Electron scattering differential cross sections for C2H2, C2H4, and C2H6 by gas phase electron diffraction - binding effects

Experimental differential cross sections for 40 keV electrons scattered by C₂H₂, C₂H₄ and C₂H₆ molecules were measured using the gas electron diffraction method in the range of the scattering variable s from s = 1 A^?1 to s = 30 A^?1. The differential cross sections for neon were also measured and compared with calculated differential cross sections to calibrate the diffractograph. Experimental differential cross sections show significant deviations with respect to theoretical differential cross sections calculated from the Debye-Ehrenfest model, mainly in the range of small scattering angles. The observed differences are connected to chemical binding effects. From the experimental data, an estimation of the binding energy was carried out. The deduced values: ?0.58 ± 0.20 au for C₂H₂, ?0.94 ± 0.30 au for C₂H₄ and ?1.23 ± 0.40 au for C₂H₆ are in agreement with those obtained by thermochemical methods.     

Dissociation of hydrogen molecules in collisions with light alkali ions. II. Li+-H2

The dissociation of a ground state H₂ molecule in single collisions with a Li⁺ ion has been studied using a time of flight technique over a large range of center of mass scattering angles (30° ? υ ? 180°) and collision energies (16 eV < E_cm < 55.5 ev).The results have been transformed into the center of mass system to obtain inelastic differential cross sections (contour maps). In contrast to most other scattering experiments on collision induced dissociation, the results at high energies (E_cm > 40 eV) cannot be explained by a two-step mechanism. Instead dissociation appears to occur in a time comparable to the collision time. The results are consistent with several collision models. Of these the spectator model in which only one of the atoms of the molecule is struck by the incident ion is favored since it is in good agreement with the differential cross sections for backward scattering.     

Multiple collisions in molecular beam scattering experiments

Due to the forward peaked differential cross section for elastic atom—atom scattering the effect of multiple collisions has to be considered in the analysis of crossed beam measurements of the total cross section and especially of the small angle differential cross section at large values of the beam attenuation. At angles θ ≈ θ₀, with θ₀ the quantum mechanical scaling angle of the elastic differential cross section, the correction for the latter case amounts to 20% at beam attenuations I/I₀ = exp(?1). Firstly, a careful analysis of the probabilities for single and multiple scattering is given, resulting in an expression for the measured beam signals which is correct for all values of the beam attenuation. The probability for multiple scattering is then calculated for an inverse power potential V(r) = ?C_sr^?s, with s = 4 through s = 7, which include both the case of ion—atom scattering (s = 4) and atom—atom scattering (s = 6). The results are given as effective differential cross sections σ_n(θ) for n-fold scattering. They are described by a single, simple analytical function with four free parameters that have been determined for n = 2, 3 and 4 by a least squares method. The σ_n(θ) are normalised to the total cross section Q.     

Intramolecular multiple scattering in electron diffraction from fluoro-methyl halides

Relative elastic differential cross sections for scattering of 1 keV electrons from CF₃H, CF₄, CF₃Cl, CH₃F and CH₃Cl molecules were measured for momentum transfer from 3 Å^?1 to 29 Å^?1. The oscillatory residuals remaining after substraction of the atomic scattering and the molecular interference contributions calculated in the independent atom model are ascribed to the influence of intramolecular multiple scattering. The data reflect the dominant contributions of the CF₃-group and show larger oscillations than obtained from triple scattering calculations according to the method of Liu and Bonham using the second Born approximation.     

Electron scattering with H2S and PH3 molecules

Calculated total, differential and momentum transfer cross sections are reported for the vibrationally elastic scattering of electrons from H₂S and PH₃ molecules in the range of energy 0.1–50 eV. The scattering process is approximated by two incoherent scatterings caused, separately, by a central field and a long-range electric dipole interaction. The central field is calculated with a spherical approximate molecular wave function, in which the exchange interaction is treated in two ways: (i) exactly within the accuracy of the molecular wave function; (ii) approximately by a local model potential. The scattering by the central field is calculated with partial wave expansion technique, while the scattering by the electric dipole potential is calculated by using the first Born approximation for a rotating dipole model with experimental values of the dipole moments of H₂S and PH₃. The total cross sections are approximated by the incoherent sum of the cross section due to the central potential and the cross section of 00→10 rotational transition caused by the electric dipole potential. The effects of the polarization interaction are also tested. The contribution of small-angle scattering to the integral cross section is analyzed for these weakly polar molecules with some quantitative comparison.     

Rotational excitation in electron-molecule scattering at intermediate collision energy: A two-centre scattering model

A simple two-centre scattering model is discussed, which leads to compact closed form differential cross sections for rotationally inelastic scattering from diatomic molecules. The model elucidates in a simple way the rotational rainbow structure of the cross sections for both initially rotating and nonrotating molecules. Surprisingly good agreement with extensive computations and experimental measurements fore-Na₂ scattering at 150–300 eV is observed.     

