Effect of focusing of primary electrons on their reflection from a crystal and on the associated Auger emission

The orientational dependence for different groups of secondary electrons — quasi-elastically scattered, inelastically reflected with excitation of a plasmon and with ionization of the core level M _4.5, and the Auger electrons M _4.5 VV — are measured in the primary electron energy range 0.6–1.5 keV. The data are obtained for a Nb (100) single crystal by varying the azimuthal angle of incidence of the primary beam, with complete collection of secondaries. A relationship is established between the processes of focusing and defocusing of the electrons that have penetrated into the crystal in the 〈110〉 and 〈133〉 directions, which differ substantially in the atomic packing density. Specific details of the Auger orientation effect, due to the focusinginduced variation of the flux density of the reflected electrons, are identified and explained. The contributions, both of anisotropy of ionization of the core level and of variation of the backscattering intensity, to the angular dependence of Auger emission and reflection with ionization loss are estimated. The possibilities of using such orientational dependences for an element-sensitive analysis of the local atomic structure of surfaces are assessed. Zh. Tekh. Fiz. 67, 117–123 (August 1997)     

Coherent amplification of beams of atoms inelastically scattered by the Bose-Einstein condensate

The subject of consideration is coherent amplification of a beam of impurity atoms inelastically scattered by a system of ultracold atoms with collectively excited modes. A kinematic model of weak localization of a new type is used that provides a straightforward explanation for this phenomenon and also makes it possible to derive the angular dependences of the scattering intensity. Based on this model, angular and energy criteria for the existence of the new-type weak localization in an ultracold system of atoms (the Bose-Einstein condensate) are determined. Particular emphasis is on how the principle of indistinguishability influences the weak localization of a beam of atoms inelastically scattered by the Bose-Einstein condensate when scattered and condensed atoms are identical.     

Coherent inelastic electron reflection from a random medium with a sharp boundary

The weak localization of electrons inelastically scattered in a random medium with a sharp boundary is considered. An inelastic electron collision is accompanied by the excitation of a single bulk plasmon. The coherence of electron scattering results from the interference of electron waves related to two possible realizations of the process in which an electron excites a bulk plasmon and undergoes high-angle elastic scattering by chaotically arranged force centers. The sharpness of the boundary means that the statistically averaged length scale and depth of the surface mocroroughnesses are much smaller than the decay length of the wave field of fast electrons in the medium. The same condition is also imposed on the tail size of the electron density of the medium in vacuum. The theory developed makes it possible to determine the bulk-plasmon generation intensity by measuring the ratio of the electron fluxes inelastically and elastically reflected from the surface of a random medium. For this purpose, one should find the dependence of the ratio of these fluxes on three angles, namely, the polar angle of incidence of electrons, the polar angle of electron exit from the medium, and the azimuth angle between the projections of the velocities of the incident (v) and escaping (v′) electrons on the surface plane. Optimum conditions for the detection of this specific azimuth dependence are theoretically grounded for the case where both electron collisions occur in the near-surface region.     

Observation of ionization in a crystal interferometer

We present a new interferometric setup where interference of a fast probe electron affects the ionization cross section of an atom. Interference is detected in the intensity of the inelastically scattered electrons at the Bragg scattering angle in transmission. The crystal serves both as a target for core ionization and as a beam-splitting and phase-shifting device.     

Deconvolution of inelastic background signal from XPS spectra of homogeneous solids

For noble and transition metals, the product of the inelastic electron mean free path and the differential inelastic scattering cross section is a weak function of both the particular metal and the electron energy. It is demonstrated that this property can be useful in the removal of inelastically scattered electrons from XPS spectra of homogeneous solids.     

An extension of the mean free path approach to X-ray absorption spectroscopy

In the partial electron yield (PEY) acquisition mode commonly used in X-ray absorption spectroscopy (XAS) both elastically and inelastically scattered electrons are acquired, the latter contribution dominating the detector signal. Hence, the majority of the inelastic scattering events will not result in signal attenuation as happens in the case of X-ray photoelectron spectroscopy (XPS). To determine the respective changes in the effective mean free paths (MFP) we have performed XPS and near edge X-ray absorption fine structure (NEXAFS) spectroscopy measurements for a series of self-assembled monolayers of alkanethiols on gold substrates. The length of the alkyl chain and, therefore, the film thickness was varied. In agreement with expectations, the obtained MFPs for the Au 4f photoelectrons and C_KLL Auger electrons in the PEY acquisition mode (with the respective inelastic contributions) exceed the corresponding values for the Au 4f and C_KLL electrons of the same kinetic energies in the constant final state acquisition mode. Furthermore, the effective PEY-MFP for the C_KLL Auger electrons increased with decreasing retarding voltage of the PEY detector, which correlates with the enhanced contribution of the inelastically scattered electrons in the acquired signal. The results obtained are of importance for the analysis of XAS spectra of thin organic films and polymers.     

