ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTAngular momentum decoupling approximations. Current status, successes, and difficultiesD. J. Kouri and D. E. FitzCite this: J. Phys. Chem. 1982, 86, 12, 2224–2231Publication Date (Print):June 1, 1982Publication History Published online1 May 2002Published inissue 1 June 1982https://doi.org/10.1021/j100209a017Request reuse permissionsArticle Views30Altmetric-Citations23LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (869 KB) Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThe utility of the CS and IOS approximations for calculating generalized phenomenological cross sections in atom-diatom systemsD. E. Fitz, D. J. Kouri, W. K. Liu, F. R. McCourt, D. Evans, and D. K. HoffmanCite this: J. Phys. Chem. 1982, 86, 7, 1087–1096Publication Date (Print):April 1, 1982Publication History Published online1 May 2002Published inissue 1 April 1982https://doi.org/10.1021/j100396a008RIGHTS & PERMISSIONSArticle Views28Altmetric-Citations13LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (940 KB) Get e-Alerts

Close-coupled (CC) and coupled-state (CS) calculations of kinetic theory relaxation and production cross sections are presented for the system H2 at infinite dilution in a bath of He. Performing these calculations for the same potential has allowed a test to be made of the efficacy of the CS procedure for use in calculating kinetic theory cross sections, especially those determining the Senftleben–Beenakker effects (SBE) in transport phenomena. The CS procedure is found to work extremely well (better than 1% agreement with CC results) for those cross sections that are predominantly elastic, to work rather well for relaxation cross sections determined either by reorientation of energetically inelastic collisonal events (about 10% agreement with CC results), and to work relatively poorly for production cross sections. In fact, the CS procedure for light molecules fares only marginally better than the IOS procedure for heavier molecules in the calculation of production cross sections. Finally, using only CC results, the sensitivity of the shear viscosity SBE is shown to be sufficient to distinguish easily between two recently obtained ab initio potentials for the H2–He system.

Infinite-order sudden approximation (IOSA) calculations of the phenomenological production and relaxation cross sections governing the magnetoviscosity effect have been undertaken for the system N2 at infinite dilution in He for the purpose of testing the usefulness of the IOSA procedure. Three l-labeling schemes (IL, FL, and AVL) have been employed and the results obtained for each of the three types of cross sections occuring in the viscomagnetic effect have been compared. For the relaxation cross sections σT( j′j‖Ek), σ(1)η( j′j‖Ek), and σ(2)η( j′j‖Ek), the IL/FL and AVL results differ by less than 5% on the average, but for the production cross sections σTη( j′j‖Ek), the three schemes IL, FL, AVL give widely differing results (one order of magnitude and sign). Thermally averaged phenomenological cross sections at 77.5 K were obtained for three potentials of the MSV type: one obtained from beam experiments and two using the beam scattering isotropic part and modified anisotropy parameters. For one of the modified anisotropic potentials giving reasonable agreement of the cross section σT calculated using the IOSA procedure and obtained from experiment, initial close-coupled calculations were performed at a kinetic energy of 54 cm−1. The IOSA AVL procedure gave results for j, j′ = 1, 3 differing by as much as 30% for σT( j′j‖Ek), and σ(κ)η( j′j‖Ek) and by as much as a factor of 2 for σTη( j′j‖Ek). Tentatively, it appears that in order to calculate production cross sections with reasonable confidence and accuracy, it will be necessary either to modify the CSA and IOSA methods or to use the more accurate CC procedure.

Calculations are reported for a model collision system using the l-average coupled states [CS(lav)] approximation. These results are compared against exact close coupling and corrected centrifugal sudden (CCS) results of McLenithan and Secrest. The uncorrected CS(lav) results are found to be more accurate for the McLenithan–Secrest model than the CCS results. (AIP)

The coupled states approximation is extended to treat combined fine structure and rotational state transitions in 2P atom–1Sg+ diatom scattering. CS calculations of opacities and degeneracy averaged integral cross sections for F(2P)+H2(1Sg+) nonreactive collisions agree well with the CC results of Lester and Rebentrost. The present, nonunitarized form of the CS approximation leads to a selection rule which forbids j′1 j′2 j12m12→j1 j2 j12-m12 transitions when j12 = half-odd integer values. This selection rule is not present in an exact treatment.

Full close coupled (CC), close coupled vibration-energy sudden rotation (CCES), distorted wave vibration-energy sudden rotation (DWES), and quasiclassical trajectory (QCT) techniques have been applied to treat H2 colliding perpendicularly with an uncorrugated, rigid, infinitely massive surface. Calculations were performed in the 1 eV energy range for the special case in which the H2 rotational angular momentum remains parallel to the surface. The qualitative features of the vibrationally elastic scattering processes are reasonably described by the QCT method even for conditions when the total rotational inelasticity is considerably greater than elasticity. The CCES and DWES methods qualitatively predict correctly that surfaces can produce large amounts of rotational angular momentum transfer but considerably overestimate the degree. The DWES method qualitatively predicts the importance of the nearly resonant vibrational to rotation energy transfer process but also considerably underestimates the probability of inelastic vibrational collisions. The CC results clearly indicate the importance of rotational-translational, vibrational-translational, and vibrational- rotational energy transfer in molecule-surface collisions.

Reported are calculations of rotational energy transfer in collisions of Cl2 molecules with a rigid, smooth surface, using both sudden approximations and quasi-classical trajectories. High probabilities are found for very large Δj transitions compared to corresponding gas-phase collisions: thus molecular collisions with walls can be extremely efficient in producing rotational transitions.

