蔽效应对氦原子三重微分散射截面的影响,同时对截面中形成各峰的碰撞机理做了详细的探讨.研究结果表明:在入射能较低时,各种屏蔽效应对氦原子的三重微分散射截面幅度以及角分布均存在一定影响,并且形成各峰的碰撞机理直接影响截面的变化规律.     

Reactive scattering of a supersonic alkali atom beam: K + Br2, BrCN,SnCl4, PCl3, CCl4, CH3I

Angular distribution measurements of reactive scattering of a supersonic potassium atom beam by a series of molecules are reported with initial kinetic energy (～ 5 kcal mole^-1) above the thermal energy range. The narrow Laval nozzle velocity distribution gives improved resolution over thermal energy measurements. Total reaction cross sections are found to decrease with energy. Differential reaction cross sections for Br₂, BrCN and CCl₄ show increased forward scattering compared with thermal energies but for CH₃I there is no change to within experimental error. The BrCN scattering is compatible with spectator-stripping dynamics, though this limit has not been reached in the Br₂ scattering. The SnCl₄ differential reaction cross section appears not to be compatible with a single peak in the centre of mass recoil velocity distribution. It is suggested that high and low velocity contributions to the intensity may arise from a long-lived collision complex dissociating by two reaction paths.     

Partonic scattering cross sections in the QCD medium

A medium modified gluon propagator is used to evaluate the scattering cross section for the process gg→gg in the QCD medium by performing an explicit sum over the polarizations of the gluons. We incorporate a magnetic screening mass from a non-perturbative study. It is shown that the medium modified cross section is finite, divergence free, and is independent of any ad-hoc momentum transfer cut-off parameters. The medium modified finite cross sections are necessary for a realistic investigation of the production and equilibration of the minijet plasma expected at RHIC and LHC.     

Generalized parton distributions and deeply virtual Compton scattering in color glass condensate model

Within the framework of the color glass condensate model, we evaluate quark and gluon generalized parton distributions (GPDs) and the cross section of deeply virtual Compton scattering (DVCS) in the small-x_B region. We demonstrate that the DVCS cross section becomes independent of energy in the limit of very small x_B, which clearly indicates saturation of the DVCS cross section. Our predictions for the GPDs and the DVCS cross section at high energies can be tested at the future Electron–Ion Collider and in ultra-peripheral nucleus–nucleus collisions at the LHC. PACS  12.38.Mh; 13.60.Fz; 13.85.Fb; 24.85.+p; 25.20.Dc     

The dipole pomeron and pp scattering

A dipole Pomeron model is applied to high energy pp scattering. It is shown that the model reproduces both: the dip structure in the differential cross section and the break in the slope at small ¦t¦. The model indicates the existence of a hard core inside the proton.Submitted to the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.Helpful discussions with A. I.Bugrij, N. A.Kobylinsky, V. V.Serebryakov and B. V.Struminsky are acknowledged.     

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.     

New opportunities for quantitative analysis as applied to reflected electron energy loss spectroscopy of Fe/Si structures

The feasibility of determining the elemental composition, chemical state, and element distribution across the depth in a subsurface region using the computer simulation of the electron inelastic scattering cross section is demonstrated with iron layers on silicon substrates. Analysis is carried out based on the dielectric theory and on the experimental determination of the product of the electron inelastic mean free path by the inelastic scattering cross section from reflected electron energy loss spectra.     

Medium corrections to the reaction cross section for low energy pion4He scattering

We investigate the effects of the Pauli principle and the nucleon binding on the reactive content of the single scattering optical potential. The binding and exclusion principle effects are calculated for low energy pion-⁴He scattering. A careful treatment of the Pauli principle enables us to determine a pion nucleon energy shift representing binding effects from the requirement that the reaction channel opens at the correct threshold energy. We find that binding and Pauli effects lead to a reduction of the reaction cross section by about 30–50% and (expect for very low energies) to a slight increase of the elastic cross section by 5–10%.     

Nonperturbative gluon radiation and energy dependence of elastic scattering

The energy dependence of the total hadronic cross sections is caused by gluon bremsstrahlung which we treat nonperturbatively. It is located at small transverse distances about 0.3 fm from the valence quarks. The cross section of gluon radiation is predicted to exponentiate and rise with energy as s(delta) with delta = 0.17+/-0. 01. The total cross section also includes a large energy independent Born term which corresponds to no gluon radiation. The calculated total cross section and the slope of elastic scattering are in good agreement with the data.     

Global and local fluctuations in multiplicity and transverse energy for central ultra-relativistic heavy-ion interactions

We present results from a comparison between experimental data and model calculations, in this case represented by the Fritiof model, regarding global and local fluctuations in the distributions of transverse energy and charged particle multiplicity. The results indicate that the observed fluctuations originate predominantly from the distribution of emitting sources, i.e. either the number of participating nucleons or the number of binary collisions. The apparently larger widths of the distributions observed in restricted regions of phase space, are explained to be of purely statistical nature. As a result of the analysis the cross section for events with energy densities much larger than the typical value for a central collision is limited. The very small scales, normally associated with studies of intermittent behaviour, are not within the scope of this paper. The results of the analysis are essentially independent of whether intermittence is of importance in the reactions or not.     

Neutron-proton charge exchange scattering between 190 MeV and 590 MeV

Differential cross sections of the np charge exchange scattering between 190 MeV and 590 MeV have been measured by detecting the scattered protons in an angular range of 0^° θ_lab 18^°. The cross section at 0^° as well as the logarithmic slope of the angular distribution are found to be almost energy independent, in contrast to previous experiments, but in agreement with recent LAMPF data.