Elastic Integral Cross Sections Research Articles

Electron-impact study of the PH radical using theR-matrix method

The PH radical is an interesting case to study because of its ${\ensuremath{\pi}}^{2}$ electronic configuration, which leads to the three low-lying electronic states, $X$ ${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$, $a$ ${}^{1}\ensuremath{\Delta}$, and $b$ ${}^{1}{\ensuremath{\Sigma}}^{+}$. The singlet states possess long lifetimes, because direct combination with the ground state is not allowed. This is similar to the ${\mathrm{O}}_{2}$ case. The $\mathit{R}$-matrix method is employed to calculate elastic differential and integral cross sections, momentum-transfer cross sections, and inelastic cross sections. The energy range is 0--10 eV. The Hartree-Fock ground-state configuration of PH is $1{\ensuremath{\sigma}}^{2}2{\ensuremath{\sigma}}^{2}3{\ensuremath{\sigma}}^{2}1{\ensuremath{\pi}}^{4}4{\ensuremath{\sigma}}^{2}5{\ensuremath{\sigma}}^{2}2{\ensuremath{\pi}}^{2}$. We have included thirty-seven target states in the trial wave function of the scattering system in our best model. Each target state is represented by a configuration interaction (CI) wave function. In our CI model, we freeze ten electrons in orbitals $1\ensuremath{\sigma}$, $2\ensuremath{\sigma}$, $3\ensuremath{\sigma},$ and $1\ensuremath{\pi}$; the remaining six electrons are free to move among the seven orbitals $4\ensuremath{\sigma}$, $5\ensuremath{\sigma}$, $6\ensuremath{\sigma}$, $7\ensuremath{\sigma}$, $8\ensuremath{\sigma}$, $2\ensuremath{\pi},$ and $3\ensuremath{\pi}$. Our CI model yields a dipole moment of 0.67 D at the equilibrium PH bond length, ${R}_{e}$, of 2.687 ${a}_{0}$; this dipole moment compares favorably with the experimental value 0.70 D. We have carried our scattering calculations in one state with the CI wave function and thirty-seven-state model. We have detected a stable anionic bound state ${}^{2}{B}_{1}$ of PH at various bond lengths of PH molecule. The vertical electron affinity value is 0.97 eV, which is in excellent agreement with experimental value of 1.00 eV. We have included up to $g$ partial waves in the scattering calculations. The contribution of higher partial waves is accounted for by using a Born-closure procedure.

Elastic electron scattering fromCF3I

Experimental results are reported for elastic differential and integral cross sections for electrons scattering from ${\mathrm{CF}}_{3}$I. These measurements were made at ten incident electron energies in the range 10--50 eV, with a scattered electron angular range of ${20}^{\ifmmode^\circ\else\textdegree\fi{}}$--${135}^{\ifmmode^\circ\else\textdegree\fi{}}$. Where possible, comparison is made to the only other comprehensive experimental set of results available in the literature [M. Kitajima et al., J. Phys. B 35, 3257 (2002)] and to calculated cross sections from the Schwinger multichannel with pseudopotentials method [M. H. Bettega et al., J. Phys. B 36, 1263 (2003)]. In general, quite good agreement is found between the present results and those of the earlier studies.

Cross sections for electron scattering by carbon disulfide in the low- and intermediate-energy range

In this work, we report a theoretical study on e{sup -}-CS{sub 2} collisions in the low- and intermediate-energy ranges. Elastic differential, integral, and momentum-transfer cross sections, as well as grand total (elastic + inelastic) and absorption cross sections, are reported in the 1-1000 eV range. A recently proposed complex optical potential composed of static, exchange, and 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 comparison between our calculated results and the existing experimental and/or theoretical results is encouraging.

Potential elastic electron scattering by atoms in the spin-polarized approach

A model based on the local spin density approximation has been suggested to describe elastic potential electron scattering by atoms with half-filled subshells. This model is applied to the case of electron scattering by such atoms having one s1-, p3-, d5- or f7-subshell (i.e. Ag, Sb, Mn and Eu). The angular dependences of asymmetry functions and differential cross sections (DCSs) both with and without taking into account absorption effects, integral elastic, absorption, diffusion and viscosity cross sections have been calculated at the 10 eV collision energy. Similar characteristics have been calculated for the Mn atom at the 20 eV energy. DCSs are calculated both in the local (spin-unpolarized) and local spin density (spin-polarized) approximations and compared with each other. Some cross sections for Ag, Mn, Eu atoms are compared with available experimental and theoretical data.

