A complete decoupling of Faddeev-like equations for three arrangement systems; applications to HH2 collision

doi:10.1016/0301-0104(76)80065-1

Chemical Physics

Volume 15, Issue 3, 15 July 1976, Pages 363-368

https://doi.org/10.1016/0301-0104(76)80065-1 Get rights and content

Abstract

A complete decoupling of time-dependent Faddeev-like equations for three identical particles is presented in terms of an operator formalism. No restriction to pairwise additive interaction needs to be made. Our decoupled equations can be looked at as being a generalization of the special decoupled versions of Faddeev and Lovelace in so far as they include all irreducible representations of the permutation group S₃. Thus, the new equations also apply to three composite particles of any spin. An application is made for the system composed of three H-atoms. In particular we show how the cross sections of ortho—para transitions are directly related to the transition operators obtained from the decoupled equations.

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Cited by (7)

Integral equation approach to atom-diatom exchange processes
1989, Physics Reports
This review presents a discussion of integral equation approaches to exchange collisions between an atom and a diatomic molecule which result from a straightforward extension of the Lippmann-Schwinger equation originally devised for inelastic collisions. The extension to N arrangement channels is done via a N × N matrix W which is responsible for the explicit couplings between the various arrangement channels. Different choices of the W matrix elements lead to different sets of integral equations; several of these are well known, whereas others are new. In addition to the theoretical derivations and analysis we refer to their coordinate representation, discuss numerical aspects and also present accurate results of the three-dimensional three-channel system H + H₂. In addition, an approximate set of integral equations is derived within the framework of the infinite-order sudden approximation. These equations are numerically tractable for most systems of interest and are known to yield relevant results.
Few-body processes in atom-diatom collisions
1981, Nuclear Physics, Section A
This contribution reviews recent progress on theories of atom-diatom collisions at thermal and hyperthermal energies. Following an overview of the types of theories being applied to triatomic systems,,it describes interaction potentials from a point of view relevant to few-body methods. Wavemechanical methods and results are reviewed for reactive collisions on single potential energy surfaces, including wavefunction propagation, basis expansion and purely numerical approaches. Reactions on multiple potential surfaces are briefly described, as well as approximations and models. Wave-mechanical treatments of dissociation are also considered. Applications of transition operator methods are reviewed, starting with results on two-atom transition operators and continuing with three-atom collisions at thermal and hyperthermal energies, including results of multiple-collision expansions.
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Collinear reactive scattering of H on H<inf>2</inf> in the magnus approximation
1976, Chemical Physics
As an approximation to reactive and nonreactive scattering of H on H₂, the first order Magnus approximation is applied for solving the time dependent Faddeev-like equations in both the arrangement-coupled and the identical-particle decoupled versions. Within this approach the probabilities for para—para, para-ortho and ortho—ortho hydrogen scattering are calculated in the collinear configuration. The para—ortho transition probabilities are compared with those obtained from close coupling calculations. Adopting the Porter—Karplus surface, the reaction threshold for space—ortho conversion is found at 0.2 eV which agrees with that obtained from the close coupling calculations.
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¹: Work performed in partial fulfillment of the requirements for the Ph.D. degree, Fachbereich Physik, University of Kaiserslautern, Federal Republic of Germany.

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A complete decoupling of Faddeev-like equations for three arrangement systems; applications to HH2 collision

Abstract

Chem. Phys.

Phys. Letters

J. Chem. Phys.

Phys. Rev.

J. Chem. Phys.

J. Chem. Phys.

A complete decoupling of Faddeev-like equations for three arrangement systems; applications to HH₂ collision