Validity of approximate methods in molecular scattering: Thermal HCl–He collisions

A simple, direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given. Connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed. Simple procedures for calculating cross sections for specific transitions are discussed and many older model formulas are given clear derivations. Total (summed over rotation) differential, integral, and transport cross sections, useful in the analysis of many experiments involving nonspherical molecules, are shown to be exceedingly simple: They are just averages over the potential angle of cross sections calculated using simple structureless spherical particle formulas and programs. In the case of vibrationally inelastic scattering, the IOSA, without further approximation, provides a well-defined way to get fully three dimensional cross sections from calculations no more difficult than collinear calculations. Integral, differential, viscosity, and diffusion cross sections for He–CO2 obtained from the IOSA and a realistic intermolecular potential are calculated as an example and compared with experiment. Agreement is good for the complete potential but poor when only its spherical part is used, so that one should never attempt to treat this system with a spherical model. The simplicity and accuracy of the IOSA make it a viable method for routine analysis of experiments involving collisions of nonspherical molecules.

Potential anisotropy effects on inelastic differential cross sections

Differential scattering cross sections for excitation of helium by electron impact from its ground state to its $2^{1}P$ excited state have been measured at four incident electron energies in the range 26-55.5 eV for scattering angles between 10\ifmmode^\circ\else\textdegree\fi{} and 70\ifmmode^\circ\else\textdegree\fi{}, and at 81.6 eV for scattering angles between 10\ifmmode^\circ\else\textdegree\fi{} and 80\ifmmode^\circ\else\textdegree\fi{}. These differential cross sections have been placed on an absolute scale by normalizing them to the experimental absolute integral cross sections of Jobe and St. John. These experimental differential and integral cross sections have been compared with the results predicted by the Born approximation, and by several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering by various Ochkurlike approximations. The calculations provide reliable tests of these scattering theories since they are made using the accurate generalized oscillator strengths of Kim and Inokuti. As expected, these first-order theories are poor near threshold and exchange is important at high scattering angles for all energies. Further, the absolute magnitude of the calculated integral and small-angle differential cross sections is too large and is within 50% of experiment only at energies greater than 80 eV. These first-order models are in qualitative agreement with the experimental angular dependence at 34-81.6 eV for scattering angles between 10\ifmmode^\circ\else\textdegree\fi{} and 40\ifmmode^\circ\else\textdegree\fi{}. At higher scattering angles (corresponding to momentum transfers greater than about 1.6 a.u.), the calculated differential cross sections fall well below the experimental ones. The phase between the direct and exchange scattering amplitudes was found to be important at all energies, and is apparently not predicted correctly by any of the first-order models examined here. Some approximations for the exchange (e.g., Ochkur approximation and the post interaction form of the Ochkur-Rudge approximation) were found to be better for integral cross sections and some (e.g., prior Ochkur-Rudge approximation) were better for differential cross sections. The use of good analytic self-consistent-field (SCF) wave functions for both the ground and excited states was tested by computing generalized oscillator strengths from them and comparing these results with the calculations using the accurate generalized oscillator strengths. The SCF functions yield differential cross sections in quantitative disagreement (20%) with the accurate results, although the energy and angle dependence of the cross sections is predicted qualitatively correctly.

