Angular distributions of electrons in the (e, 3e) reaction

The differential cross sections for the Kr (e, 3e) Kr⁺⁺ reaction are calculated (by using correlated wave function) in the case of high incident energy (5 keV) for the three terms of the final Kr⁺⁺ (4p ⁴) ion. We have performed an ab initio calculation on the basis of the first Born approximation using correlated wave functions for the target. The agreement with the first available (e, 3e) experimental data is fairly good. Other typical experimental situations are proposed and discussed.     

Binding energies at different momenta for the valence orbitals of HCl by the binary (e, 2e) method

The binding energy spectra for the valence orbitals of hydrogen chloride have been obtained using the binary (e,2e) method at 1200 eV. The strength of the innermost valence orbital (4σ) is severely split among several ion states in the energy range 25 to 41 eV. The measured cross sections are compared with results of calculations using contracted Gaussian basis sets of double-zeta quality, and with a one-particle Green's function calculation.     

Laser-assisted (e, 2e) collisions in helium

The influence of a strong laser field on the dynamics of fast (e, 2e) collisions in helium is analyzed in the asymmetric, coplanar geometry. The interaction of the laser field with the incident, scattered and ejected electrons is treated in a non-perturbative way, while the remaining interactions are treated by using first order perturbation theory. Detailed calculations are performed for an incident electron energyE _{k i}=600 eV, an ejected electron energyE _{k B}=5 eV and a scattering angle θ _A =4°. The influence of the laser parameters (photon energy, intensity and direction of polarization) on the angular distribution of the ejected electron is analyzed. We find that in general the triple differential cross sections are strongly dependent on the dressing of the projectile and the target by the laser field.     

Correlation of the total cross section for electron scattering by molecules with 10–22 electrons, and some molecular parameters at intermediate energies

Accurate experimental values of the total cross section (σ_T) for electron scattering by molecules (CH₄, NH₃, N₂, CO and CO₂) in the energy range 0.5 to 5 keV have been analysed to obtain correlations with molecular properties. A formula for σ_T, as a function of the number of target electrons and molecular polarizabilities, has been deduced. This empirical expression reproduces to within 6% our experimental results for the abovementioned molecules and has been used to obtain results for other molecular targets with 10 to 22 electrons. Total cross sections show reasonable agreement with the experimental and theoretical data for this energy range.     

Theoretical premises for experimental verification of the deviations from the wannier threshold behaviour

The Wannier [1] theory describes the escape of two electrons from a charged core in the threshold domain. Its modification [3] is applied to some features of the double escape processes which were not analyzed previously in due extent. The behaviour of the total cross sections for a small, but finite, energy excessE above the threshold is described incorporating the deviations from the well known Wannier power law. The processes with the escape of electron and positron from the core are also considered. The energy dependence of the spin asymmetryA in (e, 2e) collisions is analyzed in connection with the recent experimental data (which seem to manifest some dependenceA(E) in the near-threshold domain contrary to the conventional Wannier theory). The theory suggests the requirements for the accuracy of the experiments intended to verify the Wannier threshold laws and detect the deviations from them.     

Dissociative Excitation of Even Doublet Levels of the Cobalt Atom in Electron Collisions with Cobalt Dichloride Molecules

The dissociative excitation of the even doublet levels of the cobalt atom upon the collisions of cobalt dichloride molecules with 100-eV monoenergetic electrons was experimentally studied. Dissociative excitation cross sections for transitions from these levels turned out to be greater than the corresponding cross sections of direct excitation in electron-atom collisions (except for the e ² P _1/2 level). The total excitation cross sections (including the contribution of cascade population) were determined for ten levels.     

Regioselective One‐Step Synthesis and Topological Chirality of trans‐3, trans‐3,trans‐3 and e,e,e [60]Fullerene‐Cyclotriveratrylene Tris‐adducts: Discussion on a Topological meso‐Form

The C₃‐symmetrical [60]fullerene‐cyclotriveratrylene (CTV) tris‐adducts (±)‐ 1 (with a trans‐3,trans‐3,trans‐3 addition pattern) and (±)‐ 2 (with an e,e,e addition pattern) were prepared in 11 and 9% yield, respectively, by the regio‐ and diastereoselective tether‐directed Bingel reaction of C₆₀ with the tris‐malonate‐appended CTV derivative (±)‐ 3 (Scheme). This is the first example for tris‐adduct formation by a one‐step tether‐directed Bingel addition. Interchromophoric interactions between the electron‐rich CTV cap and the electron‐attracting fullerene moiety have a profound effect on the electrochemical behavior of the C‐sphere (Fig. 4 and Table 1). The fullerene‐centered first reduction potentials in compounds (±)‐ 1 and (±)‐ 2 are by 100 mV more negative than those of their corresponding tris[bis(ethoxycarbonyl)methano][60]fullerene analogs that lack the CTV cap. A particular interest in (±)‐ 1 and (±)‐ 2 arises from the topological chirality of these molecules. A complete topology study is presented, leading to the conclusion that the four possible classical stereoisomers of the e,e,e regioisomer are topologically different, and, therefore, there exist four different topological stereoisomers (Fig. 6). Interestingly, in the case of the trans‐3,trans‐3,trans‐3 tris‐adduct, there are four classical stereoisomers but only two topological stereoisomers (Fig. 7). An example of a target molecule representing a topological meso‐form is also presented (Fig. 8).     

