Inelastic scattering of charged particles by atoms using the Thomas-Fermi statistical method

We describe a method of calculating the differential cross section for the inelastic scattering of charged particles by atoms based on the statistical model of the atom. For the most general form of the potential of the atom we obtain an analytical expression for the differential (with respect to the energy of the electron ejected from the atom) cross section of inelastic scattering. It is shown that the statistical method of Thomas-Fermi is applicable when the energy of the ejected electron is sufficiently high.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 92–96, September, 1986.     

Relative contribution of various factors to the formation of the energy spectrum of fast, medium-energy, charged particles and ions transmitted through a thin target with fluctuations of the target thickness

The characteristics of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil are investigated theoretically and experimentally as functions of the angle of incidence of the beam on the target. Analytical expressions for the average characteristics of the transmitted-particle energy spectrum are determined for the case of small-angle scattering. The combined influence of various factors affecting the formation of the energy spectra is taken into account: systematic stopping of particles in the medium, fluctuations of the particle energy losses in inelastic collisions, bending of the particle trajectories due to multiple elastic scattering, and fluctuations of the target thickness. It is shown that the contributions of these factors to the width of the transmitted-particle energy spectrum depend differently on the angle of incidence of the beam on the target surface. On the basis of this differentiation it is inferred from the experimental dependence of the width of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil on the angle of incidence of the beam that fluctuations of the particle energy losses in inelastic collisions are the predominant factor in the formation of the proton energy spectra. Zh. Tekh. Fiz. 67, 81–93 (May 1997)     

Focusing of electrons reflected from a crystal with loss of energy

A study is made of the features arising in the spatial distributions of reflected electrons as a result of a focusing effect. Experiments are conducted on single-crystal Mo (100) with primary electron energies of 0.5–2 keV and detection of electrons which lose fixed amounts of energy up to 300 eV. An analysis of the data establishes the dependence of the electron focusing efficiency on the amount of energy loss. It is shown that when electrons are reflected with single losses through plasmon excitation, the magnitude of the effect is determined mainly by the average number of scattering atoms encountered by an electron along its path to the surface. When the energy losses are high, defocusing owing to multiple elastic and inelastic scattering of the electrons is found to predominate. Zh. Tekh. Fiz. 68, 128–133 (June 1998)     

Most likely ensemble with a given average energy prepared by a single slit

We discuss an ensemble of particle selected by a single slit within the statistical model of quantization reported earlier. We look for the most probable distribution of the position of the particle with a given average energy by applying Jaynes’s maximum entropy principle. We first show that the most likely ensemble with the lowest possible average energy is given by the quantum mechanical ground state of a particle trapped inside the slit. We further show that in general it takes a larger energy to collect the beam of particles into a target position with a higher precision.     

电子束放射照相的特性与参数优化

短脉冲强激光产生的电子束具有源尺寸小、脉宽窄、准单能谱等特点, 在放射照相诊断中具有独特作用. 本文通过分析电子在材料中散射并采用蒙特卡罗方法数值模拟, 研究了100 keV到几百MeV能量电子束对有厚度起伏或存在界面的靶的透视, 并与质子、X射线束透视结果比较, 给出了电子束放射照相的特性与参数优化: 基于电子在材料中非弹性散射或能量损失, 选用能量使其射程与靶厚度接近的电子束来诊断靶厚度不均匀性; 基于电子在材料中的弹性散射, 选用射程超过靶厚度的电子束来诊断靶界面.     

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.     

Estimation of ion scattering by atomic chains on single crystal surfaces

Estimation of ion movement close to atomic chains taking into account the elastic and inelastic energy losses and vacancy type imperfections was performed on the basis of a model of binary interactions of ions with the atoms of a crystal.

An analysis of results shows that at scattering by atomic chains a phenomenon which makes a substantial contribution to scattering by the single crystal surface the inelastic energy losses exceed the single scattering ones by a factor of 5–6.     

Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.     

The measured energy loss of high energy electrons in copper and lead

The energy distributions of electrons of about 53, 75 and 93 MeV have been measured before and after passing through copper absorber of thickness up to 5.726 g/cm² and lead absorbers of thickness up to 2.825 g/cm². Earlier data for aluminum absorbers are reviewed. The electrons were accelerated by the LINAC of the Naval Postgraduate School. The most probable energy losses agree with the theory of Blunck and Westphal for all thicknesses; the half widths agree except for large thicknesses, where they are smaller than theoretical values for lead, in agreement for copper, and larger for aluminum. Large numbers of electrons of energy less than 30 MeV are observed in the distributions of transmitted electrons, particularly for thick absorbers and higher values of atomic number. These are apparently the result of multiple processes in the absorbers.     