The coupled states approximation is extended to treat combined fine structure and rotational state transitions in /sup 2/P atom--/sup 1/S/sub g//sup +/ diatom scattering. CS calculations of opacities and degeneracy averaged integral cross sections for F(/sup 2/P)+H/sub 2/(/sup 1/S/sub g//sup +/) nonreactive collisions agree well with the CC results of Lester and Rebentrost. The present, nonunitarized form of the CS approximation leads to a selection rule which forbids j/sup prime//sub 1/ j/sup prime//sub 2/ j/sub 12/m/sub 12/..-->..j/sub 1/ j/sub 2/ j/sub 12/-m/sub 12/ transitions when j/sub 12/ = half-odd integer values. This selection rule is not present in an exact treatment.

CC and l-average CS calculations of degeneracy averaged differential cross sections and Δm-integral cross sections have been performed for Hez.sbndCO at E = 60 cm−1 and E = 80 cm−1, for HDz.sbndNe at E = 254 cm−1, and for Hez.sbndH2 at E = 1520 cm−1. The lavz.sbndCS degeneracy averaged differential cross sections are generally in good agreement with the CC cross sections. The previously observed shifts in the diffraction oscillations for odd rotationally inelastic transitions for Hez.sbndCO and HDz.sbndNe do not occur due to proper phase choice and l̄ = lav choice rather than l̄ = 1 or l′. The lavz.sbndCS approximation gives reliable results for most Δm-integral cross sections except for those σcs(jm, jm′) cross sections for which the CC cross sections σ(jm;jm′) and σ(jm′;jm) differ by a large amount.

Close coupled expressions for phenomenological cross sections which describe transport properties of atom–diatom mixtures are obtained in the total-J coupling scheme and are related to the bracket integrals of kinetic theory. Coupled states and infinite order sudden expressions for the generalized phenomenological cross sections using initial, final, and average l-labeling are also given. Particular care is taken to use a phase convention for the CS and IOS approximations which is consistent with the Arthurs–Dalgarno formalism and which gives the correct behavior of degeneracy averaged differential cross sections.

The effect of phase choice and partial wave parameter choice on CS and IOS inelastic degeneracy averaged differential cross sections is studied. An approximate simplified CS scattering amplitude for ?=1/2(l′+l) is derived and is shown to have a form which closely resembles the McGuire–Kouri scattering amplitude for odd Δj transitions and reduces to it for even Δj transitions. The choice of phase in the CS wave function is shown to result in different approximations which yield significantly different shapes for the degeneracy averaged differential cross section. Time reversal symmetry arguments are employed to select the proper phase choice. IOS calculations of the degeneracy averaged differential cross sections of He–CO, He–Cl and Ne–HD using ?=1/2(l+l′) and the phase choice which ensures proper time reversal symmetry are found to correct the phase disagreement which was previously noted for odd Δj transitions using ?=l or l′ and either the time reversal phase or other phase choices.

The recently proven multichannel spectral theorem for time delay is explored with the goal of providing a useful expression for ’’lifetimes’’ of bimolecular collisions. The theorem is reduced to an approximate relationship between the classical time delay and the classical excess density of states. Numerical studies on collinear atom–diatom systems confirm the accuracy of the classical relationship and a simple geometric interpretation of the excess density of states for these systems is provided. Results on the sensitivity of collisional time delays to variations in potential surface well depths and system masses are presented. the time delays being simply obtained from the excess density of states.

Calculations are performed in the compled states approximation for rotational transitions of HD–Ne at E=31.5 meV, using the correct phase (CP) choice3,4 and the potential of Buck, et al1(AIP)

A sudden approximation recently derived by Cross using a semiclassical treatment of the orbital motion is recast into a form which permits factorization of differential and integral degeneracy averaged cross sections, opacities as a function of final angular momentum quantum number, the scattering amplitude, and the phenomenological cross section which describes spectral line broadening. Calculations are done using an average of initial and final orbital angular momentum quantum numbers for the partial wave parameter for ArN2, ArTIF, H+H2 and Li+H2. The results indicate that the method is a good approximation for integral cross sections and opacities when the energy sudden approximation is valid and when the coupling of the orbital motion is important.

The l-average CS and IOS approximations are extended to treat fine structure transitions in 2P atom–1S atom scattering. Calculations of degeneracy averaged probabilities and differential cross sections for Na(2P)+He(1S) collisions in the CS and IOS methods agree well with the CC results. The present nonunitarized form of the CS approximation fails to properly predict all of the jm→j′m′ sections and in particular leads to a selection rule forbidding jm→j–m transitions for j=half-odd integer values.

The factorization expression for degeneracy averaged differential cross sections reported by Goldflam et al. and also by Khare is tested using accurate close coupling input for He CO. The results illustrate the accuracy of factorization expressions in describing detailed scattering phenomena.

Starting from kinetic theory collision integrals obtained from a generalized Boltzmann equation for a linear molecule in a bath of atomic perturbers and using Liouville (vector) space algebra, general expressions are derived for the three cross sections determining the shear viscosity Senftleben–Beenakker effects. These expressions are presented in terms of S-matrix elements in the total-J representation since this representation is especially useful for dynamical calculation and approximation procedures. Coupled-states and infinite-order–sudden dynamical approximations are then introduced and expressions obtained for the three cross sections in initial-l, final-l, and average-l labeling schemes. All cross sections simplify greatly when initial or final-l labeling is employed but little or not at all when average-l labeling is used. Nonetheless, even when the latter choice is made, less work will be involved than would be required for the corresponding full close-coupled or coupled-states calculation.