Absolute Elastic Differential Cross Sections Research Articles

Time-of-flight electron scattering from molecular hydrogen: Benchmark cross sections for excitation of the X1Σg+→b3Σu+ transition

The electron impact $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition in molecular hydrogen is one of the most important dissociation pathways to forming atomic hydrogen atoms, and is of great importance in modeling astrophysical and industrial plasmas where molecular hydrogen is a substantial constituent. Recently, it has been found that the convergent close-coupling (CCC) cross sections of Zammit et al. [Phys. Rev. A 95, 022708 (2017)] are up to a factor of 2 smaller than the currently recommended data. We have determined normalized differential cross sections for excitation of this transition from our experimental ratios of the inelastic to elastic scattering of electrons by molecular hydrogen using a transmission-free time-of-flight electron spectrometer, and find excellent agreement with the CCC calculations. Since there is already excellent agreement for the absolute elastic differential cross sections, we establish benchmark differential and integrated cross sections for the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition, with theory and experiment being essentially in complete agreement.

Absolute cross section measurements for the scattering of low- and intermediate-energy electrons from PF3. I. Elastic scattering.

We report absolute elastic differential cross sections (DCSs) for electron collisions with phosphorus trifluoride, PF3, molecules (e- + PF3) in the impact energy range of 2.0-200 eV and over a scattering angle range of 10°-150°. Measured angular distributions of scattered electron intensities were normalized by reference to the elastic DCSs of He. Corresponding integral and momentum-transfer cross sections were derived by extrapolating the angular range from 0° to 180° with the help of a modified phase-shift analysis. In addition, due to the large dipole moment of the considered molecule, the dipole-Born correction for the forward scattering angles has also been applied. As a part of this study, independent atom model calculations in combination with screening corrected additivity rule were also performed for elastic and inelastic (electronic excitation plus ionization) scattering using a complex optical potential method. Rotational excitation cross sections have been estimated with a dipole-Born approximation procedure. Vibrational excitations are not considered in this calculation. Theoretical data, at the differential and integral levels, were found to reasonably agree with the present experimental results. Furthermore, we explore the systematics of the elastic DCSs for the four-atomic trifluoride molecules of XF3 (X = B, N, and P) and central P-atom in PF3, showing that, owing to the comparatively small effect of the F-atoms, the present angular distributions of elastic DCSs are essentially dominated by the characteristic of the central P-atom at lower impact energies. Finally, these quantitative results for e- - PF3 collisions were compiled together with the previous data available in the literature in order to obtain a cross section dataset for modeling purposes. To comprehensively describe such a considerable amount of data, we proceed by first discussing, in this paper, the vibrationally elastic scattering processes whereas vibrational and electronic excitation shall be the subject of our following paper devoted to inelastic collisions.

Absolute elastic differential cross sections for PF3 molecule by electron impact: A comparative study with XF3 (X = B, C, N and CH) molecules

SynopsisWe report absolute electron elastic scattering differential cross sections (DCSs) from PF3 molecules. The crossed-beam method was used in conjunction with the relative flow technique (using helium as the reference gas) to obtain absolute values. Very good agreement between the experimental DCSs and those calculated with the IAM-SCAR method has been found for the higher impact energy (above 50 eV). We have also compared the measured DCSs for PF3 with experimental results for other fluorine compounds, XF3 (X = B, C, N and CH), as well as with those derived from the calculated atomic fluorine cross sections multiplied by a factor of 3.

Elastic differential cross sections for C₄F₆ isomers in the 1.5-200 eV energy electron impact: similarities with six fluorine containing molecules and evidence of F-atom like scattering.

We report absolute elastic differential cross sections for electron interactions with the C4F6 isomers, hexafluoro-1,3-butadiene (1,3-C4F6), hexafluoro-2-butyne (2-C4F6), and hexafluorocyclobutene (c-C4F6). The incident electron energy range is 1.5-200 eV, and the scattered electron angular range for the differential measurements varies from 15° to 150°. In all cases the absolute scale of the differential cross section was set using the relative flow technique, with helium as the reference species. Atomic-like behaviour in these scattering systems is shown here for the first time, and is further investigated by comparing the elastic cross sections for the C4F6 isomers with other fluorinated molecules, such as SF6 and CnF6 (n = 2, 3, and 6). We note that for all the six-F containing molecules, the scattering process for electron energies above 30 eV is indistinguishable. Finally, we report results for calculations of elastic differential cross sections for electron scattering from each of these isomers, within an optical potential method and assuming a screened corrected independent atom representation. The level of agreement between these calculations and our measurements is found to be quite remarkable in all cases.

