Close-coupling Cross Sections Research Articles

Electron-impact ionization of the Pb atom

Electron-impact ionization cross sections are calculated for the ground configuration of the Pb atom. Time-dependent close-coupling cross sections for the direct ionization of the 6s and 6p subshells leading to single ionization are calculated with and without a polarization potential. Configuration-average distorted-wave cross sections for the direct ionization of the 6s and 6p subshells leading to single ionization are also calculated with and without a polarization potential. We find the time-dependent close-coupling cross sections using a polarization potential to be in good agreement with convergent-close-coupling cross sections using a polarization potential. The total direct ionization cross sections are compared to two sets of experimental measurements. The differences between the direct ionization cross sections and the experimental measurements are mainly due to indirect ionization cross sections coming from the 6s^2 6p^2 rightarrow 6s 6p^3 excitation followed by autoionization.Graphic

Application of molecular convergent close-coupling cross sections in a collisional radiative model for the triplet system of molecular hydrogen

Collisional radiative (CR) models for molecular hydrogen are of high relevance for performing qualitative and quantitative analysis of excited-state population densities measured in plasmas or predicting the dependence of plasma emission on parameter variations. Although the development of such models for H2 started decades ago, major uncertainties still exist regarding the most important set of input parameters, namely the cross sections for electron-impact excitation. The deviations between cross sections from different datasets are particularly pronounced in the energy region close to the threshold energy, strongly increasing the uncertainty of CR models applied to low-temperature plasmas. This paper presents experimental validation of a set of newly calculated non ro-vibrationally resolved electron-impact cross sections calculated for the triplet system of H2 using the molecular convergent close-coupling method in the adiabatic-nuclei formulation. These cross sections are implemented into a CR model based on the flexible solver Yacora. A first comparison of CR calculations with the different datasets to experimentally-determined population densities is performed at a planar ICP discharge for varying pressure (between 1 and 10 Pa) and RF power (between 700 and 1100 W). For the experimentally-accessible electron temperature and density range (2.5–10 eV and 1.8–3.3 × 1016 m−3, respectively), very good agreement between the model and experiment is obtained using the new data set, in contrast to previously used cross sections.

Electron-impact ionization of the Kr atom

Electron-impact ionization cross sections are calculated for the ground configuration of the Kr atom. Time-dependent close-coupling cross sections for the direct ionization of the 4s and 4p subshells leading to single ionization are found to be a factor of 2 smaller than distorted-wave calculations due to the presence of strong continuum correlation effects. With the inclusion of relatively small excitation-autoionization contributions, the total single ionization cross sections for Kr are found to be slightly larger than crossed-beams experimental measurements.

Mixed quantum/classical theory for rotationally and vibrationally inelastic scattering of open-shell molecules and its application to the NH(X3Σ-) + He collisional system.

We developed the mixed quantum/classical theory (MQCT) for rotationally and vibrationally inelastic scattering of a diatomic molecule in a 2S+1Σ electronic state with a closed-shell atom. In this approach, the rotational (and vibrational) fine-structure states of the molecule are treated quantum-mechanically, whereas the relative motion of collisional partners is treated classically. This theory is benchmarked against full quantum (close-coupling) calculations for the NH(X3Σ-) + He system. Good agreement is found in all cases, and MQCT reproduces all main features of energy dependence of the cross section, except narrow scattering resonances at very low energies. Our method recovers propensity rules that govern values of close-coupling cross sections. Particularly, MQCT correctly predicts that the magnitudes of F-conserving transitions are significantly larger than those of F-changing ones. This new development makes MQCT a viable candidate for obtaining fine-structure resolved rotational rate coefficients at higher temperatures and for complex polyatomic systems where the standard full quantum treatment is computationally infeasible.

