Electron-impact study of the S2molecule using theR-matrix method

We have employed the R-matrix method to compute elastic (integrated and differential), momentum-transfer, excitation, and ionization cross sections for electron impact on the NH radical. The target states are represented by including correlations via a configuration interaction technique. The results of the static exchange, correlated one-state configuration interaction, and 19-state close-coupling approximation are presented. We have detected a stable anionic bound state {sup 2{Pi}} of NH{sup -} having the configuration 1{sigma}{sup 2}2{sigma}{sup 2}3{sigma}{sup 2}1{pi}{sup 3}. The data of the momentum-transfer cross section, generated from the differential cross section, is used to compute effective collision frequencies over a wide electron temperature range (200-30 000 K). The ionization cross sections are calculated in the binary-encounter Bethe model in which Hartree-Fock molecular orbitals at self-consistent levels are used to calculate kinetic and binding energies of the occupied molecular orbitals. We have included up to the g partial wave (l=4) in the scattering calculations. For this dipolar molecule we have used a Born-closure top-up procedure to account for the higher partial waves for the convergence of the cross section.

We report normalized experimental and theoretical differential cross sections for elastic electron scattering by ${\mathrm{C}}_{4}$H${}_{4}$O (furan) molecules from a collaborative project between several Brazilian theoretical groups and an experimental group at California State Fullerton, USA. The measurements are obtained by using the relative flow method with helium as the standard gas and a thin aperture target gas collimating source. The relative flow method is applied without the restriction imposed by the relative flow pressure condition on helium and the unknown gas. The experimental data were taken at incident electron energies of 1, 1.5, 1.73, 2, 2.7, 3, 5, 7, 10, 20, 30, and 50 eV and covered the angular range between ${10}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${130}^{\ifmmode^\circ\else\textdegree\fi{}}$. The measurements verify observed ${\ensuremath{\pi}}^{*}$ shape resonances at $1.65\ifmmode\pm\else\textpm\fi{}0.05$eV and $3.10\ifmmode\pm\else\textpm\fi{}0.05$ eV scattering energies, in good agreement with the transmission electron data of Modelli and Burrow [J. Phys. Chem. A 108, 5721 (2004)]. Furthermore, the present results also indicated both resonances dominantly in the $d$-wave channel. The differential cross sections are integrated in the standard way to obtain integral elastic cross sections and momentum transfer cross sections. The calculations employed the Schwinger multichannel method with pseudopotentials and were performed in the static-exchange and in the static-exchange plus polarization approximations. The calculated integral and momentum transfer cross sections clearly revealed the presence of two shape resonances located at 1.95 and 3.56 eV and ascribed to the ${B}_{1}$ and ${A}_{2}$ symmetries of the ${C}_{2v}$ point group, respectively, in very good agreement with the experimental findings. Overall agreement between theory and experiment regarding the differential, momentum transfer, and integral cross sections is very good, especially for energies below 10 eV.

The results of ab initio scattering calculations for low-energy electron collisions with the B${}_{2}$ molecule using the $R$-matrix method have been presented. The differential and momentum-transfer cross sections along with effective collision frequency over a wide electron temperature range (300--30 000 K) are computed at the one-state close-coupling level. In this work, 61-state close-coupling calculations are performed to compute the integral cross sections (elastic and excitations). We investigated five resonances: two in the excitation cross sections of $A{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}$, two in the excitation cross sections of $a{\phantom{\rule{0.16em}{0ex}}}^{5}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{\ensuremath{-}}$ and one in both $b{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Delta}}_{g}$ and $c{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}$ excited states. The Born correction for the dipole-allowed transition ($X{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{\ensuremath{-}}$ to $A{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}$) has been carried out to account for the contribution of partial waves higher than the $g$ wave ($l=4$) up to which the $R$-matrix scattering calculations are carried. We have detected a stable anionic bound state ${}^{2}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}$ of B${}_{2}^{\ensuremath{-}}$ having the configuration $1{\ensuremath{\sigma}}_{g}^{2}$ $2{\ensuremath{\sigma}}_{g}^{2}$ $1{\ensuremath{\sigma}}_{u}^{2}$ $2{\ensuremath{\sigma}}_{u}^{2}$ $1{\ensuremath{\pi}}_{u}^{3}$. The ionization cross sections are calculated in the binary-encounter Bethe model in which Hartree-Fock molecular orbitals at a self-consistent level are used to calculate kinetic and binding energies of the occupied molecular orbitals. We have also evaluated scattering length for electron-B${}_{2}$ collisions at the one-state close-coupling level (6.8${a}_{0}$) and at the static exchange plus polarization level (6.2${a}_{0}$).