Elastic electron scattering in krypton in the energy range from 5 to 10 eV

Differential cross sections for elastic electron scattering in krypton have been measured at the energies of $5,7.5$, and $10$ eV over the scattering angle range from ${30}^{\ifmmode^\circ\else\textdegree\fi{}}$ to ${180}^{\ifmmode^\circ\else\textdegree\fi{}}$. The measurements for backward scattering employed the magnetic angle-changing technique. These differential cross sections have been integrated to yield the elastic integral and momentum transfer cross sections at the above energies. These new results are compared with the most recent measurements and calculations of the respective cross sections in krypton. The dependence of the differential cross sections on atomic polarizability of the heavier rare gas atoms argon, krypton, and xenon has also been investigated over the electron energy range $5--30$ eV and for forward, backward, and intermediate scattering angles.

Low energy electron scattering from polyatomic targets

Low energy elastic electron scattering cross-sections from water and several alcohols are presented. This paper addresses accurately measuring quantitative differential elastic scattering cross-sections, using the relative flow method with an aperture source, and focuses on the long range dipole interaction of the scattering electron with these polar targets. The electron-dipole interaction dominates the scattering for these molecules and contributes significantly to their integral elastic cross-sections.

Cross sections for electron collisions with dimethyl ether (CH3OCH3)

We present an experimental study for elastic electron-dimethyl ether scattering. Relative flow technique is used to determine the absolute cross sections. Elastic differential and integral cross sections measured in the 100–1000 eV are reported.

Absolute elastic differential and integral cross sections for the CF2 radical for electron impact energies below 20 eV

This presentation details the first measured elastic differential cross sections (DCS) and integral cross sections (ICS) for electron scattering from the CF2 radical below 20eV, along with calculations using the Schwinger multichannel (SMC) method. Where possible comparison is also made to results from earlier calculations. Preliminary work towards measuring the CF2 elastic DCS is also presented.

Exact inclusion of exchange in calculations of cross sections for vibrational excitation of N2 by low-energy electrons

Elastic and inelastic differential and integral cross sections for low-energy vibrational excitation of N2 by electron impact are calculated by solving vibrationally coupled scattering equations. Unlike previous calculations of this type, which used model-exchange potentials, the present formulation incorporates exchange effects rigorously. The resulting coupled integrodifferential equations are solved using a combination of linear-algebraic and R-matrix-propagator techniques. Theoretical differential cross sections for both resonant and non-resonant scattering are compared to recent absolute measurements by Allan (2005 J. Phys. B: At. Mol. Opt. Phys. 38 3655), with special attention given to the region of the 2Πg shape resonance near 2.4 eV and to disagreements between theory and experiment at non-resonant energies above this region.

Absolute elastic differential cross sections for electron scattering byC6H5CH3andC6H5CF3at 1.5–200 eV: A comparative experimental and theoretical study withC6H6

We present absolute differential cross sections (DCS) for elastic scattering from two benzene derivatives ${\text{C}}_{6}{\text{H}}_{5}{\text{CH}}_{3}$ and ${\text{C}}_{6}{\text{H}}_{5}{\text{CF}}_{3}$. The crossed-beam method was used in conjunction with the relative flow technique using helium as the reference gas to obtain absolute values. Measurements were carried out for scattering angles $15\ifmmode^\circ\else\textdegree\fi{}--130\ifmmode^\circ\else\textdegree\fi{}$ and impact energies 1.5--200 eV. DCS results for these two molecules were compared to those of ${\text{C}}_{6}{\text{H}}_{6}$ from our previous study. We found that (1) these three molecules have DCS with very similar magnitudes and shapes over the energy range 1.5--200 eV, although DCS for ${\text{C}}_{6}{\text{H}}_{5}{\text{CF}}_{3}$ increase steeply toward lower scattering angles due to the dipole moment induced long-range interaction at 1.5 and 4.5 eV, and (2) that the molecular structure of the benzene ring significantly determines the collision dynamics. From the measured DCS, elastic integral cross sections have been calculated. Furthermore, by employing a corrected form of the independent-atom method known as the screen corrected additive rule, DCS calculations have been carried out without any empirical parameter fittings, i.e., in an ab initio nature. Results show that the calculated DCS are in excellent agreement with the experimental values at 50, 100, and 200 eV.