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.     

Streuung von 25 keV-Elektronen an Gasen

The angular distribution of 25 kev electrons scattered elastically and inelastically by molecular hydrogen has been measured in the angular range 7·10^?4≦?≦4,3·10^?2. By the separation of the inelastically scattered electrons observation of deviations from the Debye Ehrenfest theory of the electron diffraction by molecules at small angles is possible. These deviations are due to the alteration of the electron density distribution of the hydrogen atoms induced by the bonding. The energy loss spectra at different scattering angles (energy resolution ≈1 ev) shows a strong peak atΔE=12,6 ev. At larger angles forΔE>15 ev a continuum appears. That part of the inelastic processes which leads to ionization of the molecule is raising with increasing scattering angle. Normalization of the experimental values to the theoretical elastic differential cross section enables comparison of the angular distribution of the 12,6 ev energy loss with the distribution calculated byRoscoe. The shape of the experimental curve is in fairly good agreement with the calculated one but the experimental values at small angles are 20–30% higher. For zero angle the energy loss spectrum is taken with better resolution (≈0,04 ev). It shows vibrational states of the Lyman and Werner band and higher terms. The probability of the excitation of some vibrational states of the Werner band (square of the overlapp integral) calculated here is inspite of the required approximations in excellent agreement with the measurement, while Hutchisson's result fails for the Lyman band.     

Elastic and inelastic contributions to the auger electron appearance potential spectrum of titanium

The energy distribution of electrons contributing to the L-shell Auger electron appearance potential spectrum of a polycrystalline titanium surface has been measured. The Auger electron appearance potential spectrum is obtained by differentiating the total secondary electron yield of an electron bombarded sample as a function of incident electron energy. At the threshold for scattering from a core level the secondary yield increases. Most of the electrons contributing to this increase have energies below 30 eV, and result from secondary processes following Auger recombination of the core hole. The elastic yield decreases at the threshold, however, due to opening a new channel for inelastic scattering. A comparison of the elastic yield spectrum (DAPS), the total yield spectrum (AEAPS) and the soft X-ray yield spectrum (SXAPS), shows very similar line shapes, but differences in the relative strengths of the lines.     

Nature of coherent enhancement of inelastic electron scattering from disordered media

The mechanism of weak localization of relatively fast electrons scattered with a fixed energy loss from disordered media is examined. The main focus of this paper is to put forward an explanation for why coherent enhancement of electron scattering in the inelastic-scattering channel takes place at angles which differ from π. A simplified kinematic model is proposed to determine the basic properties of the weak localization of electrons in the inelastic scattering channel. The model easily reproduces the range of scattering angles typical for the weak localization of electrons with fixed energy loss. The procedure does not require calculation of the contribution from the crossed diagrams. The results agree with those based on the dynamical theory associated with the calculation of the crossed and ladder diagrams. It is possible to follow the transition from the weak localization of the new type to the ordinary weak localization with decreasing energy loss. The weak localization of the new type is in accord with the weak localization of regular type if the energy loss is about the energy of an optical phonon.     

Inelastic electron collisions with Rydberg atoms

The standard classical method of computer simulation is used for evaluation of the inelastic cross section in electron collisions with a highly excited (Rydberg) atom. In the course of collision, the incident and bound electrons move along classical trajectories in the Coulomb field of the nucleus, and the scattering parameters are averaged over many initial conditions. The reduced ionization cross section of a Rydberg atom by electron impact approximately corresponds to that of atoms in the ground states with valence s-electrons and coincides with the results of the previous Monte Carlo calculations. The cross section of an atom transition between Rydberg atom states as a result of electron impact is used for finding the stepwise ionization rate constant of atoms in collisions with electrons or the rate constant of three-body electron-ion recombination in a dense ionized gas because these processes are determined by kinetics of highly excited atom states. Surprisingly, the low-temperature limit of electron temperatures is realized when the electron thermal energy is lower than the atom ionization potential by about three orders of magnitude, as follows from the kinetics of excited atom states. The article is published in the original.     

Deconvolution of loss features from electron spectra

The problem of deconvoluting loss features from energy spectra of electrons emitted from solids is investigated. A new formula is found for the case of an exponentially decreasing intensity from the solid surface of electron emitters. This as well as a formula for the case of a homogeneous distribution of electron emitters is studied in detail. Central in the formulas is the cross section for inelastic scattering. Under the assumption that angular deflection of electrons can be ignored the formulas are exact, i.e. the effect of all multiple scattering events is included. Through numerical calculations on Al spectra the effect of deconvolution is tested, and it is demonstrated that a small deviation from the exact procedure can result in spurious structure in the deconvoluted spectrum.     

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.     