Relative integrated cross sections are measured for rotationally inelastic scattering of NO(2Pi(1/2)),hexapole selected in the upper lambda-doublet level of the ground rotational state (j = 0.5), in collisions with He at a nominal energy of 514 cm(-1). Application of a static electric field E in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the state-selected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laser-induced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, [formula: see text], which is equal to within a factor of (- 1) to the molecular steric effect, S(i-->f) is identical with (sigma(He-->NO) - (sigma(He-->ON))/(sigma(He-->NO) + sigma(He-->ON)). The dependence of the integral inelastic cross section on the incoming lambda-doublet component is also observed as a function of the final rotational (j'), spin-orbit (omega'), and lambda-doublet (epsilon') state. The measured steric asymmetries are significantly larger than previously observed for NO-Ar scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NO-He collisions is not very sensitive to the value of omega'. However, the lambda-doublet propensities are very different for [omega=0.5(F1)-->omega'= 1.5(F2)] and [omega=0.5(F1)-->omega'=0.5(F1)] transitions. Spin-orbit manifold conserving collisions exhibit a propensity for parity conservation at low deltaj, but spin-orbit manifold changing collisions do not show this propensity. In conjunction with the experiments, state-to-state cross sections for scattering of oriented NO(2Pi) molecules with He atoms are predicted from close-coupling calculations on restricted coupled-cluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R.Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electron-pair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry S(i-->f) of the inelastic cross sections at Etr= 514 cm(-1) is in reasonable agreement with that derived from the present experimental measurements for both spin-manifold conserving (F1-->Fl) and spin-manifold changing (F1 --F2) collisions, except that the overall sign of the effect is opposite. Additionally, calculated field-free integral cross sections for collisions at Etr = 508 cm(-1) are compared to the experimental data of Joswig et al. [J. Chem. Phys.85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy Etr= 491 cm(-1) is compared to experimental data of Westley et al. [J. Chem. Phys. 114, 2669 (2001)] for the spin-orbit conserving transition F1 (j = 0.5) -F1f (j' = 3.5).

Time-dependent wave packet state-to-state quantum dynamics study of the abstraction reaction S(3P) + H2(v = 0, j = 0) on 13A″ electronic state

Using a Beer–Lambert attenuation approach, we report measured total cross sections (TCSs) for positron scattering from vinyl acetate (C4H6O2) in the incident positron energy range 0.15–50 eV. In addition, we also report an independent atom model with screening corrected additivity rule computation results for the TCSs, differential and integral elastic cross sections, the positronium formation cross section and inelastic integral cross sections. The energy range of these calculations is 1–1000 eV. While there is a reasonable qualitative correspondence between measurement and calculation for the TCSs, in terms of the energy dependence of those cross sections, the theory was found to be a factor of ∼2 larger in magnitude at the lower energies, even after the measured data were corrected for the forward angle scattering effect.

Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m transitions. A systematic study of a number of centrifugal sudden approximations is made and discussed. A new method is presented for improving these approximations, which recouples the approximate solutions. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its correction for Ne+HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the coupled states approximation gives excellent results for orientation averaged transitions, but fails dramatically for state-selected m transitions. The corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart. The extension of this correction technique to the energy sudden and the infinite order sudden approximations is discussed.

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.

Electron impact ionization cross sections of C2H4 molecule

Close-coupling (CC) calculations of electron-ion recombination cross sections using the R-matrix method are presented and benchmarked with available experimental measurements. The electron-ion recombination process, including resonant and non-resonant recombination may be unified as a natural extension of the coupled-channel approximation, as traditionally employed for photoionization and electron-ion scattering. Recombination cross sections can be calculated to the same accuracy by employing similar eigenfunction expansions for the target ion. Detailed results are obtained for electron recombination with C V, C VI, O VIII and Fe XXV. Several sets of theoretical calculations are reported and discussed: non-relativistic CC in LS coupling, relativistic CC in the Breit-Pauli approximation, with radiative attenuation and fine structure, and the relativistic distorted-wave approximation. The theoretical results are in very good agreement with highly accurate experimental measurements at the Heidelberg test storage ring for C V, C VI and O VIII, and the electron-ion beam trap at Livermore for Fe XXV. We discuss the overall effect of radiation damping of all resonances on effective cross sections and rates, important for H- and He-like ions. In addition to agreement with experimental data, the validity of the CC calculations is demonstrated by the continuity between the calculated photorecombination, dielectronic recombination and electron impact excitation cross sections. Certain issues related to the works of Badnell et al (1998 J. Phys. B: At. Mol. Opt. Phys. 31 L239) and Robicheaux (1998 J. Phys. B: At. Mol. Opt. Phys. 31 L109) are also addressed.

