CS Approximation Research Articles

On the choice of phase in the CS and IOS approximation

With the recognition that the angular momentum representations of unit position and momentum directional states must have different but uniquely related phases, the previously presented expression of scattering amplitude in terms of IOS angle dependent phase shifts must be modified. This resolves a major disagreement between IOS and close coupled degeneracy averaged differential cross sections. It is found that the phase factors appearing in the differential cross section have nothing to do with any particular choice of decoupling parameter. As a consequence, the differential cross section is relatively insensitive to the choice of CS decoupling parameter. The phase relations obtained are also in agreement with those deduced from the Born approximation.

Coupled states study of nonreactive F(2P)+H2(1Σ+g) collisions

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.

On j z-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 ℓ̄ choice and the degree and direction of jz preservation. Away from the forward direction, the simplest choice obeying time reversal symmetry ℓ̄=(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.

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)

Interpretation of ES, CS, and IOS approximations within a translational–internal coupling scheme. III. Exact and CS molecule–molecule cross sections

Properties of exact and centrifugal sudden translational–internal reduced S matrices are given for general molecule–molecule collisions. The structure of energy-dependent and kinetic cross sections appropriate for linearized kinetic theory are described, both exactly and within the CS approximation. Connection with analogous total-J coupling scheme expressions is made in the Appendix.

CS and IOS approximations for fine structure transitions in Na(2P)–He(1S) collisions

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.

Erratum: Magnetic transitions in the initial-l labeled interpretation of the CS approximation. Computations for He+HCl

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On difficulties with a total angular momentum labeled CS approximation

The J-labeled version of the CS approximation for atom–diatom collisions is carefully examined. It is shown that a consistent treatment leads to unphysical and unrealistic features of the scattering amplitude and definite polarization cross sections. The most serious of these are (i) infinite total cross sections and (ii) rotationally inelastic transitions for spherically symmetric potentials.

Magnetic transitions in the initial-l labeled interpretation of the CS approximation. Computations for He+HCl

Calculations of Arthurs–Dalgarno space frame differential and integral cross sections for intermultiplet transitions, quantized with respect to the incident rotational angular momentum, are carried out for He + HCl collisions using the initial-l labeled version of the coupled states (CS-li) method given recently by Khare. Comparisons with accurate close coupling results of Monchick are made and the CS-li results for integral polarization cross sections are found to be at least semiquantitative, with the best agreement occurring for inelastic j0→j, and for m0≠m collisions. Elastic depolarization differential cross sections 𝒥m(dσ/dΩ)(j0m0→jm) are most accurate in the forward and backward directions, while the inelastic cross sections 𝒥m(dσ/dΩ)(j0m0→jm) are accurate only in the backward direction. In the midangular region, the magnitudes of the depolarization cross sections are inverted so that those starting from m0=0 are too large, and those with increasing initial m0 are too small.