A detailed comparison of experimental and theoretical elastic cross sections for low-energy electron scattering by ethyne (${\mathrm{C}}_{2}{\mathrm{H}}_{2}$), taken earlier in our group by Gauf et al. [Phys. Rev. A 87, 012710 (2013)], and some of its methylated derivatives, propyne (${\mathrm{C}}_{3}{\mathrm{H}}_{4}$), and the isomers 1-butyne and 2-butyne ($n\ensuremath{-}{\mathrm{C}}_{4}{\mathrm{H}}_{6}, n=1,2$), taken here, are presented. The present differential cross sections were measured at incident electron energies ranging from 1 eV to 30 eV and for scattering angles from ${5}^{\ensuremath{\circ}}$ to ${130}^{\ensuremath{\circ}}$ using the relative flow method with an aperture gas source. Our earlier work was taken over a larger energy range of up to $100\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. The theoretical calculations were carried out for impact energies up to $30\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, employing the Schwinger multichannel method with pseudopotentials in the static-exchange plus polarization approximation. In addition to the differential cross sections, we present the integral and momentum transfer cross sections with which we discuss the shape resonances present in these systems and other physical phenomena, such as the presence of Ramsauer-Townsend minimum. We also compare our theoretical and experimental results with previous data that are available in the literature.

In the present work we report cross sections for electron collisions with the isomers propene (C3H6) and cyclopropane (c-C3H6). Electron-scattering differential cross sections (DCS) are reported for measurements carried out for energies 1.5-100 eV and the angular range of 20 degrees-120 degrees. Elastic integral cross sections (ECS), DCS, and momentum-transfer cross sections (MTCS) are reported for calculations carried out using the Schwinger multichannel method with pseudopotentials for the energy range of 2.0-40 eV and angular range of 0 degrees-180 degrees. The resemblance of the pi* shape resonance in the cross sections, observed at 1.5-2.0 eV for propene, to those in C2H4 and C2F4 clearly points to the effect of the double bond in the molecular structures for these molecules. Below 60 eV, we observed clear differences in peak positions and magnitudes between the DCS, ECS, and MTCS for C3H6 and c-C3H6, which we view as the isomer effect.

Currently there are no reliable theoretical approaches for calculating fully differential cross sections (FDCSs) for low-energy electron-impact ionization of large molecules. We have recently proposed the orientation-averaged molecular orbital (OAMO) for calculating cross sections averaged over molecular orientations. In this paper, we use the OAMO to calculate distorted wave Born approximation (DWBA) and molecular three-body distorted wave (M3DW) Born approximation FDCS for electron-impact ionization of the nitrogen molecule. Both coplanar symmetric and asymmetric FDCSs are investigated in the energy range of 35.6-400 eV. By comparing with the experimental data, we found that the M3DW is reasonably accurate in this energy range. We also found that the postcollision interaction plays a sufficiently important role and that the DWBA is not reliable.

Elastic differential and momentum transfer cross sections are reported for electron scattering by H2O at impact energies ranging from 4 to 50 eV. The iterative Schwinger variational method in the fixed-nuclei, static-exchange approximation is used to calculate the low partial wave scattering amplitudes and the higher partial wave contributions are included via closure using the Born approximation for a point-dipole. Comparison of our calculated cross sections with recent experimental and other theoretical results is encouraging.

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.

Propene (C3H6) is considered to be an important molecule in the field of plasma science due to it being recognized as a by-product of plasma irradiation at the diverter regions and plasma facing walls in modern fusion devices. This article reports electron scattering elastic, momentum transfer, differential and excitation cross sections of propene. The rate coefficients for the elastic and momentum transfer cross sections are also reported. The data reported in this article are considered to be important in the field of plasma physics due to their direct influence on plasma modeling applications. Two theoretical methods were used for the present study; the R-matrix method for low energy and spherical complex optical potential formalism for high energy. The R-matrix calculation was performed using the correlation-consistent polarized valence-only triple-zeta basis set and a reasonable agreement with the target properties was obtained. The scattering calculations were then performed using these parameters to compute various cross sections. The present cross sections compare reasonably well with the only available data in the literature. More experimental studies of a similar nature are encouraged for the validation of the present results.

The BBK model is modified by the introduction of effective Sommerfeld parameters for both symmetric and asymmetric geometries on an empirical basis, while still maintaining the philosophy that all three Coulomb interactions are included on an equal footing. The triple differential cross sections for electron-impact ionization of atomic helium at an incident energy of 40 eV in an asymmetric geometry are calculated. Results of this approach are compared with the absolute measurements and the only existing theoretical results of the convergent close-coupling method.

