Arrangement channel approach to atom–diatom reactive systems: Theory and accurate three-dimensional probabilities for the H+H2 system

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Abstract
In this work is presented an integral equation approach to exchange collisions between an atom and a diatomic molecule which result from a straightforward extension of the Lippmann–Schwinger equation originally devised to inelastic collisions. The extension to N‐arrangement channels is done via a N×N matrix W which is responsible for the explicit coupling among the various arrangement channels. Different choices of the W matrix elements lead to different sets of integral equations; one of these, in which the W matrix elements are assumed to be dependent on the three orientation angles γα; α=λ, ν, k only, is discussed in detail. In addition to the theoretical derivations, we refer to the corresponding coordinate representation, discuss numerical aspects and present accurate results of the three‐dimensional–three‐channel H+H2 system.