Time-of-flight electron scattering from molecular hydrogen: Benchmark cross sections for excitation of the X1Σg+→b3Σu+ transition

The electron impact $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition in molecular hydrogen is one of the most important dissociation pathways to forming atomic hydrogen atoms, and is of great importance in modeling astrophysical and industrial plasmas where molecular hydrogen is a substantial constituent. Recently, it has been found that the convergent close-coupling (CCC) cross sections of Zammit et al. [Phys. Rev. A 95, 022708 (2017)] are up to a factor of 2 smaller than the currently recommended data. We have determined normalized differential cross sections for excitation of this transition from our experimental ratios of the inelastic to elastic scattering of electrons by molecular hydrogen using a transmission-free time-of-flight electron spectrometer, and find excellent agreement with the CCC calculations. Since there is already excellent agreement for the absolute elastic differential cross sections, we establish benchmark differential and integrated cross sections for the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition, with theory and experiment being essentially in complete agreement.

Quantum close coupling calculation of transport and relaxation properties for Hg-H2 system

Quantum mechanical close coupling calculation of the state-to-state transport and relaxation cross sections have been done for Hg-H2 molecular system using a high-level ab initio potential energy surface. Rotationally averaged cross sections were also calculated to obtain the energy dependent Senftleben-Beenakker cross sections at the energy range of 0.005–25,000cm−1. Boltzmann averaging of the energy dependent Senftleben-Beenakker cross sections showed the temperature dependency over a wide temperature range of 50–2500K. Interaction viscosity and diffusion coefficients were also calculated using close coupling cross sections and full classical Mason-Monchick approximation. The results were compared with each other and with the available experimental data. It was found that Mason-Monchick approximation for viscosity is more reliable than diffusion coefficient. Furthermore, from the comparison of the experimental diffusion coefficients with the result of the close coupling and Mason-Monchick approximation, it was found that the Hg-H2 potential energy surface used in this work can reliably predict diffusion coefficient data.

Three-dimensional quantum mechanical studies of the H + H2 and F + H2 reactions

New results are presented for quantum mechanical reactive scattering in H + H2, including a comparison of close-coupling cross sections for para to ortho conversion with results obtained through momentum decoupling approximations. Information-theoretic analysis of product rotational distributions is given for one total energy. Results are also presented of the first three-dimensional coupled-channel study of the F + H2 reaction, showing the energy dependence of the probability distribution for vibrational excitation and population inversion.

Close coupling calculations for rotational relaxation of CO in argon: Accuracy of energy corrected sudden scaling procedures and comparison with experimental data

Fully quantal scattering calculations are carried out for CO in argon using both the close coupling (CC) and coupled states (CS) methods. CC and CS cross sections σ(j→j′) generally agree to within 15% or less with the exception of those corresponding to low Δj=|j′−j| values at low j where differences may reach 50%. The discrepancy arises mostly from efficient collisions with large orbital angular momentum, where the rotation of the quantization axis can no longer be neglected. Then, the CC calculations were used to test a scaling procedure based on the energy corrected sudden (ECS) approximation: given a set of basic cross-section σ(j→0), is it possible to predict the entire σo(j→j′) relaxation matrix? The ECS procedure yields reasonable agreement, on average, at the 13% level. However it fails at reproducing the Δj=1 cross sections in cases where the concept of a mean adiabaticity factor losses its physical meaning since the duration of the efficient collisions varies too much with the orbital angular momentum. On that basis, we have examined another question: the validity of an inversion procedure, based on the ECS scheme. Is it possible to determine the basic cross sections σ(j→0) starting from the knowledge of the easily measurable diagonal elements σo(j→j)? The ECS inverted basic rates agree with the CC ones to within about 20% up to j=15 and strongly diverge for higher j while the inversion leads to an overestimation of the mean duration of the efficient collisions. Then, using a high resolution Raman spectrometer, we recorded the Q-branch head of the fundamental band of CO in mixture with Ar at three temperatures, 87, 195, and 300 K, and total pressures up to 1.25 bar. Line-mixing effects in experimental Raman profiles are compared with CC theoretical predictions. Finally the close coupling results are also used to predict rotational relaxation times measured in free jets.