Distorted wave theory of scattering of nucleons with intermediate energies on nuclei

In the context of nonrelativistic theory in the distorted wave approximation, a three-dimensional form of analytical expression for the differential cross section of scattering of nucleons with intermediate energies on atomic nuclei is derived. In the context of this theory, the main parameters of elastic scattering of protons with incident energy of 1 GeV on the ²⁰⁸Pb nucleus are determined. For inelastic scattering of protons with nuclear surface vibrations, giant multipole resonances in the excited nucleus are investigated for the collective nucleus model. The energy losses of the scattered proton are calculated together with the energies of giant dipole and quadrupole resonances and nuclear surface vibration energy. This allows the deformation parameter of the excited nucleus to be calculated.     

Crystal field of Yb<Superscript>3+</Superscript> tetragonal centers in the YbRh<Subscript>2</Subscript>Si<Subscript>2</Subscript> intermetallic compound

The spectra of electron paramagnetic resonance and inelastic neutron scattering in crystals of the heavy-fermion intermetallic compound YbRh₂Si₂ are interpreted. The phenomenological potentials of the crystal electric field of Yb³⁺ tetragonal centers and the parameter of the Hamiltonian for the spin-orbit interaction of electrons are determined from the experimental energy level schemes. A comparison of the results obtained from experimental data on electron paramagnetic resonance, inelastic neutron scattering, and Mössbauer spectroscopy shows that the most probable ground state of Yb³⁺ ions in the YbRh₂Si₂ crystal is the Kramers doublet Γ _t6 ^? .     

Correlation effects in electron-ion collisions in a strong laser field

We examine elastic and inelastic scattering of electrons by ions in intense laser light. A method of numerical investigation of the scattering characteristics based on regularizing the Coulomb singularity is proposed. We show that over a broad range of parameter values the transport scattering cross section is weakly dependent on the intensity of the high-frequency field. We detect a significant modification of the dependence of the effective inelastic scattering cross section. We also show that the energy exchange with the field is determined by a fairly small group of electrons, called the representative electrons. Finally, we propose a qualitative model that explains our results by the fact that the leading contribution is provided by inelastic collisions of electrons with relatively small impact parameters traversing the region important for the interaction at large angles. Zh. éksp. Teor. Fiz. 115, 463–478 (February 1999)     

Quantification of surface effects: Monte Carlo simulation of REELS spectra to obtain surface excitation parameter

The surface excitation effect is investigated by using the quantum mechanical frame work of complex self-energy of electrons which interact with a bounded semi-infinite medium. In the self-energy formalism, differential inverse inelastic mean free path (DIIMFP) has contributions from bulk and surface plasmons. Monte Carlo simulation of the interaction of electrons with a solid medium and surface has been performed. The surface excitation parameter (SEP) is then obtained from the simulated reflection electron energy loss spectroscopy (REELS) spectra. The calculated SEP results by Monte Carlo simulation are compared with the previous calculations of total surface excitation probability, which was estimated by a numerical integration of surface term of DIIMFP. The contribution merely due to surface excitations towards REELS spectra is extracted by subtracting the two Monte Carlo simulated REELS spectra that based on the two models of electron inelastic scattering, i.e. a full surface model (SM) and a pure bulk model (BM). The surface excitations found to be significant at low energy losses and diminish at higher energy losses whereas the bulk plasmon contributions show opposite behavior and are negligible at lower energy losses. The average number of surface excitations is then evaluated by the computation of ratio of the integrated surface contribution to the elastic peak. The calculated results for Ag are found to be reasonably in agreement with our previous results for total probability of surface excitations and other reported experimental data for SEP. Surface correction factor (SCF) is calculated using SEP for several metals and is compared with the reported ratio of SCF with Ni sample as reference.     

Multiplicity of charged particles in electron-induced showers developing in oriented silicon and tungsten crystals

A more than twofold increase in the average multiplicity of charged particles in electromagnetic showers initiated by electrons with an energy of 26 GeV in tungsten crystals 2.7, 5.8, and 8.4 mm thick, oriented along the 〈111〉 axis, in comparison with misoriented crystals is shown. For a silicon crystal 20 mm thick, oriented along the 〈110〉 axis, at an electron energy of 28 GeV, the average multiplicity of charged particles increases by a factor of ～1.6. The widths of the orientation dependences of the average multiplicity of charged particles in electron-induced showers in silicon and tungsten crystals are proportional to the crystal thickness and depend on the electron energy as E ^?1/2.     