Electron scattering from trans 1,3-butadiene molecule: cross-sections, oscillator strength and VUV photoabsorption cross-sections

Electron energy-loss spectra for the butadiene molecule were measured in the scattering angular range of 2.0° to 8.0°, in an energy-loss range from 2 to 50 eV, using 1000 eV incident electrons. The absolute generalized oscillator strength (GOS) and inelastic cross section have been determined for the \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 11B u transition. The absolute elastic differential cross section was also determined spanning an angular range from 2.0° to 40.0°. From a small angle electron energy-loss spectrum, the optical oscillator distribution (photoabsorption spectrum) for the butadiene molecule was obtained in the 2 to 100 eV photon energy range. Accurate ab initio calculations have been performed, within the First Born Approximation, for generalized oscillator strength (GOS) and excitation energies for the \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 11B u and \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 21A g transitions. Our results emphasize the importance of using highly correlated wavefunctions and accurate methodologies in the calculation of the GOS for electron impact-induced electronic transitions in molecules.

Absolute cross sections for elastic electron scattering from methylformamide

Elastic electron scattering from gaseous methylformamide ($N$-methylformamide, C${}_{2}$H${}_{5}$NO) has been investigated. Absolute elastic differential cross sections (DCSs) were determined both experimentally and theoretically for the incident energies from 50 to 300 eV. The measurements were performed using a cross-beam technique, for scattering angles from 20\ifmmode^\circ\else\textdegree\fi{} to 110\ifmmode^\circ\else\textdegree\fi{}. Relative elastic DCSs were measured as a function of both the angle and the incident energy and the absolute DCSs were determined using the relative flow method. The calculations of electron interaction cross sections are based on a corrected form of the independent-atom method, known as the SCAR (screen corrected additivity rule) procedure and using an improved quasifree absorption model. Calculated integral cross sections have been presented, as well, both for methylformamide and formamide, in the energy range 10--1000 eV, and discussed. The results are compared with and discussed regarding existing data for other small molecules representing building blocks of large biomolecules.

Differential elastic electron scattering cross sections for CCl4 by 1.5–100 eV energy electron impact

We report absolute elastic differential, integral and momentum transfer cross sections for electron interactions with CCl(4). The incident electron energy range is 1.5-100 eV, and the scattered electron angular range for the differential measurements varies from 15°-130°. The absolute scale of the differential cross section was set using the relative flow technique with helium as the reference species. Comparison with previous total cross sections shows good agreement. Atomic-like behaviour in this scattering system is shown here for the first time, and is further investigated by comparing the CCl(4) elastic cross sections to recent results on the halomethanes and atomic chlorine at higher impact energies [H. Kato, T. Asahina, H. Masui, M. Hoshino, H. Tanaka, H. Cho, O. Ingólfsson, F. Blanco, G. Garcia, S. J. Buckman, and M. J. Brunger, J. Chem. Phys. 132, 074309 (2010)].

Influence of sulphur atom on the qualitative behavior of electron impact total cross sections of some sulphur containing molecules

Absolute elastic differential cross sections (DCS) have been measured experimentally for several sulphur containing molecules such as SF6, CS2, DMS and DMSO using a novel high resolution electron spectrometer. The measured DCS’s were extrapolated in the forward and backward angles using a tenth order legendre polynomial based least squares fitting technique. Total cross sections (TCS) were determined by integrating the DCS over all angles for each incident energy. The influence of the sulphur atom on the molecular TCS is studied by comparing the qualitative behavior of electron impact cross sections for the sulphur containing molecules against the TCS of the sulphur atom at each incident energy. Theoretical calculations based on independent atom model are also presented as a guide to understand the nature of the electron-molecule collision processes measured in this study.

Elastic electron scattering from formamide molecule

Elastic electron scattering from gaseous formamide (H2NCHO) has been investigated. Absolute elastic differential cross sections (DCSs) were determined both experimentally and theoretically. The measurements were performed using a cross beam technique, for the incident energies of 100, 150 and 300eV and scattering angles from 20° to 110°. Relative elastic DCSs were measured as a function of the angle and the absolute DCSs were determined using the relative flow method. The calculations of electron interaction cross sections are based on a corrected form of the independent-atom method, known as the SCAR (screen corrected additivity rule) procedure and using an improved quasifree absorption model. Calculated results agree very well with the experiment.