Scattering of low-energy electrons byC2H4O

We report elastic integral, differential, and momentum transfer cross sections for collisions of low-energy electrons with ethylene oxide $({\text{C}}_{2}{\text{H}}_{4}\text{O})$. We employed the Schwinger multichannel method with pseudopotentials in the static-exchange and static-exchange-polarization approximations, for energies from 0.7 to 20 eV. Experimental studies on vibrational excitation of ${\text{C}}_{2}{\text{H}}_{4}\text{O}$ by electron impact reported two shape resonances at around 2.6 and 4.8 eV, while another experimental study on total cross sections reported shape resonances at around 2.7 and 4.6 eV. Our integral cross section shows a peak at around 5 eV which is a shape resonance belonging to the ${B}_{2}$ symmetry. We have not found another low-energy shape resonance in our calculations.

Electron scattering by trimethylene oxide, c-(CH2)3O, molecules

Electron-scattering cross sections have been determined for trimethylene oxide, cyclic (CH(2))(3)O molecule, both experimentally and theoretically. The absolute total cross section (TCS) has been measured over energies from 1 to 400 eV using a linear electron-transmission method. The obtained TCS generally decreases with rising energy, except for the 3-10 eV range, where some resonantlike structures are discernible. Integral elastic cross section (ECS) and ionization cross section (ICS) have been also calculated up to 3 keV in the additivity rule approximation and the binary-encounter-Bethe approach, respectively. Their sum, ECS+ICS, is in a good agreement with the measured TCS. Comparison of the TCS energy dependence for trimethylene oxide with that for its isomeric open-chain counterpart--acetone, (CH(3))(2)CO, has also been made. Moreover, examination of experimental TCSs for the cyclic (CH(2))(n)O, n=2-4, ether series reveals that the intermediate-energy molecular TCSs for members of that family can be nicely represented as a sum of the effective TCSs for particular constituents of the molecule, i.e., methylene groups and oxygen atom. Finally, based on these partial TCSs, the TCS for the c-(CH(2))(5)O--the next member of the series--has been determined and compared with the respective ECS+ICS values computed here for this compound.

Elastic and related transport cross sections for singly charged ion–atom scattering of light metals (Li, Be, B) and hydrogen

Elastic differential and integral cross sections are calculated using a fully quantum-mechanical treatment and new, highly accurate potential curves, for collisions of light metal atoms (Li, Be, B) or their singly charged ions with hydrogen ions or atoms and their isotopes, over the six-decade range of centre-of-mass collision energy 0.0001–100 eV. In addition, the momentum transfer and viscosity cross sections, relevant to transport modelling, have been computed along with results of the classical trajectory Monte Carlo (CTMC) method in an extended energy range (0.01–10000 eV). The CTMC results, though less accurate, also include the inelastic processes of charge transfer, excitation and ionization, enabling improved assessment of the accuracy achieved through comparison of the results of the cross sections obtained with two methods in the overlapping energy range. We also study a fully neutral system, Li + H, using both methods. All of the data calculated here are explicitly tabulated on the World Wide Web for convenient use in plasma modelling and we find a mass-dependent scaling of the cross sections for the hydrogen isotopes.

Modified effective-range theory for low energy ${\sf e}$ -N2 scattering

We analyze the low-energy e-N2 collisions within the framework of the modified-effective range theory (MERT) for the long-range potentials, developed by O’Malley et al. [J. Math. Phys. 2, 491 (1961)]. In comparison to the traditional MERT we do not expand the total cross-section in the series of the incident momentum ħk, but instead we apply the exact analytical solutions of the Schrodinger equation for the long-range polarization potential, as proposed in the original formulation of O’Malley et al. This extends the applicability of MERT up to few eV regime, as we confirm using some simplified model potential of the electron-molecule interaction. The parameters of the effective-range expansion (i.e. the scattering length and the effective range) are determined from experimental, integral elastic cross-sections in the 0.1–1.0 eV energy range by fitting procedure. Surprisingly, our treatment predicts a shape resonance that appears slightly higher than experimentally well known resonance in the total cross-section. Agreement with the experimentally observed shape-resonance can be improved by assuming the position of the resonance in a given partial wave. Influence of the quadrupole potential on resonances is also discussed: we show that it can be disregarded for N2. In conclusion, the modified-effective range formalism treating the long-range part of the potential in an exact way, reproduces well both the very low-energy behavior of the integral cross-section as well as the presence of resonances in the few eV range.