Inelastic collision cross sections of CH(X 2Π) with He(1S) on new ab initio surfaces

Full close-coupled (CC) integral inelastic cross sections were determined for collisions between CH(X 2Π)(N′=1) and He. These calculations are based on new ab initio CEPA (coupled electron pair approach) potential energy surfaces computed by Abdallah et al. These theoretical CC cross sections confirm a previous prediction of preferential population of final states levels in which the electronic wave function of the CH molecule is antisymmetric with respect to reflection in the plane of the molecule. These results are compared with the experimental results of Macdonald et al. At all energies the discrepancies were in most cases less than 7% of the ratio of the sum of the cross sections for the four transitions into levels of nominal A″ reflection symmetry divided by the sum of the cross sections for the four transitions into levels of nominal A′ reflection symmetry. Nevertheless, there is substantial disagreement in the magnitudes of the ratios particularly for the transitions with larger inelasticity.

Time-dependent quantum mechanical calculations on H + O2 for total angular momentum J > 0: Comparing different dynamical approximations

The H + O2 → OH + O reaction has been studied with a time-dependent wave packet method for total angular momentum J>0 using three different approximations: the J-shifting approximation, the helicity conserving approximation, and the truncated basis approximation. Both reaction probabilities and reaction cross sections are calculated and compared to recent rigorous close coupling calculations (E. M. Goldfield and A. J. H. M. Meijer, J. Chem. Phys., 2000, 113, 11055). Our results show significant deviations from the close coupling reaction probabilities for all approximations studied. As a result the approximate cross sections do not agree very well with the close coupling cross sections. We also compare our results to an approximate J-shifting type method due to Varandas (A. J. C. Varandas, Mol. Phys., 1995, 85, 1159). Our comparisons show the deficiencies of the different approximate methods for this reaction and emphasize the need to perform rigorous calculations.

Analysis of threshold effects in ultracold atomic collisions

At the ultracold temperatures which occur in cold atom traps and Bose-Einstein condensates, only a few partial waves contribute to the scattering of ground-state alkali-metal atoms, and cross sections are extremely sensitive to threshold effects. We present an analysis of these threshold effects, using a generalized multichannel quantum defect theory (GMQDT) to construct a close-coupled scattering wave function which is analytic in energy across thresholds. We illustrate the theory using the hyperfine transitions in $\mathrm{N}\mathrm{a}+\mathrm{N}\mathrm{a}$ collisions, and show that it gives results completely equivalent to the usual close-coupled cross sections. The virtue of the GMQDT is that it treats both open and closed channels on an equal footing, and all interchannel dynamics is summarized in a single real symmetric matrix $\mathbf{Y}(E)$ which is essentially constant across thresholds (and often over excursions of energy which exceed the hyperfine splittings). The multichannel threshold energy behavior can then be related to calculable properties of the individual channels that are being closed. Many of the smaller spin depolarization cross sections are determined by very long-range ${\ensuremath{\alpha}}^{2}{/R}^{3}$ spin-spin interactions which are not well treated by GMQDT, and we correct these specific elements with a perturbative distorted-wave approximation which yields the observed threshold dependences and brings the GMQDT into perfect agreement with the exact close-coupled results.

Evolution of e--He differential cross sections at 64.6 eV with different geometries

The distorted wave Born approximation is used to calculate the He (e, 2e) triple differential cross section at 64.6 eV in the different kinematical geometries, namely: (i) non-coplanar symmetric scattering angles with symmetric as well as asymmetric energy sharing; (ii) coplanar asymmetric with one scattering angle fixed and the other one variable; (iii) coplanar asymmetric with angular separation between the two outgoing electrons constant. The spin average static exchange (with the exchange part taken in equivalent local approximation) interaction potential is used. Two important characteristic features of the observed differential cross sections in non-coplanar geometry, namely: (i) a common point in the cross section curve for the two outgoing electrons at with the incident direction projected on the detection plane for all the energy sharing states and (ii) a deep minimum for the angular separation of between the detection plane and the electron beam have been fully supported. In coplanar asymmetric geometry, results are in agreement with the scaled up (by a constant factor of 1.8) convergent close-coupling cross sections.

Absolute, cascade-free cross sections for the 2S-->2P transition in Zn+ using electron-energy-loss and merged-beams methods.

