Electron scattering by nitrogen molecules

Gillan, Charles J.; Nagy, O; Burke, P G; Morgan, L A; Noble, C. J.

doi:10.1088/0022-3700/20/17/032

Cited by 117 publications

(59 citation statements)

References 37 publications

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“…Experimental data shown include results from the present time-of-gight (solid circles) and crossedbeam (solid squares) exP™nts as well as measured data by Kennerly [46] (open circles), Ferch, Raith, and Schweiker [55] (solid squares), Jost et al [53] (solid triangles), and Baldwin [40] (open squares). Theoretical results are shown from the present BF FNO calculations (solid curve), R-matrix calculations of Civilian et al [28] (long-dashed line), hybrid-theory calculations by Chandra and Temkin [34] (short-dashed curve), and partial di6'erential equation calculations of~eatherford and Temkin [3g] (dot-dashed curve). theoretical ICSs.…”

Section: Rksuits: Intkgrai Crqss Sectionsmentioning

confidence: 99%

“…[28]. In addition, explicitly resonant vibrational excitation in e-N2 collisions has been explored in R-matrix calculations by Schneider, LeDourneuf, and Lan [25], optical-potential calculations by Herman et al [26], via a model-based treatment by Wadehra and Drallos [31], and in numerous papers based on the aforementioned boomerang model [21 -23].…”

Section: Intrqductiqnmentioning

confidence: 99%

“…[57] (closed squares) and theoretical results from hybrid-theory calculations by Chandra and Temkin [34] (medium-dashed line), Schwinger multichannel DCSs of Huo et al. [30] (short-dashed line), and R-matrix calculations of Ciillan et al [28] (long-dashed line). This procedure differs significantly in implementation from our original version, as described by Crompton and Morrison [111]in a study of e-H2 scattering.…”

Section: Rksuits: Intkgrai Crqss Sectionsmentioning

confidence: 99%

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Detailed theoretical and experimental analysis of low-energy electron-N2scattering

et al. 1995

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We have carried out a comprehensive theoretical and experimental study of electron scattering from molecular nitrogen at energies below 10.0 eV. In the theoretical component of this project we have generated differential and integral cross sections for elastic scattering and vibrational excitation in converged vibrational close-coupling calculations. In the experiments, we have measured dift'erential cross sections for these processes at scattering angles from 20' to 130 in a crossed-beam experiment at a large number of energies between 0.55 and 10 eV and, in a complementary time-of-Right experiment, total cross sections at energies between 0.08 and 10.0 eV. The measured angular distributions have been extrapolated to 0 and 180 using a procedure based on a nonlinear least-squares fit constrained by known physical properties of the e-Nz scattering matrix; numerical integration of the resulting extrapolated distributions yields integrated cross sections with almost no error beyond that inherent in the measured angular data. We find generally good agreement between the present experimental and theoretical cross section, particularly at energies near the H~r esonance near 2.39 eV. In previous studies of scattering in this region, such comparisons have been made problematical by the difhculty of ascertaining the appropriate theoretical scattering energy. We recommend here a protocol for resolving this problem for both elastic scattering and vibrational excitation.PACS number(s): 34.80.6s

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Section: Rksuits: Intkgrai Crqss Sectionsmentioning

confidence: 99%

Section: Intrqductiqnmentioning

confidence: 99%

Section: Rksuits: Intkgrai Crqss Sectionsmentioning

confidence: 99%

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Detailed theoretical and experimental analysis of low-energy electron-N2scattering

et al. 1995

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“…We have used a new code, developed by a consortium of workers in the U.K., which uses the R-matrix method [7,8] to study electron scattering by CO 2 for energies up to 10 eV. This code includes exchange exactly and evaluates all multicenter integrals in closed form.…”

Section: (Received 2 September 1997)mentioning

confidence: 99%

Virtual States and Resonances in Electron Scattering byCO2

Morgan

1998

Phys. Rev. Lett.