Relativistic (e, 2e) collisions on atomic inner shells in symmetric geometry

We report here on an (e, 2e) experiment at relativistic electron energies (E ₀=300 keV and 500 keV) in coplanar symmetric geometry. Absolute triple differential cross section measurements forK-shell ionisation of gold, silver and copper are compared with a number of simple first order approximations. Appreciable discrepancies between theory and experiment are found, which reduce with decreasingZ and increasing primary energy. The theoretical calculations show that spin flip effects are important in symmetric geometry, in earlier works these had been neglected.     

Total cross sections of electron collisions with S atoms; H2S,OCS and SO2 molecules (Ei ≥ 50 eV)

Collisions of intermediate to high energy electrons are considered with S-atoms as well as H₂S, OCS and SO₂ molecules as targets. We employ e^- atom total cross sections calculated in the complex optical potential, to calculate e^--molecule total cross sections in a simple and a modified Additivity Rule. Our total (elastic + inelastic) cross sections above 50 eV, fare reasonably well as compared to various experimental and theoretical data. The calculated inelastic cross sections serve as the upper limit of total ionization cross sections. Results are presented graphically from about 10 to 5000 eV.     

The Orthogonal (e,e,e)‐Tris‐Adduct of 9,10‐Dimethylanthracene with C60‐Fullerene: A Hidden Cornerstone of Fullerene Chemistry. Preliminary Communication

Tris(9′,10′‐dimethyl[9,10]ethanoanthracene[11′,12′: 1,9;11″,12″: 16,17;11′′′,12′′′: 30,31])[5,6]fullerene C₆₀, the orthogonal (e,e,e)‐tris‐adduct of C₆₀ and 9,10‐dimethylanthracene, was obtained from [4+2]‐cycloaddition (Diels–Alder reaction) at room temperature. The thermally unstable orange red (e,e,e)‐tris‐adduct was purified by chromatography and was isolated in the form of red monoclinic crystals. Its C₃‐symmetric addition pattern was established spectroscopically. Its structure could be further investigated by single crystal X‐ray diffraction. The (e,e,e)‐tris‐adduct of C₆₀ and 9,10‐dimethylanthracene has earlier been suggested as intermediate and reversibly formed critical component in ‘template directed’ addition reactions of C₆₀. This previously elusive compound has now been isolated and structurally characterized.     

Electron scattering and dissociative attachment by SF6 and its electrical-discharge by-products

Discrete electron-molecule processes relevant to SF₆ etching plasmas are examined. Absolute, total scattering cross sections for 0.2–12-eV electrons on SF₆, SO₂, SOF₂, SO₂F₂, SOF₄, and SF₄, as well as cross sections for negative-ion formation by attachment of electrons, have been measured. These are used to calculate dissociative-attachment rate coefficients as a function ofE/N for SF₆ by-products in SF₆.     

Critical charges of simple coulomb molecular systems: One‐two electron case

We consider some Coulomb systems with several infinitely massive centers of charge Z and one or two electrons: (Z,e), (2Z,e), (3Z,e), (4Z,e), (2Z,e,e), and (3Z,e,e). It is shown that the physical, integer charges Z = 1,2,… do not play a distinguished role for the total energy and for the equilibrium configuration of a system, giving no indication of a charge quantization. By definition, a critical charge Z_cr for a given Coulomb system (nZ,e) or (nZ,e,e) is a charge which separates the domain of the existence of bound states from the domain of unbound states (the domain of stability), the continuum (the domain of instability). For all the above‐mentioned systems critical charges Z_cr as well as equilibrium geometrical configurations are found. Furthermore, an indication to a branch point singularity at Z = Z_cr with exponent 3/2 was obtained. It is demonstrated that in the domain of the existence the optimal geometrical configuration for both (nZ,e) at n = 2,3,4 and (nZ,e,e) at n = 2,3 corresponds to the Platonic body. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Ionisation dynamics at intermediate momentum transfer: an (e, 2e) investigation on argon