Mechanisms of photo double ionization of helium by 530 eV photons

We have measured fully differential cross sections for photo double ionization of helium 450 eV above the threshold. We have found an extremely asymmetric energy sharing between the photoelectrons and an angular asymmetry parameter beta approximately 2 and beta approximately 0 for the fast and slow electrons, respectively. The electron angular distributions show a dominance of the shakeoff for 2 eV electrons and clear evidence of an inelastic electron-electron scattering at an electron energy of 30 eV. The data are in excellent agreement with convergent close-coupling calculations.     

Multiple photoionization of atoms and small molecules by synchrotron radiation

Absorption of one VUV photon by an atom or a molecule can induce the ejection of several electrons through different processes. Such multiple ionization processes, studied by coincidence electron spectroscopy, provide a wealth of information on electron correlations. A magnetic bottle electron time of flight spectrometer implemented on synchrotron radiation centers has allowed the efficient detection in coincidence of two, three and up to five electrons with good energy resolution. The branching ratios of the different processes are easily extracted from the experimental spectra due to the constant transmission of the spectrometer. Multiple Auger decay was observed in rare gases atoms after inner-shell ionization, while core-valence and core-core initial double ionization followed by Auger decay are other pathways to multiple ionization. For molecules, Coulomb explosion with energy released in ionic fragments may occur after multiple ionization, nevertheless, coincidence electron spectroscopy can also provide a clear interpretation for peculiar decay channels in molecules.     

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.     

Electron Kinetics in the Cathode Region of a Glow Discharge and in Hollow Cathodes

On the basis of an improved cascade model a multi-group theory for studying the electron kinetics in the cathode region of a glow discharge and in hollow cathodes is developed. The secondary electrons newly created by ionization are taken into account. The electrons are divided in groups with respect to the interval where they were created or where they made an inelastic collision. The inelastic collisions and the forward scattering are assumed to dominate. The mean energies of two neighbouring groups are taken to be different by the ionization energy or by parts of it. For the flux densities of the various electron groups a set of ordinary first order differential equations and corresponding boundary conditions are obtained and solved for He. These formulae are valid for any electric potentials. The results relatively well agree with those of Monte Carlo simulations. The first Townsend ionization coefficient differs substantially from that resulting from the Townsend formula. The velocity distribution function spatially varies and contains several groups of fast electrons. Using the detour factor the angular scattering can be included in the calculations.     

Nondipole parameters of TDCS for electron impact ionization and drag current

A comprehensive study is undertaken of angular distributions of electron knock-out from atomic targets by fast electrons with a small transfer of momentum. The general expressions for the parameters of the triple differential cross-section of impact ionization in the optical limit are derived. The calculated parameters are compared with those of the angular distribution of electrons ejected from an atom in the process of photoionization. In these processes, when the multipole transitions are involved, the one-to-one correspondence between the photoionization and impact ionization parameters disappears. The nondipole transitions lead to the backward/forward asymmetry of the angular distribution of ejected electrons that is absent in the dipole approximation for ionization by both fast electrons and photons. Using the He atom as an example, the character of the asymmetry for these two processes is qualitatively different and the backward/forward asymmetry results in macroscopic directed motion of secondary electrons accompanying the passing of a fast electron beam through gas or plasma. The general formulas for this drag current are derived and applied to gaseous He.     

Inelastic scattering of an X-ray photon by a manganese atom

The influence of multiplet and many-particle effects on the shape and magnitude of the double differential cross section of resonant inelastic scattering of a linearly polarized X-ray photon by a free atom with an open shell in the ground state within the energy range of the K ionization threshold is theoretically investigated using a manganese atom as an example. The radial relaxation of electron shells, spin-orbit and multiplet splittings, configuration mixing in intermediate scattering states, and Auger and radiative decays of newly formed vacancies are taken into account. The results of the calculation are predictive.     

On the theory of quantum interference between inelastic and elastic electron scattering events

The mechanism of weak localization of relatively fast electrons scattered with a fixed energy loss from disordered media is examined. The main focus of this paper is to put forward an explanation why coherent enhancement of electron scattering in the inelastic-scattering channel takes place at angles which differ from π. A simplified kinematic model is proposed to determine the basic properties of the weak localization of electrons in the inelastic scattering channel. The model reproduces easily the range of scattering angles typical of the weak localization of electrons with a fixed energy loss. The procedure does not require calculation of the contribution from the crossed diagrams. The results agree with those based on the dynamical theory associated with the calculation of the crossed and ladder diagrams. It is possible to follow the transition from the new type of weak localization to the ordinary weak localization with decreasing energy loss. The new-type weak localization is in agreement with the regular weak localization if the energy loss is approximately equal to the energy of an optical phonon. Zh. éksp. Teor. Fiz. 111, 1001–1015 (March 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.