Elastic scattering of electrons from alanine

The quantum dynamics calculations of the H + HS (v = 0, j = 0) reaction on the 3A' and 3A″ potential energy surfaces (PESs) are performed using the reactant coordinate based time-dependent wave packet method. State-averaged and state-resolved results for both channels of the title reaction are presented in the 0.02-1.0 eV collision energy range and compared with those carried out with quasi-classical trajectory (QCT) method. Total integral cross sections (ICSs) for both channels are in excellent agreement with previous quantum mechanical (QM)-Coriolis coupling results while poorly agree with the QCT ICSs of the exchange channel, particularly near the threshold energy region. The product rotational distributions show that for the abstraction channel, the agreement between our QM and the QCT results improves with increasing collision energy. For the exchange channel, our calculations predict colder rotational distributions as compared to those obtained by QCT calculations. Although the QM total differential cross sections (DCSs) are in qualitatively good agreement with the QCT results, the two sets of the state-to-state DCSs with several peaks exhibit great divergences. The origin of the divergences are traced by analyzing the QM DCS for the H + HS (v = 0, j = 0) → H2 (v' = 0, j' = 0) + S reaction on the 3A″ PES at Ec = 1.0 eV. It is discovered that several groups of J partial waves are involved in the reaction and the shape of the DCS is greatly altered by quantum interferences between them.

An apparatus is described for measuring the inelastic differential cross section for vibrational excitation in collisions of diatomic molecules with monoenergetic ions at laboratory energies between 10 and 50 eV. The method consists of measuring the time of flight of single ions with a time amplitude converter and displaying the results on a 100 channel pulse height analyzer. From the shift in the time of flight relative to that expected for elastic scattering the final state of the molecule excited in a single collision is identified. By studying only central collisions with almost zero impact parameter rotational excitation is strongly suppressed. Measured times of flight after collisions of monoenergetic Li+ ions with H2 show that with increasing energy the most probable vibrational quantum jump increases from 0→1 to 0→2,0→3 etc. Contrary to the usual assumption of a small steric factor for vibrational excitation the results show that the inelastic cross section is larger than the elastic cross section. Using reported potential parameters the energy dependence of the most probable excited state is compared with the calculations of Secrest and Johnson for a one-dimensional collinear collision. The satisfactory agreement suggests that the steric factor is close to 1. From measurements at different scattering angles at 10 eV the integral inelastic cross section is found to be about 0.2 A2 corresponding to a differential cross section of 0.4 A2/sr. Measured values of integral and differential total cross sections for Li+-He andLi+-H2 are reported and compared with theory. Direct dissociation of D2 by Li+ in the energy range from 25 to 55 eV was not observed, yielding an upper limit for the cross section of 4 · 10−4 A2/sr.

Previously reported measurements of the absolute experimental electron excitation cross section for the O (³P → ³S°) transition (1304 Å) at 100 eV have been extended to a wide range of incident energies from 16.5 to 200 eV. Both the O I and H I (n = 2) cross sections were measured simultaneously, and the H I (n = 2) cross sections were compared with previous results as a test of experimental reliability. The O I differential cross sections vary smoothly with incident energy and are flatter with scattering angle at the lower incident energies, as expected. The absolute integral cross section is found to agree with the theoretical shape and magnitude at higher energies. Comparison is made between fluorescence cross sections of Zipf and Erdman and present direct electron excitation cross sections. At low energies the direct excitation cross section is roughly 50% of the fluorescence cross section, suggesting that the cascade contribution to 1304‐Å fluorescence from excitation of the 2³P and other states is about the same magnitude as direct excitation. Generalized oscillator plots of the 100‐, 150‐, and 200‐eV data demonstrate the applicability of the Born approximation. Present results for the H I (n = 2) integral cross sections agree with previous results within 15%.

A rigorous formal theory of relaxation phenomena within the framework of the averaged jz-conserving coupled states (jzCCS) (Ajz) approximation is developed. Using the expressions obtained in this paper, the Ajz approximation is shown to yield pressure broadening cross sections which are in exact agreement with full close coupling results for a He+HCl model system. Previous jzCCS approximations to pressure broadening cross sections, which were in complete disagreement with close coupling for all systems studied, are shown to be the result of incorrect labeling of jzCCS T-matrices by total angular momentum J rather than by the effective orbital angular momentum ?. The correctly labeled results are not only found to be highly accurate but also considerably simpler than the expressions resulting from incorrectly labeled jzCCS T-matrices. Expressions are also derived for NMR spin–lattice relaxation cross sections within the Ajz approximation. Because the decoupled dynamical equations may be solved much more easily than the full exact CC ones, it is now feasible for the Ajz pressure broadening and spin–lattice relaxation cross sections to be computed in an iterative procedure. This will enable one to use such experimental data as a tool for determining molecular interactions.