Low-energy positron–nitrogen-molecule scattering: A rovibrational close-coupling study

We have calculated the elastic scattering and rotational excitation cross sections for e−–N2 scattering at 30 and 50 eV using quantum chemical techniques specially designed to be applicable to elastic and inelastic electron scattering by general polyatomic molecules. The angle dependence of the sum of the elastic and rotational excitation differential cross sections is in good agreement with experiment at all scattering angles at both energies, but at 50 eV the difference from experiment exceeds the experimental uncertainty at small scattering angles and near the minimum of the differential cross section. At large scattering angles the rotational excitation cross sections are predicted to exceed the elastic scattering cross sections. The absolute cross sections agree with experiment at some angles but at other angles are as much as 51% (30 eV or 90% (50 eV) higher; this may be due at least in part to the difficulty of putting the experimental results on an absolute scale.

A laboratory frame close coupling method retaining six rotational states (j=0, 2, 4, 6, 8, 10) has been employed to studye+−N2 scattering. In the static potential the terms upto the moments (λ) 10 are retained. Two polarization potentials BTAD (Morrison et al.) and CP (Perdew and Zunger) are used in the calculation. The elastic and rotational (0–2, 0–4 and 0–6) excitation cross sections upto the incident positron energy 9.07 eV are reported. Present total cross sections (sum of the elastic and rotational excitation cross sections) are in fair agreement with the measured values in the energy region 2 eV to positronium formation threshold.

Calculated total, differential, and momentum-transfer cross sections are reported for the vibrationally elastic scattering of electrons from ${\mathrm{H}}_{2}$O and ${\mathrm{NH}}_{3}$ molecules in the range of energy 0.5--20 eV. The total cross sections are approximated by a sum of the rotationally elastic ones and the rotational transition from ground to first excited state (00\ensuremath{\rightarrow}10). The first-order Born approximation with the rotating-molecule model is used in the calculation of the first rotational excitation cross section. The experimental value of the dipole moments of ${\mathrm{H}}_{2}$O and ${\mathrm{NH}}_{3}$ are used in this step of the calculation. Spherically approximate molecular wave functions are applied to calculate the spherical part of the interactions of the incident electron with the molecule and the rotationally elastic-scattering cross section, in which the static and exchange interactions are calculated exactly within the accuracy of the molecular wave function and a parameter-free correlation-polarization potential is used to account for the polarization effect. The agreement of the differential cross sections with the experimental data is good at small angles and reasonably good at intermediate and large angles. Good agreement with measured values is obtained for the momentum-transfer cross sections. Total cross sections are reported with theoretical results on the e-${\mathrm{NH}}_{3}$ system below 10 eV. The possible sources of the discrepancies between the current theoretical and experimental results are analyzed for the total cross sections at very low energies by a quantitative consideration of the contributions of very strong forward scattering at near-zero angles to the total cross sections.

A reliable set of electron collision cross sections for water vapor, including elastic, rotational, vibrational, and electronic excitation, electron attachment, and ionization cross sections, is estimated by the electron swarm method. In addition, anisotropic electron scattering for elastic and rotational excitation collisions is considered in the cross section set. Electron transport coefficients such as electron drift velocity, longitudinal diffusion coefficient, and effective ionization coefficient are calculated from the cross section set by Monte Carlo simulation in a wide range of E/N values, where E and N are the applied electric field and the number density of H2O molecules, respectively. The calculated transport coefficients are in good agreement with those measured. The obtained results confirm that the anisotropic electron scattering is important for the calculation at low E/N values. Furthermore, the cross section set assuming the isotropic electron scattering is proposed for practical use.

Cross sections for the rotational excitation in vibrationally elastic e-+CH4 collisions have been measured for the impact energies 0.5, 5, 7.5 and 10 eV. Absolute state-to-state cross sections have been determined from the broadened energy loss peaks by using an analysis of Shimamura (1983). The results are compared with calculations of Jain and Thompson (1983) and of Abusalbi et al (1983). In the resonance region the cross sections for pure rotational excitation are larger than Jain and Thompson predicted, whereas their relative angular dependences-especially for the impact energy 5 eV-seem to follow the experimental curves. At 0.5 eV only weak rotational excitation occurs, and the experimental and theoretical cross sections are in agreement within experimental error.

