Inelastic collisions between an atom and a diatomic molecule. I. Theoretical and numerical considerations for the close coupling approximation

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Abstract
The close coupled differential equations for rotational excitation in collisions between an atom and a diatomic molecule are reformulated. Although it is equivalent to other formulations, it is computationally more convenient and gives a simpler expression for differential cross sections. Questions concerning real boundary conditions and the unitarity of the S matrix are discussed. Stormer’s algorithm for solving coupled differential equations is introduced for molecular scatterings. This numerical procedure, which is known to be very useful in nuclear scattering problems, has to be modified for molecular systems. It is capable of treating the case where all channels are open as well as the case where some of the channels are closed. This algorithm is compared with other typical procedures of solving coupled differential equations.