Schwinger Variational Method Research Articles

Photoionization cross-sections and asymmetry parameters for GeH 4 in the VUV region

We report calculated cross-sections and photoelectron angular distributions for photoionization out of the two outermost orbitals of GeH 4 for photon energies ranging from near threshold to 50 eV. The iterative Schwinger variational method in the exact static-exchange level is used to obtain the continuum photoelectron orbitals. Our calculated results show a remarkable similarity between the photoionization properties of the outermost valence orbitals of silane and germane.

Vibrational elastic and excitation cross-sections for electron–nitric oxide collisions

In this work, we report a theoretical study on electron-impact vibrational transitions of an open-shell molecule in the low and intermediate energy range. More specifically, calculated differential and integral cross-sections for the (ν′=0→ν=0,1,2,3, and 4) vibrational transitions in NO are reported in the 5–40 eV range. A complex optical potential composed by static, exchange, correlation–polarization plus absorption contributions (SEPa), derived from a molecular wave function, is used to describe the electron–molecule interaction dynamics. The Schwinger variational iterative method combined with the distorted-wave approximation is applied to calculate fixed-nuclear scattering amplitudes. Further, vibrational scattering amplitudes are obtained using the adiabatic-nuclear approximation. Comparison of our theoretical results with the existing experimental data shows good overall qualitative agreement, and in some cases quantitative agreement is also observed.

Cross sections for elastic electron–hydrogen sulfide collisions in the low- and intermediate-energy range

In this work, we present a joint theoretical and experimental study on electron-${\mathrm{H}}_{2}\mathrm{S}$ collisions in the low- and intermediate-energy range. More specifically, we report measured elastic differential, integral, and momentum-transfer cross sections in the (100--500)-eV energy range. In addition, calculated elastic cross sections in the (0.5--500)-eV energy range are also reported. The measurements were performed using a crossed electron beam--molecular beam geometry. The angular distributions of the scattered electrons were converted to absolute cross sections using the relative flow technique. Theoretically, an optical potential is used to represent the electron-molecule interaction. The Schwinger variational method combined with the distorted-wave approximation is used to solve the scattering equations. The comparison between our calculated and measured results as well as with other available experimental and theoretical data in the literature is encouraging.

Cross section and asymmetry parameter calculations for the C1sphotoionization ofCH4,CF4,andCCl4

We have computed cross sections and asymmetry parameters for the C 1s photoionization of CX{sub 4} (X=H, F, Cl) using the Schwinger variational method with Pade corrections. We present a comparative study that shows the influence of the identity of the X atom on the computed cross sections. Predicted cross sections are in good agreement with available photoionization and photoabsorption experimental data. We conclude that the presence of heavy outer atoms produces resonance structures in the photoionization cross sections and in the asymmetry parameters. We find a single nonvalence resonant state in the photoionization of CF{sub 4} and multiple resonances in CCl{sub 4} that have significant d-orbital character in the vicinity of the Cl atoms.

Photoionization of CF 4 in the VUV region

We present calculated results of photoionization cross sections and photoelectron angular distributions for ionization out of the five outermost valence orbitals of CF 4 for photon energies ranging from near threshold to 55 eV. The Schwinger variational iterative method, using an exact static-exchange plus a model correlation–polarization potential, is applied to obtain the continuum photoelectron orbitals. The quantitative agreement between our calculated results and the experimental data is fair. Moreover, our study is capable of identifying most structures seen in experimental results for both cross sections and asymmetry parameters.