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The R-matrix method has been used to investigate structures observed in low energy scattering of electrons by CO 2 . We are able, by directly locating S-matrix poles in the complex momentum plane, to confirm that the large threshold cross section is due to the presence of a virtual state. This is the first ab initio calculation to locate such a state. As the molecule is bent, we are able to follow its behavior and show that it eventually becomes a true bound state. The low energy 2 P u shape resonance is found to split into two components, which behave differently as the molecule is bent.[S0031-9007 (98)05439-8] PACS numbers: 34.80.GsElectron scattering by carbon dioxide is of considerable interest in a variety of applications, such as atmospheric physics and gaseous electronics, and has consequently been the subject of much study. The low energy integrated cross sections have two distinctive features which, although first observed many years ago (see [1] for early references), are still not well understood. The first is a marked rise in the integrated cross section as the scattering energy decreases to zero. Morrison [2] has shown that this behavior was consistent with the existence of a virtual state of the CO 2 2 system. A virtual state is not a physical state, rather it is a feature of the system, which occurs at a nonphysical energy, that profoundly influences the scattering cross sections. Mathematically, it corresponds to a pole in the scattering matrix on the negative imaginary momentum (k) axis close to the origin. Morrison's model was subsequently criticized by Lucchese and McKoy [3] who demonstrated that his polarization potential was too strong. More recent calculations [4,5] have been relatively unsophisticated and have generally omitted the very low energy region. The second feature is a resonance at about 4 eV. Cartwright and Trajmar [6] have recently argued, on the basis of the anomalous shapes of the vibrationally inelastic differential cross sections at this energy, that the resonance cannot be a simple shape resonance, as had been previously assumed, but is a composite structure which includes at least one Feshbach resonance.We have used a new code, developed by a consortium of workers in the U.K., which uses the R-matrix method [7,8] to study electron scattering by CO 2 for energies up to 10 eV. This code includes exchange exactly and evaluates all multicenter integrals in closed form. Polarization effects and virtual electronic excitation processes are included in a completely ab initio manner. We included in our trial wave function, in addition to the ground state, all states having the configurations suggested by Cartwright and Trajmar as possible parents for a Feshbach resonance, i.e., CO 2 ͓K1p 3 g 5s g , P g ͔ and CO 2 ͓K1p 3 g 2p u , S 2 u , S 1 u , D u ͔. Calculations were carried out in C 2y symmetry with the molecule in the yz plane.We used small complete active space configuration interaction (CASCI) wave functions, where the active space consisted of the 6a 1 , 7a 1 , 2b 2 , 4b 1 ,...

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“…For other cases, the NR method is not very popular because of its sensitivity of the convergence rate on the initial guess and the difficulty in obtaining the numerical solution of a matrix of dimension N and its inversion. This also explains why a powerful hybrid 7 of NR and Picard iteration (where even the number of unknowns is high, up to 10 3 , the N can be only less than 10 2 ) only finds application in numerical solution of OZ integral equation systems, but has not found any application in numerical soution of the density profile equation in the classical DFT. Because the calculation of the matrix and its inversion can be done analytically on a grid for the case of OZ integral equation, but cannot be done in the case of DFT.…”

Section: Introductionmentioning

confidence: 99%

Rapidly convergent procedure to solve the density profile equation in the classical density functional theory

Zhou¹

2006

J Comput Chem

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An efficient recursive procedure to solve the density profile equation in the classical density functional theory (DFT) using an inverse Broyden method is described. The present iterative procedure is free of calculation of the Jacobian matrix, and its inversion unavoidable for the well-known Newton-Raphson (NR) method and its variants. Numerical calculation indicates that only the approximate solution and iterative matrix of the lower bulk density case are employed as the corresponding initial guesses of the higher bulk density case, the present recursive procedure can converge quickly to the physical solution with an accuracy of epsilon = 10(-14); therefore, the procedure provides an efficient numerical algorithm for the theory in which acquirement of a density profile of high accuracy is a key step. Extensive numerical calculation shows the advantage of the present inverse Broyden method over Broyles' mixing procedure and a modified Powell hybrid algorithm (a variation of the NR method).

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Electron scattering by nitrogen molecules

Cited by 117 publications

References 37 publications

Detailed theoretical and experimental analysis of low-energy electron-N2scattering

Detailed theoretical and experimental analysis of low-energy electron-N2scattering

Virtual States and Resonances in Electron Scattering byCO2

Rapidly convergent procedure to solve the density profile equation in the classical density functional theory

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