Neutral scattering and vibrational excitation in K+Br2 Collisions

Differential cross sections are presented for neutral scattering of K atoms in collisions with Br₂ molecules in the energy range from 20 to 150 eV. In addition energy-loss spectra for the scattered K atoms are shown. The differential cross sections show a large peak near the forward direction. The energy-loss spectra point to considerable vibrational excitation at small angles. The results are attributed to reneutralization from an ion-pair state formed during the collision. In some cases this process can involve three potential surface crossings. The experimental results can be reproduced in simple trajectory calculations on diabatic potential surfaces. The calculations show that the forward scattering is rainbow scattering, caused by the internal motion of the Br₂^? molecular ion during the collision. There is no analog to this rainbow in atom-atom scattering. The internal moti is also responsible for the observed vibrational excitation.     

On the sudden approximation of cross: computational tests and factorization of cross sections and related scattering phenomena

A sudden approximation recently derived by Cross using a semiclassical treatment of the orbital motion is recast into a form which permits factorization of differential and integral degeneracy averaged cross sections, opacities as a function of final angular momentum quantum number, the scattering amplitude, and the phenomenological cross section which describes spectral line broadening. Calculations are done using an average of initial and final orbital angular momentum quantum numbers for the partial wave parameter for ArN₂, ArTIF, H⁺H₂ and Li⁺H₂. The results indicate that the method is a good approximation for integral cross sections and opacities when the energy sudden approximation is valid and when the coupling of the orbital motion is important.     

Classical differential cross sections and rotational energy transfer distributions for realistic ion—molecule potentials in the CPST limit

Classical differential cross sections, rotational energy transfer distributions at specified scattering angles and the first moments of the rotational energy transfer distributions are calculated for two ion—molecule systems: K⁺ ?CSCl and Li⁺ ?CO. The deflection angles and change in angular momentum are calculated using classical perturbation scattering theory (CPST). Monte Carlo techniques are then used to calculate the orientation averaged total differential cross sections and the rotational energy transfer distributions. Results are compared with experiment and agreement is found to be satisfactory. These two systems represent two extremes in anisotropy. For Li⁺ ?CO a strong classical rainbow peak is still seen in the differential cross section, while in the K⁺ ?CSCl system the rainbow is complete quenched. In the rotational energy transfer distributions of both systems, rotational rainbow peaks are clearly observed. The calculations also predict a leveling off of the first moment of the rotational energy transfer distribution at high angles, corresponding to the transition to repulsive scattering. On the basis of these results some comments are made on the nature of classical rainbow scattering for anisotropic systems.     

Rotational excitation in the Ar+N2 system.: A computational study of opacity functions and differential cross sections by the P-helicity decoupling approximation

Rotational excitation in the Ar+N₂ system is investigated using the P-helicity decoupling approximation. The accuracy of this approximation is demonstrated. Opacity functions, elastic and inelastic differential cross sections are computed. The results agree reasonably well with those available from molecular beams scattering experiments. The energy dependence and oscillatory structure of the differential cross sections is discussed. It is explained by an interference mechanism very similar in nature to that of elastic scattering. The relative role of the short- and long-range anisotropies, kinematics factors and type of transition in determining the shape of the inelastic differential cross sections is analyzed in some detail.     

State-selected ion-molecule reactions: H+2(ν) + He → HeH+ + H and He + H+ + H

Total cross sections for production of HeH⁺ and H⁺ in the reaction of state-selected H⁺₂ (v = 0 to 6) with He at 3.1 eV c.m. collision energy are measured by means of the threshold-photoelectron/photoion coincidence method, using pulsed synchrotron radiation. Both reaction cross sections are observed to rise with vibrational energy. The H⁺/HeH⁺ branching ratio, which is determined directly, remains approximately constant at about 0.3 for v ⩽ 3 and rises gradually for higher levels to reach the value 1.3 for v = 6. For v ⩽ 3 both reactions involve hard-type collisions and result in large-angle scattering. In contrast, at higher v levels, the HeH⁺ becomes essentially forward scattered with respect to the incident He direction, but with a velocity greater than that expected from the spectator stripping model. The H⁺ products are backward scattered with respect to the incident H⁺₂ for v ⩽ 1 and receed faster from the He atom than the H products. This observation directly leads to the conclusion that collision-induced dissociation from v = 0 and 1 involves transitions to the first excited potential-energy surface.     

Measurements of differential cross sections for vibrational quantum transitions in scattering of Li+ on H2

A pulsed monoenergetic ⁷Li⁺ ion beam (lab. energy 10–40 eV) is scattered from a highly collimated (= 1.5°) H₂ nozzle beam. The time-of-flight spectrum of the ions scattered in the forward laboratory direction shows both a fast peak corresponding to forward center-of-mass scattering and a slow peak corresponding to wide-angle center-of-mass scattering. These peaks have been further resolved to show contributions from individual vibrational quantum transitions. From an analysis of the time-of flight spectra the differential inelastic cross sections for a wide range of angles and energies between 2 eV <E_cm < 9 eV have been determined. The spectra also contain information on rotational inelastic cross sections.     