Absolute, cascade-free excitation cross sections in an ion have been measured for the resonance $^{2}$S${\ensuremath{\rightarrow}}^{2}$P transition in ${\mathrm{Zn}}^{+}$ using electron-energy-loss and merged electron-ion beams methods. Measurements were carried out at electron energies of below threshold to 6 times threshold. Comparisons are made with 2-, 5-, and 15-state close-coupling and distorted-wave theories. There is good agreement between experiment and the 15-state close-coupling cross sections over the energy range of the calculations.

Close-coupling cross sections for electron-impact excitation of Kr28+

Coupling effects among the channels for collisional excitation of 2${s}^{2}$2${p}^{4}$, 2s2${p}^{5}$, and 2${p}^{6}$ configurations of oxygenlike krypton have been reinvestigated and found to be small. In an earlier publication, it was reported that coupling to the 2s2${p}^{5}$ $^{3}\ifmmode^\circ\else\textdegree\fi{}$ state has a strong influence on the cross section \ensuremath{\sigma}(2${\mathit{s}}^{2}$2${\mathit{p}}^{4}$ $^{3}$P\ensuremath{\rightarrow}2${\mathit{p}}^{6}$ $^{1}$S). That apparent coupling is shown to be due to an inconsistency involving orthogonality and correlation functions. We solve the correct set of coupled integrodifferential equations using the niem, \ensuremath{\Sigma}, and rmatrix codes. All three calculations are performed using the same atomic states and the same configurations to describe the target. We find very good agreement among the cross sections obtained from all three codes. We also calculated distorted-wave cross sections for the same set of transitions. The distorted-wave results are nearly identical to the results obtained with the close-coupling codes.

Collisional energy transfer involving molecules in 1II electronic states: fully quantum study of collisions of Li 2(B 1II u) with He and Ne

Infinite-order-sudden (IOS), coupled-states (CS) and close-coupled (CC) calculations for collisions of Li 2 (B 1II u) with He and Ne are reported, based on a representation of the potential energy surfaces introduced by Poppe. We explore the range of validity of the CS and IOS approximations and analyse the quantum interference effects in the integral cross sections. For both homonuclear and heteronuclear molecules in 1II electronic states we discuss, within the IOS approximation, when asymmetries will exist in the cross sections for upward ( J → J + Δ J), as compared to downward ( J → J - Δ J) transitions. In addition, also within the IOS approximation we show that the J → J + Δ J across sections will not be invariant with respect to the A-doublet level of the initial state. The CC cross sections are compared with previous and current experimental results. Good agreement is found for the magnitude of both the integral cross sections and the cross section asymmetries. The present study as well as previous experimental investigations show that the asymmetry pattern appears to be extremely sensitive to the interaction potential.

The scattering of slow electrons by lithium atoms; improved cross section estimates for transitions between states with n=3

The previously published five-state close-coupling total cross sections of Moores (1986) are considered with an improved estimate of the contribution from partial cross sections corresponding to large values of the total angular momentum using the unitarised Bethe approximation and Burgess sum rule method (1974) as given by Whelan (1986). Results are presented for transitions between the 3s, 3p and 3d states of a range of energies.

Coupling effects in electron-impact excitation of oxygenlike krypton

Coupling effects among the channels for collisional excitation of 2s/sup 2/2p/sup 4/, 2s2p/sup 5/, and 2p/sup 6/ configurations of oxygen-like krypton have been investigated by comparing six-, five-, four-, three-, and two-state close-coupling (CC) cross sections for the electron collision energy range 26.2 Ryless than or equal toEless than or equal to500 Ry. We discovered the surprising result that the calculated three-state CC (3CC) cross sections for the transition from the ground state to the 2p/sup 6/ /sup 1/S/sup e/ and the two-state CC cross section to the other excited states are reduced (considerably (45%) for the former) when the 2s2p/sup 5/ /sup 3/P/sup o/ channel is added to the 5CC approximation. In addition, the 3CC cross section sigma(2p/sup 4/ /sup 3/P/sup e/--2p/sup 6/ /sup 1/S/sup e/) is diminished by a factor of 100 at 26.2 Ry by the addition of the 2s2p/sup 5/ /sup 3/P/sup o/ state. Approximations which omit the 2s2p/sup 5/ /sup 3/P/sup o/ state overestimate the cross sections.