Substitution effects in elastic electron collisions with CH3X (X=F, Cl, Br, I) molecules

We report absolute elastic differential, integral, and momentum transfer cross sections for electron interactions with the series of molecules CH(3)X (X=F, Cl, Br, I). The incident electron energy range is 50-200 eV, while the scattered electron angular range for the differential measurements is 15 degrees-150 degrees. In all cases the absolute scale of the differential cross sections was set using the relative flow method with helium as the reference species. Substitution effects on these cross sections, as we progress along the halomethane series CH(3)F, CH(3)Cl, CH(3)Br, and CH(3)I, are investigated as a part of this study. In addition, atomic-like behavior in these scattering systems is also considered by comparing these halomethane elastic cross sections to results from other workers for the corresponding noble gases Ne, Ar, Kr, and Xe, respectively. Finally we report results for calculations of elastic differential and integral cross sections for electrons scattering from each of the CH(3)X species, within an optical potential method and assuming a screened corrected independent atom representation. The level of agreement between these calculations and our measurements was found to be quite remarkable in each case.

Vacuum ultraviolet electron impact excitation of the styrene molecule: cross sections and oscillator strengths

The vacuum ultraviolet electronic excitation of the styrene molecule has been studied in the 0–50 eV energy range, using angle-resolved electron-energy-loss spectroscopy at an incident energy of 1 keV. Intense new features have been observed at 10.3, 11.8, 13.7 and 17.1 eV. They were tentatively assigned to high-energy transitions originating from σ electrons or to double excitations involving π electrons. The absolute generalized oscillator strengths and absolute inelastic differential cross sections have been determined for the band centred at 5.3 eV, associated with the 2,3 1A′←1 1A′ transitions. The absolute elastic differential cross section has also been determined over an angular range of 2.5°–22.0°. The valence photoabsorption spectrum of styrene, derived from the electron-energy-loss spectrum, is compared to a previously measured benzene spectrum in the 3–45 eV energy range.

An apparatus for measuring absolute electron scattering cross sections for molecular radicals

Electron collision cross sections for highly reactive CFx (x = 1–3) radicals are required to model technological plasmas. In spite of their importance to industry, experimental studies of electron interactions with CFx radicals are rarely reported in the literature. A new apparatus for measuring absolute elastic differential cross sections for molecular radicals is reported and a sample absolute cross section for the CF2 radical is presented to demonstrate the application of this experiment.

Cross sections for elastic and inelastic electron scattering from carbon disulfide

Electron energy-loss spectra, measured as a function of the scattering angle, have been obtained for a carbon disulfide molecule, CS2, in the excitation energy range from 0 to 45 eV. The incident electron energy was 1000 eV. The absolute generalized oscillator strength (GOS) and absolute inelastic differential cross section have been determined as a function of the square of the momentum transfer (K2) for the intense allowed transition 1Σ+u ← 1Σ+g, centred at 6.3 eV. The absolute elastic differential cross section was also determined spanning an angular range from 1.5° to 10°. It is well known that at high incident energies and small scattering angles electrons behave like pseudo photons. The CS2 photoabsorption spectrum was consequently obtained by extrapolation from the measured small angle electron energy-loss spectrum. The result shows a good resemblance to the atmospheric spectrum of Jupiter, following comet impact.

Absolute differential cross sections for elastic and inelastic electron scattering from benzene with 1 kev impact energy

The absolute generalized oscillator strength and absolute inelastic differential cross section have been determined, as a function of the momentum transfer, for the 1E1u + 1B1u ← 1Ag transition in the benzene molecule. A previously described electron energy-loss spectrometer, featuring a Wien-filter velocity analyser, has been used. Employing 1000 eV incident electron energy and 1.0 eV energy resolution, absolute oscillator strength distribution as a function of electron energy loss was obtained in the 2–8° scattering angle range. The absolute elastic differential cross section was also determined spanning an angular range of 2°–14°. The photoabsorption spectrum converted from the electron energy-loss spectrum was compared with the interstellar extinction curve where we confirm the proportionality between the cross section and extinction.

Absolute differential cross sections for elastic and inelastic electronscattering from N2O with 1 keV impact energy

Angle-resolved electron energy-loss spectra for the nitrous oxide (N2O) molecule have been measured at an impact energy of 1 keV. Thespectra cover an excitation energy range from 0 to 50 eV and an angularrange from 1.5° to 10.0°. The absolute inelasticdifferential cross section and the generalized oscillator strength (GOS)for the D 1Σ+←X 1Σ+ transition (9.6 eV) were determined in the 0.05-2.22 au K2range. The absolute elastic differential cross section was also determinedspanning an angular range from 1.5° to 15.5°.