The number of electron–ion pairs and the distribution of excited species created by the passage of an intense electron beam in a gas are important parameters for many applications. The previously published values for molecular nitrogen rely on a differential ionization cross section that uses a number of fitting parameters and excitation cross sections determined from analytical fitting functions [S. P. Slinker, A. W. Ali, and R. D. Taylor, J. Appl. Phys. 67, 679 (1990)]. Slinker used cross section fits to solve the Boltzmann equation which was then used to compute the important beam-impact parameters. In this work, it is shown that an alternative approach based on the continuous slowing down approximation (CSDA) can be used to compute the energy expended per electron-ion pair and the distribution of excited gas species. This method results in an integral equation that can be solved iteratively and converges rapidly. The binary-encounter Bethe (BEB) differential ionization cross section is used [Y. K. Kim and M. E. Rudd, Phys. Rev. A 50, 3954 (1994); W. Hwang, Y.-K. Kim and M. E. Rudd, J. Chem. Phys. 104, 2956 (1996)]. The BEB model naturally extends to relativistic energies and has no free parameters. This makes the BEB considerably easier to use than previous models based on fitting parameters. The BEB model requires orbital constants obtained from quantum chemistry calculations. To demonstrate the technique, the electron-beam impact parameters are computed for nitrogen gas. The tabulated low-energy excitation cross sections are extended to relativistic energies using Bethe's asymptotic value for the inelastic cross sections [M. Inokuti, Rev. Mod. Phys. 43, 297 (1971)]. It is shown that the results for the energy expended per electron–ion pair as well as the distribution of excited states agree with published experimental values and are similar to previously published theoretical results.

We report a joint theoretical and experimental study on elastic scattering of electrons from halothane (CF3CHBrCl). The theoretical differential, integral and momentum transfer cross sections were obtained with the Schwinger multichannel method implemented with pseudopotentials (SMCPP), and with the independent atom model with screening corrected additivity rule including interference effects (IAM-SCAR+I). The differential cross sections measurements were conducted for incident electron energies of 10, 20, 30 and 50 eV, while the scattered electron angular range varied from 7° to 100°. At these energies the present experimental differential cross sections are in reasonable agreement with both SMCPP and IAM-SCAR+I calculations. As expected, the two theoretical methodologies agree well with each other as the electron impact energy increases. We also discuss the presence of low-energy resonances and a bound anion state identified in our SMCPP calculations.

Ab initio calculations and normalized experimental measurements of the differential, momentum transfer and integral cross sections for vibrationally elastic scattering of low-energy electrons from orthoxylene, metaxylene, and paraxylene are presented. The calculated cross sections are obtained using the Schwinger multichannel method implemented with norm-conserving pseudopotentials. The differential cross sections are measured at incident energies from 1 to 30 eV and scattering angles from ${10}^{\ensuremath{\circ}}$ to ${130}^{\ensuremath{\circ}}$. These cross sections are compared to experimental results for toluene. The comparisons illuminate the role of molecular structure in determining the integral cross sections and the angular distributions of resonantly scattered electrons.

An analytical expression based on the binary-encounter-Bethe model for energy differential cross sections in the low binding energy regime is presented. Both the binary-encounter-Bethe model and its modified counterpart are extended to shells with very low binding energy by removing the constraints in the interference term of the Mott cross section, originally introduced by Kim et al. The influence of the ionic factor is also studied for such targets. All the binary-encounter-Bethe based models presented here are checked against experimental results of low binding energy targets, such as the total ionization cross sections of alkali metals. The energy differential cross sections for H and He, at several incident energies, are also compared to available experimental and theoretical values.

Absolute, elastic differential cross sections (DCS) for electron-propane collisions have been measured over a range of scattering angles from 10 degrees to 130 degrees and at incident kinetic energies from 2 to 100 eV. The angular distributions were extrapolated to 0 degrees and 180 degrees by a nonlinear phase shift fit and integrated numerically to obtain the integral elastic and momentum transfer cross sections. The observed DCS agree approximately with a continuum multiple scattering calculation that uses only local potentials and also with a multichannel Schwinger variational calculation. The vibrationally inelastic DCS reveal a shape resonance with a peak at 7.5 eV that is characteristic of trapping by valence orbitals with C-H antibonding character and is identical with peaks encountered in electron-methane and electron-ethane scattering.