Elastic and rotational excitation cross sections for electron–nitrous oxide collisions

AbstractWe present a theoretical study on electron–N2O collision in the low energy range. More specifically, we report calculated elastic and rotationally inelastic differential, integral, and momentum transfer cross sections in the 1.5–30‐eV range. An optical potential is used to represent the electron–molecule interaction. The Schwinger variational method is used to solve the scattering equations. In addition, the adiabatic‐nuclei‐rotation approximation is applied to calculate rotational inelastic cross‐sections. The comparison between the calculated results and the available experimental and other theoretical data in the literature is encouraging. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 260–266, 2003

Theoretical study on electron-free radical collisions: An application to SiH and SiF

We present a theoretical study of electron collisions on SiH and SiF free radicals in the low- and intermediate-energy range. More specifically, calculated elastic differential, integral and momentum transfer cross sections as well as grand total (elastic and inelastic) and absorption cross sections are reported in the (1-500)-eV energy range. A complex optical potential is used to represent the electron-radical interaction while the Schwinger variational iterative method combined with the distorted-wave approximation is used to solve the scattering equations. Comparisons were made between the calculated cross sections for SiH and SiF as well as with the existing experimental and theoretical data for electron scattering by silane molecule. Some interesting aspects of this comparison are discussed here.

Elastic and rotational excitation cross sections for electron scattering by polyatomic molecules

In this work we present a theoretical study on electron scattering by both polar and nonpolar polyatomic molecules in the low-energy range. More specifically, we report calculated elastic and rotationally inelastic differential cross sections for electron scattering by CH4, H2O, and H2S in the (2.14-30)-eV range. Exact static-exchange plus model correlation-polarization potentials are used to represent the electron-molecule interaction. The Schwinger variational iterative method is used to solve the scattering equations. In addition, the adiabatic-nuclei-rotation approximation is applied to calculate rotational cross sections. The comparison of our calculated results with experimental and other theoretical data available in the literature is encouraging.

Theoretical study on electron–free-radical scattering: An application to CF

In this work, a theoretical study on electron-CF collisions in the low- and intermediate-energy range is reported. More specifically, calculated elastic differential, integral, and momentum-transfer cross sections as well as grand total (elastic and inelastic) and absorption cross sections are presented in the (1--500)-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics, while the Schwinger variational iterative method combined with the distorted-wave approximation is used to solve the scattering equations. Comparison of the present results with existing experimental and theoretical data for electron collisions with NO (an isoelectronic molecule of CF) is made.

Elastic and absorption cross sections for electron–nitrous oxide collisions

In this work, we present a joint theoretical-experimental study on electron-${\mathrm{N}}_{2}\mathrm{O}$ collisions in the intermediate energy range. More specifically, calculated and measured elastic differential, integral, and momentum-transfer cross sections, as well as calculated total and absorption cross sections are reported. The measurements were performed using a crossed electron-beam--molecular-beam geometry. The angular distribution of the scattered electrons was converted to absolute cross sections using the relative-flow technique. Theoretically, a complex optical potential is used to represent the electron-molecule interaction dynamics in the present calculation. The Schwinger variational iterative method combined with the distorted-wave approximation is used to solve the scattering equations. The comparison of the present calculated results with the measured results as well as with the existing experimental and theoretical data shows good agreement.

Theoretical studies on electron-carbon monoxide collisions in the low and intermediate energy range

We report a theoretical study on electron–CO collisions in the low and intermediate energy range. More specifically, calculated elastic differential, integral and momentum transfer cross sections, as well as grand total (elastic+inelastic) cross sections are reported in the 2–500eV energy range. A complex optical potential is used to represent the electron–molecule interaction dynamics in the present calculation, while the Schwinger variational iterative method combined with the distorted-wave approximation is used to solve the scattering equations. The comparison of the present results with existing experimental and other theoretical data shows good agreement.