The close-coupling approximation is used to calculate integral and differential cross sections for pure vibrational excitation $\ensuremath{\sigma}(v=0\ensuremath{\rightarrow}1, \ensuremath{\Delta}j=0)$ and $\ensuremath{\sigma}(v=0\ensuremath{\rightarrow}2, \ensuremath{\Delta}j=0)$, and for simultaneous rotational-vibrational excitation $\ensuremath{\sigma}(v=0\ensuremath{\rightarrow}1, \ensuremath{\Delta}j=2)$ of ${\mathrm{H}}_{2}$ by slow-electron impact. Static-field and electron-exchange effects, long-range quadrupole, and an effective polarization potential are included in the $e\ensuremath{-}{\mathrm{H}}_{2}$ interaction. Pure vibrational cross sections are found to depend on the initial rotational state $j$ of the molecule, but the total vibrational cross section is almost independent of $j$. Cross sections are compared with experiments for energies $E\ensuremath{\le}10$ eV. For $2<E<5$ eV, $\ensuremath{\sigma}(v=0\ensuremath{\rightarrow}1,\ensuremath{\Delta}j=0)$ and $\ensuremath{\sigma}(v=0\ensuremath{\rightarrow}1,j=1\ensuremath{\rightarrow}3)$ are 50% larger than experimental values while agreement is better in the remaining energy regions. For $1<E<3$ eV, $\ensuremath{\sigma}(v=0\ensuremath{\rightarrow}2,\ensuremath{\Delta}j=0)$ is in good agreement with experiment but is understimated for $E>3$ eV. Differential scattering cross sections for vibrational excitation are found to be dominated by the polarization potential at low angles, and by the short-range potential at large angles.

The rotational excitation of HD by low-energy electron collision is discussed for the first time. In the thermal-energy region, the Born approximation is used to derive relevant cross sections semi-quantitatively. In the eV-region, the adiabatic approximation is used to discuss the problem qualitatively. It is found that except in the neighborhood of the threshold energy, the rotational excitation cross section σ( J → J +2), J being the rotational quantum number of the molecule, does not change much when H 2 is replaced by HD. For HD, transitions with odd Δ J are also allowed. However, the cross sections for these transitions are found to be fairly small. The momentum-transfer and the rotational stopping cross sections are discussed. Excitation of D 2 is also considered for comparison.

The demand for electron-impact cross sections has increased tremendously in recent years. There is, however, a special interest in such cross sections for hydrogen molecules and its isotopomers, HD and D2, because of their presence in tokamak edge plasmas, planetary atmospheres and at different astrophysical sites. This explains the need for having well validated sets of electron-impact cross sections for different processes. This work reviews the electron-scattering cross sections for elastic and inelastic processes at different electron energies for both these molecules. The elastic momentum transfer cross sections and inelastic cross sections for electron-impact rotational, vibrational and electronic excitation, emission, dissociation, ionization and dissociative electron attachment have been evaluated and well validated in this work wherever and whenever possible.

This paper investigates the nonthermal effects of electrons on the rotational excitations of the hydrogen molecule in astrophysical Lorentzian plasmas. The J = 0 ? 2 and J = 1 ? 3 rotational excitation cross sections are employed in order to obtain the rotational excitation rates of the hydrogen molecule as functions of the spectral index and temperature. It is shown that the rotational excitation rates of H2 in non-Maxwellian plasmas are smaller than those in Maxwellian plasmas in low-temperature regions (HI region). However, in high-temperature regions the rotational excitation rates of H2 in non-Maxwellian plasmas are greater than those in Maxwellian plasmas. It is found that the rotational excitation temperature for the peak position of the excitation rate decreases with the decreasing nonthermal character of the plasma. It is also shown that the nonthermal effect on the rotational excitation for the principal transition J = 0 ? 2 is stronger than that for the J = 1 ? 3 transition.

The H(+) + D(2) --> HD + D(+) reaction has been theoretically investigated by means of an exact quantum mechanical approach, a quasiclassical trajectory method, and two statistical methods based in the propagation of either wave functions or trajectories. The study addresses the possible changes on the overall dynamics of the title reaction when the D(2) diatom is rotationally excited to its v = 0, j = 1 state. In addition, the reactivity for the ground rotational state on two different potential energy surfaces (PESs), namely, the surface by Aguado et al. [J. Chem. Phys. 112, 1240 (2000)] and the PES by Kamisaka et al. [J. Chem. Phys. 116, 654 (2002)], is examined. Reaction probabilities and cross sections at 0.524 and 0.1 eV collision energies are calculated. The major differences with respect to the reaction initiated with D(2) in its ground rovibrational state are observed for the lowest collision energy E(c) = 0.1 eV. Differential cross sections have been found to depend to some extend on the PES employed. In addition, at E(c) = 0.1 eV further discrepancies in the total and rotational cross sections are noticeable.