Quantum studies of inelastic collisions of O2(X 3Σ−g) with He: Polarization effects and collisional propensity rules

We investigate rotationally inelastic cross sections of O2(X 3Σ−g) with He at a collision energy of 27 meV. Theoretical cross sections obtained from close-coupled (CC) calculations are compared with results from the infinite-order sudden (IOS) approximation. Both the CC and IOS fine-structure state-resolved cross sections exhibit a strong ΔN=ΔJ Fi conserving collisional propensity. An analysis of the general expression for state-resolved cross sections in terms of spin-independent tensor opacities clearly establishes, without the introduction of dynamical approximations, the direct connection between this propensity rule and the collisional propensity for the conservation of the orientation of the nuclear rotational angular momentum vector N. In the low-N limit, Fi changing O2–He collisions are much more strongly depolarizing than collisions that conserve the Fi symmetry level. This enhanced collisional depolarization of an initial distribution of the total molecular angular momentum vector J is related to the collisional reorientation of N that must occur in Fi changing transitions.

Theoretical study of intramultiplet transitions in collisions of atoms inP3electronic states with structureless targets:Ca(P3)+He

The quantum close-coupling (CC) treatment of collisions of an atom in a $^{3}P$ electronic state with a structureless target is developed, based on earlier work of Mies [Phys. Rev. A 7, 942 (1973)] and a ${j}_{z}$-conserving [coupled-states (CS)] simplification presented. There is no direct coupling between the $J=0$ and $J=1$ levels; transitions between these levels will occur only as a result of Coriolis coupling involving the $J=2$ state. Actual CC and CS calculations are reported for collisions of $\mathrm{Ca} 4^{3}P^{o}$ with He, based on the potential curves of Malvern [J. Phys. B 11, 831 (1978)]. In the CC results, of the three independent cross sections, $J=2\ensuremath{\rightarrow}1$ is predicted to be largest, and $J=2\ensuremath{\rightarrow}0$ smallest, over the entire range of collision energies sampled. By contrast, the CS approximation predicts the 1\ensuremath{\rightarrow}0 transition to be forbidden, and yields only fair accuracy for the CC 2\ensuremath{\rightarrow}1 and 2\ensuremath{\rightarrow}0 transitions. The coupling between spin-orbit states is also interpreted within an adiabatic model. A comparison with the experimental results of Yuh and Dagdigian (preceding paper) is made by averaging the CC cross sections over the experimental translational energy distribution. The experimental cross sections for the 2\ensuremath{\rightarrow}1 and 2\ensuremath{\rightarrow}0 transitions are 3-4 times larger than the theoretical values, and the 2\ensuremath{\rightarrow}0 cross section is found experimentally to be \ensuremath{\sim}3 times larger than the 1\ensuremath{\rightarrow}0 cross section, in direct contrast with the theoretical prediction for this ratio.

Intramultiplet mixing in collisions of calcium4s4pPJo3with helium: Measurement of state-to-state cross sections

An optical-pumping state-selection technique for the study of collisions of /sup 3/P atoms in individual spin-orbit states is described. This technique is used to determine state-to-state intramultiplet-mixing cross sections for collisions of Ca /sup 3/P/sup o/ with helium in a beam--static-gas arrangement. The derived cross sections are as follows: for J = 2..-->..J' = 1, 31.9 +- 4.2 A/sup 2/; for J = 2..-->..J' = 0, 5.5 +- 1.6 A/sup 2/; and for J = 1..-->..J' = 0, 2.0 +- 5.0 A/sup 2/. These quantities represent averages over the translational-energy distribution (average energy 0.0556 eV). In the following paper Alexander, Orlikowski, and Straub present quantum close-coupling cross sections as a function of translational energy, using the pseudopotential Ca-He interaction curves of Malvern (J. Phys. B 11, 831 (1978)). The experimental 2..-->..1 and 2..-->..0 cross sections are found to be 3 to 4 times larger than the calculated theoretical values. In contrast to the theoretical prediction for the ratio of the smaller cross sections, the 2..-->..0 cross section is found to be larger than the 1..-->..0 cross section.