Investigation of the B2Σ and test of the A2II interaction potential for Na(32P)-Ar from high-resolution differential scattering measurements

We have measured differential cross sections for scattering of laser-excited Na(3²P_{$\text{3}\text{2}$}) by Ar(¹S₀) at thermal collision energies with high angular resolution (0.1°). In the investigated range of scattering angles (1°–15°) the cross sections contain contributions from scattering along the excited state B²Σ potential (rainbow scattering) and the A²II potential (supernumerary rainbows). By performing fit calculations in which the spectroscopically determined A²II potential was adopted we were able to obtain information about the B²Σ potential. With the assumption of a Lennard-Jones (12.6) potential shape we obtain a well depth ?^BΣ = (0.14±0.02)×10^?3 au and an equilibrium distance r_m^BΣ = 10.4±1.0 au. This work presents the first experimental determination of the B²Σ potential well parameters.     

Differential cross sections for fine-structure inelastic collisions of K(42P) with Ar,Kr and N2

We report measurements of differential cross sections for fine-structure inelastic collisions of potassium (4²P_3/2-4²P_1/2 with Ar, Kr and N₂. The experiment uses crossed molecular beams and a method to detect scattering angles by the analysis of Doppler shifts in laser induced fluorescence. The experimental results for KAr are compared with calculations.     

Total scattering cross sections for ethylene by electron impact for incident electron energies from 1 to 2000 eV

We report total scattering cross sections for C₂H₄ molecule by electron impact. Calculations are performed by using two different quantum mechanical methods and they cover the energy range from 1 to 2000 eV. For low energy calculations up to 15 eV, UK molecular R‐matrix code through QUANTEMOL‐N software is used, while intermediate to high energy (15–2000 eV) calculations were carried out by applying spherical complex optical potential formalism. Comparison is made with earlier measurements and theoretical data wherever available. A shape resonance is detected around 2 eV due to the ²B_2g symmetry of an electronic state that corresponds to the temporary negative ion formation of ethylene. The differential cross sections are also calculated for the energy range from 1 to15 eV for the scattering angles between 0º and 180º. © 2013 Wiley Periodicals, Inc.     

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.     

Quasi-classical Trajectory Study of the Intramolecular Isotope Effect in the Reaction O（3p）＋H2/HD

Theoretical studies of the dynamics of the reactions O（3p）＋H2/HD（ν=0, j=0）→OH＋H have been performed with quasi-classical trajectory method （QCT） on an ab initio potential surface for the lowest triplet electronic state of H2O（aA＂）. The QCT-calculated integral cross sections are in good agreement with the earlier time-dependent quantum mechanics results. The state-resolved rotational distributions reveal that the product OH rotational distributions for O＋HD have a preference for populating highly internally excited states compared with the O＋H2 reaction. Distributions of differential cross sections show that directions of scattering are strongly dependent on the choice of quantum state. The polarization dependent generalized differential cross-sections and the distributions were calculated and a pronounced isotopic effect is revealed. The calculated results indicate that the product polarization is very sensitive to the mass factor.     

The influence of the rate of bond stretching on the differential cross sections for ion-pair formation in K + XY collisions

Experimental differential cross sections are presented for ion-pair formation in collisions between K and I₂, IBr, Br₂, ICl, Cl₂. In this sequence the vibrational frequency of the halogen molecule is increased gradually from one system to the next. Therefore this is a suitable set of cros sections for analysing the influence of the rate at which the halogen bond stretches after transition to the ionic state. The experimental data are compared with trajectory calculations on diabatic and on adiabatic potential energy surfaces. The results of the two types of calculations differ significantly; the adiabatic model gives the better agreement with experiment. The essential difference between the two models is that in the diabatic model stretching of the halogen bond starts only when the crossing seam R_c between the ionic and covalent configurations is reached, while in adiabatic scattering, pre-stretching of the halogen bond occurs as the alkali atom approaches the crossing seam. As a result of pre-stretching the electron affinity is increased, which in turn affects the endoergicity and the total and differential cross sections for ion-pair formation. At energie below the threshold for ion-pair formation, the cross section for reactive scattering is also affected.     

The N2Ar potential energy surface

The potential energy surface for the N₂Ar system has been obtained assuming a spherical average interaction previously reported from this laboratory. The angular dependence has been assessed by a combined analysis of the integral and differential scattering cross sections and sonic spectroscope data. The potential energy surface is given via a parametric model. A similar potential energy surface for O₂Ar has been obtained with the same procedure. This surface is an improvement of an earlier one, because it reproduces the differential total cross sections recently measured.