Elastic cross sections fore−−CH4collisions at intermediate energies

A joint theoretical and experimental investigation on ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{CH}}_{4}$ elastic scattering in the intermediate energy range is reported. More specifically, calculated cross sections in the (1--500)-eV incident energy range, as well as measured absolute cross sections from 100 to 500 eV, are presented. A complex optical potential consisting of static, exchange, correlation-polarization, plus absorption contributions is used to describe the electron-molecule interaction. The Schwinger variational iterative method combined with the distorted-wave approximation is applied to calculate the scattering amplitudes. The experimental absolute elastic differential cross sections are determined using the relative flow technique. In general, our calculated results are in very good agreement with our experimental data and with other experimental and theoretical results available in the literature. Our study has shown the significant role played by the absorption effects on the calculated cross sections for incident energies of 50 eV and above. The importance of the nonspherical components of the ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{CH}}_{4}$ interaction potential has also been verified in our calculations.

Elastic and total cross sections for electron-carbon dioxide collisions in the intermediate energy range

In this work, we report on a joint theoretical and experimental investigation on electron-CO2 collisions in the intermediate energy range. More specifically, the elastic differential, integral and momentum transfer cross sections as well as the grand total (elastic+inelastic) cross sections in the 30-500 eV energy range are calculated and reported. A complex optical potential consisting of static, exchange, correlation-polarization plus absorption contributions is used for the description of the electron-molecule interaction. The Schwinger variational iterative method combined with the distorted-wave approximation is applied to calculate the scattering amplitudes. In addition, experimental absolute elastic differential cross sections generated using the relative flow technique are reported in the 100-400 eV range. Comparison between the calculated results and present measured data and also existing experimental and theoretical results is encouraging.

Valence-shell angle-resolved electron energy loss spectra of SF6

Electron-energy-loss spectra of the SF6 molecule have been measured in the valence-shell region (0 - 100 eV) covering an angular range of 1.0° - 15.0°. The spectra have been measured at an impact energy of 1.0 keV. The angular dependence of the spectra showed the presence of three forbidden transitions in the region below 40 eV. Above 40 eV interesting features appear at higher scattering angles, which can be associated to nondipole many-body processes. A new feature was observed at 76 eV. The absolute elastic differential cross section has been obtained through normalization of the relative data to the experimental values found in the literature. The absolute inelastic differential cross sections for the 11.5 eV and 13.2 eV transitions have been determined. The generalized oscillator strength (GOS) for the 11.5 eV peak has been also determined in the 0.05 to 1.3 a.u. K² range. The experimentally determined value for the optical oscillator strength(0.312) for the 11.5 eV peak obtained through extrapolation of the GOS curve showed good agreement with the data found in the literature.

Elastic collisions of low- to intermediate-energy electrons from carbon dioxide: Experimental and theoretical differential cross sections

Absolute elastic differential cross sections for electron collision with carbon dioxide $({\mathrm{CO}}_{2})$ at impact energies from 1.5 to 100 eV and scattering angles from 15\ifmmode^\circ\else\textdegree\fi{} to 130\ifmmode^\circ\else\textdegree\fi{} have been measured. Also, a calculation has been made that uses two different types of close-coupling approaches and covers all scattering angles in the same energy region. The measurements are in excellent agreement with observations by other authors. They also agree with the present calculation for all energies above 10 eV. The agreement becomes less satisfactory as the energy decreases below 8 eV, particularly at scattering angles below 60\ifmmode^\circ\else\textdegree\fi{}, where the measurements show a conspicuous shoulder around this angle in the energy between 5 and 7 eV. Integral and momentum-transfer cross sections have been estimated from extrapolations to 0\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{}. Extensive comparisons with recent other theories are included.

Excitation of the methyl methacrylate molecule in the VUV range by angle-resolved EELS

Angle-resolved electron energy loss spectra for the methyl methacrylate molecule have been measured at an impact energy of 1 keV. The spectra cover an excitation energy range of 0 to 100 eV and an angular range of 2° to 10°. Within our knowledge, this is the first gas-phase excitation spectrum for MMA in this energy range. At small angles the spectra are dominated by an intense peak at 6.7 eV followed by a broad band centered at about 16 eV. As the scattering angle increases, the intensity maximum in the spectra shifts towards higher energies. The generalized oscillator strength (GOS) for the 6.7 eV peak has been determined in the 0.090 to 1.093 au K 2 range. The absolute elastic differential cross section has also been obtained through normalization of the relative data to the theoretical value, determined by using the independent atom model (IAM) approximation. CI-level theoretical calculations have been also performed in order to assign the low-lying energy states. The experimentally determined value for the optical oscillator strength (0.18) for the 6.7 eV peak showed a good agreement with the theoretical result.