Cross sections and asymmetry parameters in gas-phase photoionization ofC60

Calculations are carried out on the photoionization of ${\mathrm{C}}_{60}$ molecules in the gas phase, in particular, the photoionization of its highest occupied molecular orbital leading to the formation of ${\mathrm{C}}_{60}^{+}$ in the ${}^{2}{H}_{u}$ state. The computational treatment employs the undistorted orbitals of the neutral molecule and solves the coupled scattering equations for the ejected electron in the field of the molecular ion by using the correct static-exchange interaction within a polyatomic Schwinger variational method with Pad\'e corrections. The total cross section and photoelectron angular distributions show marked resonant features from the threshold up to photon energy of about 30 eV. In the present calculations, all resonances are one-electron resonances of the outgoing electron and are very reminiscent of those predicted for electron-scattering processes from neutral ${\mathrm{C}}_{60}.$ The physical implications of this result are analyzed and discussed.

Studies of angular distributions and cross sections for photodetachment from the oxygen molecular anion

We have studied the photodetachment from molecular oxygen anion O2− leading to eleven O2 electronic states. Both single- and multichannel scattering calculations were performed using the Schwinger variational method with the Hartree–Fock or configuration interaction approximations for the target states. Our calculated total cross sections agree well with the existing experimental data. One Feshbach resonance was found at about 5 eV above the photodetachment threshold. This resonant state has the character of the 1πu31πg4 configuration, and decays to several final channels. Our calculated partial cross sections suggest that shape resonances exist in different channels at higher energies, and the structures of these shape resonances differ from what we have seen in the photoionization from neutral molecules. The most significant feature in this photodetachment process is the channel coupling effect due to electron correlation.

Elastic and excitation cross sections for electron–formaldehyde collisions

Differential and momentum-transfer cross sections for elastic e−–CH2O scattering in the 16–80eV as well as differential and integral cross sections for the X1A1→ã3A2 excitation by electron impact in the 20–80eV range are reported. The Schwinger variational iterative method is applied to solve the elastic scattering equations, whereas the distorted-wave approximation combined with that method is applied to calculate cross sections for the inelastic process. There is a good agreement between our excitation cross sections with other theoretical data available in the literature. This comes in support of the reliability of our results for the elastic process.

Chemical collisions involving μ + mesons

The phase shifts for the chemical reaction of μ + mesons with Tritium molecular ions have been calculated using Hulthen–Kohen and Schwinger variational methods. Also the differential cross sections for different values of the wave number of the relative motion are computed. The obtained values are found to be comparable with the corresponding theoretical ones or that obtained by F. Ayoub and A. El-Shahawy [Journal de chimie physique (1986) 83]. They are, however, not far below the maximum values.

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.

Inverse problem of the wave equation and the Schwinger approximation

A new method of profile inversion for acoustic waves propagating in a medium with spherical inhomogeneity based on the Schwinger variational method is presented. The wave equation of interest is transformed into a Schrodinger equation, so that the Born approximation and the new method could also be applied at high frequencies. It is shown that the new method is stable and is more accurate than the Born approximation. To illustrate the method, an exactly solvable analytical example is presented. Also numerical examples using synthetic data, with and without additive noise, are given and the corresponding inversion results and the stability of the method are studied.

Cross section and asymmetry parameter calculation for sulfur 1s photoionization of SF6

We use the polyatomic Schwinger variational method with Padé corrections to calculate the cross section and asymmetry parameter for the sulfur 1s core level photoionization of SF6, for photon energies from threshold up to 2600 eV. Our results show very good agreement with experimental cross sections. Our asymmetry parameter show good qualitative agreement with experiment. A resonant feature at a photon energy of ≈2550 eV is found to be due to a nonvalence type resonant state which is trapped by an l=9 angular momentum barrier.

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.

Cross sections and polarization fractions for elastice−−O2collisions

The Schwinger variational iterative method and the distorted-wave approximation are combined to study elastic electron scattering by ${\mathrm{O}}_{2}$ for incident energies ranging from 5 to 500 eV. Differential, integral, and momentum transfer cross sections as well as polarization fractions are reported. A complex optical potential, which accounts for the static, exchange, correlation-polarization, and absorption contributions is used to describe the electron-molecule interaction. Comparison of our calculated results with experimental and other theoretical results is encouraging.