Elastic scattering of electrons from alanine

Differential cross sections (DCSs) for elastic scattering of electrons from alanine, have been measured using a crossed beam system for incident energies between 20 and 80eV and scattering angles from 10° to 150°. The experimental data were placed upon an absolute scale by normalisation to calculated absolute integral cross sections obtained using the corrected independent-atom method incorporating an improved quasifree absorption model. The calculated data-set includes DCSs and integral elastic and inelastic cross sections in the incident energy range between 1 and 10,000eV. These theoretical results are found to agree very well with the experimental data both in the shape and magnitude of DCSs except at the smallest scattering angles.

Interaction of slow electrons with methyl phosphate esters

We report computed cross sections for low-energy elastic collisions of electrons with the methyl esters of phosphoric acid, monomethyl, dimethyl, and trimethyl phosphate, and with phosphoric acid itself. For phosporic acid and monomethyl phosphate, polarization effects are included in the calculation, while the two larger molecules are treated in the static-exchange approximation, that is, with polarization neglected. The integral elastic cross sections exhibit broad shape resonances above 5eV that give rise to strong variations in the differential cross section with energy. However, no shape resonances are evident below 5eV. We compare our results to previous calculations and measurements and discuss their relevance to electron-induced damage to the DNA backbone.

Electron collisions with ethylene oxide molecules

The absolute total cross section (TCS) for electron–ethylene oxide (c-C2H4O) collisions was measured at electron-impact energies extending from 0.7 to 400 eV using the linear electron-transmission technique. In the present TCS energy function a distinct peak is visible near 4.6 eV which may be attributed to formation of a short-lived negative ion. Moreover, at intermediate and high energies the integral elastic (ECS) and ionization (ICS) cross sections were determined numerically. The calculated sum, ECS + ICS, is in good agreement with the experimental TCS in the overlapping energy range. Finally, the present experimental TCS for electron scattering from c-C2H4O is compared with that for its cyclic isoelectronic counterpart c-C3H6, and similarities and differences are pointed out and discussed.

Theoretical calculation of the scattering cross section for He-HF(DF,TF) collision system

For the first time, the interaction potentials of the He-HF(DF,TF) van der Waals complexes have been obtained by center of mass transformation and then employing Murrell-Sorbie potential function to fit the accurate interaction energy data, which have been computed at symmetry-adapted perturbation theory (SAPT) level. On the basis of the above results, the close coupling calculation of scattering cross sections for collision of He with HF(DF,TF) is performed by employing the fitted interaction potential. This calculation is performed at the incident energies of 50, 59.5, 86, 100 and 120 meV, respectively. The information of the elastic, inelastic and total integral cross sections were obtained, and the change tendency and characteristics of scattering cross section are discussed for He-HF(DF,TF)collision system.

Correlation–polarization effects in electron/positron scattering from acetylene: A comparison of computational models

Different computational methods are employed to evaluate elastic (rotationally summed) integral and differential cross sections for low energy (below about 10eV) positron scattering off gas-phase C2H2 molecules. The computations are carried out at the static and static-plus-polarization levels for describing the interaction forces and the correlation–polarization contributions are found to be an essential component for the correct description of low-energy cross section behavior. The local model potentials derived from density functional theory (DFT) and from the distributed positron model (DPM) are found to produce very high-quality agreement with existing measurements. On the other hand, the less satisfactory agreement between the R-matrix (RM) results and measured data shows the effects of the slow convergence rate of configuration-interaction (CI) expansion methods with respect to the size of the CI-expansion. To contrast the positron scattering findings, results for electron–C2H2 integral and differential cross sections, calculated with both a DFT model potential and the R-matrix method, are compared and analysed around the shape resonance energy region and found to produce better internal agreement.

Electron-scattering cross sections and stopping powers inH2O

Total electron-${\mathrm{H}}_{2}\mathrm{O}$ scattering cross sections have been measured from 50 to $5000\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ with experimental errors of about 5%. Integral elastic and inelastic cross sections have been calculated over a broad energy range $(1--10\phantom{\rule{0.2em}{0ex}}000\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ with an optical potential method assuming an independent atom representation. Dipole rotational excitations have also been included in the framework of the first Born approximation. From a detailed evaluation of the present results and their comparison with previous theoretical and experimental data, a set of recommended integral cross sectional data is provided. By combining these data with an average excitation energy derived from the experimental energy loss spectra, the stopping power of electrons in ${\mathrm{H}}_{2}\mathrm{O}$ has been obtained from 5 to $5000\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.