V. Khare

Infinite order sudden approximation for reactive scattering. I. Basic l‐labeled formulation

An infinite order sudden (IOS) treatment of reactive scattering is developed taking into account recent results of nonreactive collision studies on the importance of l‐labeling, nonconservation of helicity, and transformation properties of sudden approximation wave functions. The present IOS method should be sufficiently simple to apply to a number of chemically interesting atom–diatom reactions. Such applications are currently in progress.

On jz‐preserving propensities in molecular collisions. I. Quantal coupled states and classical impulsive approximations

The occurrence of jz‐preserving propensities in atom–linear molecule collisions is considered within the contexts of the quantum mechanical CS approximation and of a classical model collision system. The latter involves an impulsive interaction which is the extreme limit of the class of potentials for which the CS approximation is expected to be valid. The classical model results in exact conservation of jz along a ’’kinematic apse.’’ Quantum mechanically, the CS approximation is reformulated in a manner that clearly shows the relationship between the l choice and the degree and direction of jz preservation. Away from the forward direction, the simplest choice obeying time reversal symmetry l=(l+l′)/2, is shown to result in a propensity for preserving jz along a ’’geometric apse’’ which coincides with the kinematic apse in the energy sudden limit, and for nonenergy sudden systems only differs significantly from it close to the forward direction.

Effect of phase and orbital wave parameter choices on CS and IOS 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.

On a jz‐preserving propensity in molecular collisions. II. Close‐coupling study of state‐to‐state differential cross sections

In this paper, we present and analyze accurate close‐coupling results for polarization transition differential cross sections for Δj≠0 atom–diatom collisions. The systems considered are He+CO and He+HCl. Cross sections for polarization transitions defined with several choices of quantization axes are presented and discussed. We find that (a) the jz‐preserving cross sections are heavily favored when a generalized apse quantization scheme is used; (b) the other quantization schemes can be factorized for transitions involving lower rotor j states in terms of the dominant jz‐preserving apse quantized amplitudes; (c) this factorization implies limits on the amount of information contained in polarization measurements based on nonapse quantization axes; (d) the factorization (and, hence, its limitations) does not apply to the highest accessible rotor j states; and (e) the propensity for preserving jz when quantized along a generalized apse has important implications for the well‐known CS decoupling approximatio...

Infinite order sudden approximation for reactive scattering. II. Computational tests for H+H2

A reactive scattering infinite order sudden approximation presented earlier is applied to the H+H2 exchange reaction. Detailed results for both differential and integral reactive cross sections are presented and compared with accurate close coupling results obtained earlier by Kuppermann and Schatz. Qualitative agreement is obtained for detailed state‐to‐state cross sections and more quantitative agreement is demonstrated for cross sections summed over final states.

On magnetic transitions and the interpretation of the partial wave parameter in the CS and IOS approximations in molecular scattering theory

The recent discovery by Khare that choosing the CS partial wave parameter ? to be the initial orbital angular momentum, li, leads to a simple differential scattering amplitude for definite polarization transitions is examined in detail. It is found that the resulting scattering amplitude formula, which is a rotation of the usual McGuire–Kouri formula, predicts nonzero magnetic transitions in all frames except that whose Z axis always points in the final observation direction ?. A detailed comparison of li and lf labeling is made and it is shown that both lead to nondiagonal approximations to the p‐helicity amplitude, TJ(jλ‖j0m0), and to differential scattering amplitudes which have the proper limiting behavior at small and large scattering angles. In addition it is shown that both li and lf labeling yield identical results for all degeneracy averaged cross sections, including the general relaxation cross sections. Further, we show rigorously that if the quantization axis is along a direction perpendicular...

Integral and differential cross sections for the H2(ui = 1) + H reaction. A comparison between average-/ labelled infinite-order sudden approximation and classical treatments

Abstract The exchange reaction H 2 (ν i = 1) + H→ H 2 (νf) + H is considered in this work. Total integral and differential cross sections are presented. A comparison between classical and average- l labelled infinite order sudden approximation (IOSA) results is found to be most encouraging.

Propensity for preserving polarization in rotationally inelastic molecular collisions

The CS approximation is employed to calculate scattering amplitudes for He–CO, Ne–HD, and He–H2 collisions.(AIP)

Integral total reactive cross section calculations within the infinite order sudden approximation

Abstract The initiafl l -labelled reactive infinite order sudden (IOS) approximation as formulated recently by Khare et al. is used to calculate integral total cross sections for the H + H 2 reaction. Results are given over the energy range 0.5 to 1.0 eV. Comparisons with accurate converged close coupling (CC) and classical results are made and good agreement is obtained. The method should be useful in the theoretical analysis of experiments.

CS(lav) and computational study of degeneracy averaged differerential cross sections and Δm-integral cross sections: Hez.sbndCO, HDz.sbnd

Abstract CC and l -average CS calculations of degeneracy averaged differential cross sections and Δ m -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.sbndH 2 at E = 1520 cm −1 . The l av z.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 l = l av choice rather than l = 1 or l ′. The l av z.sbndCS approximation gives reliable results for most Δ m -integral cross sections except for those σ cs ( jm , jm ′) cross sections for which the CC cross sections σ( jm ; jm ′) and σ( jm ′; jm ) differ by a large amount.