Dynamics of the most probable energy loss by relativistic ions

Simple but very general formulas determining the parameters of the statistical distribution of inelastic energy losses (in particular, their most probable values) by relativistic ions as functions of the velocity and path length in a substance have been derived on the basis of the generalization of the classical Landau approach and steepest descent method. These expressions are more accurate than the well-known formulas and significantly expand the domains of applicability of the latter. Comparison with the numerical results confirms the high accuracy of the resulting analytical representations in wide intervals of the parameters and reveals their limitation.     

A comparative study of electron and positron penetration in silicon dioxide

Many researches are devoted to the study of silicon dioxide, a material of great interest for its use in the micro-electronics industry. This paper aims to compare the behavior of electrons and positrons when impinging on silicon dioxide targets in order to investigate the differences and the similarities. In particular, the inelastic mean free path, the stopping power, the differential elastic scattering cross-section and the total and transport elastic scattering cross-section of electrons and positrons penetrating in silicon dioxide targets are compared in order to better understand their influence in determining the implantation profiles shapes, the mean range of penetration, the maximum range of penetration and the backscattering coefficient as a function of the primary energy of the incident particles.     

Convoy electrons produced at glancing angle scattering of MeV HeH+ ions from a crystal surface

Abstract

Convoy electrons produced at glancing angle scattering of MeV HeH⁺ ions from an atomically clean (001) surface of SnTe crystal are observed. Energy spectrum of the convoy electrons shows a peak broader than that at scattering of atomic projectiles and the most probable energy of convoy electrons at HeH⁺ scattering is larger than those at scattering of isotachic He ions. This acceleration of convoy electrons is qualitatively explained by the force due to surface wake induced by Coulomb exploding fragment He²⁺ and H⁺.     

Cross sections of electron capture and electron capture ionization versus the impact parameter in collisions of a proton with multielectron atoms

The absolute differential cross sections of scattering of hydrogen atoms resulting from an electron capture and an electron capture ionization are measured for collisions of 4.5- and 11-keV protons with argon and xenon atoms. The range of scattering angles is 0°–2°. From the scattering differential cross section found experimentally, the probabilities of single-electron capture and electron capture ionization as a function of the impact parameter are calculated. The dependences of the incident particle scattering angle on the impact parameter (deviation function) for interactions with Ar and Xe atoms are calculated in terms of classical mechanics using the Moliére—Yukawa potential to describe the interaction of atomic particles. Analysis is given to the probabilities of electron capture and electron capture ionization versus the impact parameter and to the distribution of the electron density on different electron shells in a target atom versus a distance to the core. It is concluded that only electrons from the outer shell of the target atom are involved in the process of electron capture ionization. The cross section of electron capture ionization is calculated in the proton energy range 5–20 keV.     

Wirkungsquerschnitt und Winkelverteilung der elastischen und unelastischen Elektronenstreuung in Aluminiumschichten

Absolute intensity measurements of the electrons scattered by a polycrystalline Aluminium foil were carried out in the energy range between 25 and 50 keV. The electrons scattered elastically were separated from those scattered inelastically by means of a retarding field. The intensities of the electrons having passed the foil unscattered and of those which were scattered elastically into the Debye-Scherrerrings and into the continuous background can be interpreted by the assumption of reasonable thicknesses of the crystalline Aluminium and the amorphous Aluminium-Oxide. These values agree approximately with the thickness measured by light absorption. Additionally the probability of the inelastic scattering process can be deduced from these measurements. Investigations of the angular distribution were carried out in order to study the influence of the inelastic scattering on the shape of the primary beam, the rings and the continuous background. The results are discussed in detail. Some results are given in particular, concerning the increase of the half width of the rings due to inelastic scattering processes.     

Influence of incoherent scattering on stochastic deflection of high-energy negative particle beams in bent crystals

An investigation on stochastic deflection of high-energy negatively charged particles in a bent crystal was carried out. On the basis of analytical calculation and numerical simulation it was shown that there is a maximum angle at which most of the beam is deflected. The existence of a maximum, which is taken in the correspondence of the optimal radius of curvature, is a novelty with respect to the case of positively charged particles, for which the deflection angle can be freely increased by increasing the crystal length. This difference has to be ascribed to the stronger contribution of incoherent scattering affecting the dynamics of negative particles that move closer to atomic nuclei and electrons. We therefore identified the ideal parameters for the exploitation of axial confinement for negatively charged particle beam manipulation in future high-energy accelerators, e.g., ILC or muon colliders.