Relative triple differential cross section for the coplanar asymmetric (e, 2e) reaction in argon have been measured at 1.5 KeV incident energy and 40 eV ejected electron energy in several kinematics. Depending on the scattering angle, ? _a , the chosen kinematics select either ionising collisions belonging to the Bethe ridge (? _a =9.2°) or processes in the intermediate region between the pure dipolar and binary regimes. The more relevant finding is the presence of a minimum in the recoil lobe, almost opposite to the direction of the momentum transfer. This feature is qualitatively explained by a first Born model, which describes the ejected electron by a Coulomb wave-function. This result suggests that in the investigated kinematics the interaction of the slow ejected electron with the residual ion is the dominant effect beyond the first order electron-electron interactions.     

Calculation of Ionization,Excitation and Electron Capture Cross Sections for Be4++H(2s, 2p) Collisions

A computational study of Be⁴⁺+H(2s, 2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be³⁺(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.     

Scattering of fast electrons and X-rays from molecules: CH4 and C2H2

Self-consistent-field (SCF ) wave functions are used to calculate cross sections for the elastic and inelastic scattering of fast electrons and x-rays from CH₄ and C₂H₂ molecules. The effects of basis set choice and free rotation on these cross sections are investigated. The utility of an approximate scheme to correct SCF inelastic cross sections for the effects of electron correlation is examined. The probability density for the interelectronic distance, or radial intracule density, is obtained and discussed.     

Electron correlation and charge density study of N2 and O2 by high energy electron scattering

The differential elastic scattering cross sections of N₂ and O₂ for 29 keV electrons have been measured. The experiment was performed using a Möllenstedt type energy analyzer to isolate the elastically scattered electrons. The difference between the measured results and calculations from molecular Hartree-Fock wave functions reveals the electron correlation in the molecules. Using the previously measured total scattering data, the inelastic scattering cross sections are derived. Several potential energies of the target are evaluated from the cross sections. Results at small angles are analyzed in terms of molecular moments and diamagnetic susceptibilities. The scattering behavior at small angles of the N₂ measurement agrees well with several ab initio calculations.     

Differential and total (e,2e) cross sections of simple polyatomic molecules

In this paper, we present a theoretical approach to calculate differential and total ionization cross sections of polyatomic molecules by fast electron impact. More exactly, we have studied the ionization of ammonia (NH(3)) and methane (CH(4)) molecules, and previous results concerning the H(2)O molecule ionization are reported for comparison. The calculations are performed in the distorted wave Born approximation without exchange by employing the independent electron model. The molecular target wave functions are described by linear combinations of atomic orbitals. To describe the interaction between the inactive target electrons and the slow ejected electron, we have introduced a distortion via an effective potential calculated for each molecular orbital. The present theoretical calculations agree well with a large set of existing experimental data in terms of multiple differential and total cross sections.     

Doubly excited3Se,3De and3Ge states of two-electron atomic systems

Summary Time-dependent perturbation theory has been applied to calculate the doubly excited triplet statesNsns:³S^e,Npnp:³D^e andNdnd:³G^e (N=2, 3, 4,n=N+1, ... ,5) for He, Li⁺, Be²⁺ and B³⁺. A time-dependent harmonic perturbation causes simulataneous excitation of both the electrons with a change of spin state. The doubly excited energy levels have been identified as the poles of an appropriately constructed linearized variational functional with respect to the driving frequency. In addition to the transition energies, effective quantum numbers of these doubly excited states have been calculated and analytic representations of their wave functions are obtained. These are utilized to estimate the Coulomb repulsion term for these states which checks the consistency of the wave functions. These wave functions may also be used for calculating other physical properties of the systems.     

Fully relativistic study on electron impact elastic scattering from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), and Xeq+ (q = 2–6, 8)

A study is presented on the elastic scattering of electrons from N^q+ (q = 1–3), Na⁺, Ar^q+ (q = 1–3, 7–8), Xe^q+ (q = 2–6, 8) to understand the available experimental differential cross section results. A model potential approach has been utilized to describe the scattering process. The model potential includes the static, exchange, polarization and absorption potentials. The static potentialis obtained through the charge density calculated by obtaining ionic wave functions using multi-configuration Dirac-Fock (MCDF) approximation. Thereafter, the static potential is added to the suitable exchange, polarisation and absorption potentials to construct the spherically averaged complex optical potential. Using the obtained potential in the Dirac equations,these are solved with the partial wave phase shift analysis method and the differential cross sections are calculated. Results for different ions exhibit prominent interference structures in the energy versus cross section curves and show good agreement on comparison with the experimental results available in the selected energy ranges.