Cross sections at low energies for vibrationally elastic and inelastic scattering, as well as electron attachment to $\mathrm{S}{\mathrm{F}}_{6}$, have been calculated using a multichannel effective range theory (ERT) with complex boundary conditions. The most active vibrational modes, the totally symmetric mode ${\ensuremath{\nu}}_{1}$ and the infrared active mode ${\ensuremath{\nu}}_{3}$, have been included in the calculation. The ERT parameters were fitted to reproduce the experimental total and attachment cross sections. Differential elastic and vibrational excitation cross sections have been measured at 30\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{} using a spectrometer with hemispherical analyzers. The calculation reproduces correctly the magnitudes and shapes of the differential elastic and ${\ensuremath{\nu}}_{1}$, ${\ensuremath{\nu}}_{3}$, and $2{\ensuremath{\nu}}_{1}$ excitation cross sections, in particular the sharp structures at vibrational thresholds. The $s$- and $p$-wave phase shifts obtained in the present analysis differ from those recently derived by Field et al. [Phys. Rev. A, 69, 052716 (2004)].

Collision cross sections for rotational and vibrational excitation of CO by fast H atoms are calculated for two potential energy surfaces, the older Bowman–Bitman–Harding potential and the recently constructed surface of Werner, Keller, and Schinke. Both quantum mechanical and classical calculations are performed. The results obtained with the new potential energy surface are very similar to those obtained with the older potential; in particular, they do not rectify the discrepancies between the experimental and theoretical cross sections for vibrationally elastic transitions into small rotational states of CO.

Experimental and calculated absolute differential cross sections for the scattering of low-energy electrons from ethene are presented. Emphasis is on the excitation of the a 3B1u 3(pi,pi*) state, but selected elastic and vibrational excitation cross sections are also given. In contrast to earlier calculations, which were nearly a factor of 2 too large, the present calculation agrees very well with the experimental triplet excitation cross section in the threshold region. The improvement is due primarily to the inclusion of target polarization, which results in proper positioning of the pi* resonance, whose high-energy tail dominates the triplet state excitation near threshold. The present experimental elastic cross sections agree very well with recent calculations taking into account target polarization.

The atomic data of medium- and high-<i>Z</i> elements, such as electron-impact ionization and excitation cross-sections, possess extensive applications in fields such as fusion science and X-ray interactions with matter. There are atoms and ions in high energy density plasma, with different charge states and energy states ranging from ground states to highly excited states, and the cross-sections of each charge state and energy state need to be calculated. The bottlenecks limiting computational performance are the inevitable relativistic effects of medium- and high-<i>Z</i> elements and the extremely complex electronic configurations. Taking tantalum (Ta) for example, by using the relativistic Dirac-Fock theory and distorted wave model, we compute the electron-impact ionization and excitation cross-sections of Ta from the ground state atom up to Ta<sup>72+</sup> with the incident electron energy range of 1–150 keV. The detailed configuration accounting (DCA) reaction channel cross-sections are derived by summing and weighting the original detailed level accounting (DLA) cross-sections. After examining the data, two regularities are found. In terms of DLA, the pre-averaging DCA cross-sections have varying initial DLA energy levels but are typically close to each other. There is not a straightforward function that can explain the discrepancies between them. In terms of DCA, inner subshells typically contribute very little to the total cross-section as their ionization and excitation cross-sections are orders of magnitude smaller than those of outer subshells. We provide two techniques to reduce the computational costs based on the regularities. To minimize the total number of DLA reaction channels used in the computation, the initial DLA energy levels can be randomly sampled. Through a Monte Carlo numerical experiment, we determine the appropriate number of sampling points that can reduce the total number of DLA channels by an order of magnitude while maintaining a 5% error margin. In terms of impact ionization, since small cross-section DCA channels are insignificant, only a tiny portion of the DCA channels are required to preserve a 95% accuracy of the entire cross-section. It is possible to use the analytical Binary Encounter Bethe (BEB) formula to determine which DCA channels should be neglected before the computation to reduce computational costs. In terms of electron-impact excitation, just the cross-sections of the same excited subshells as the preserved ionized subshells, which are determined in the previous electron-impact ionization (EII) calculations, are needed. Finally, we compare our EII results with theoretical and experimental results. In the low incident electron energy range of below 2 keV, our results accord with the theoretical result of the 6s EII cross-section of the Ta atom and the experimental result of the total EII cross-section of the Ta<sup>1+</sup> ion. In the high energy range of below 150 keV, our results are also consistent with the theoretical result of the 1s EII cross-section of the Ta atom and the experimental result of the 1s EII cross-section of the Cu atom. Our results reasonably match the previous experimental and theoretical results in low-energy range and high-energy range, inner subshell and outer subshell, indicating the accuracy of our calculation. The proposed optimizing strategy can be applied to various medium- to high-<i>Z</i> elements and is compatible to most computation codes.

We calculate e−-N2 elastic and rotational excitation cross sections — within the ground electronic and vibrational state of the target — at low energies and compare our results to available experimental findings. In addition to the static potential we include the effect of polarization via a variationally-determined non-adiabatic polarization potential. We incorporate the effects of exchange exactly employing the linear algebraic method. Using a potential averaging technique we include the effects of the vibrational motion of the target.