Abstract
We demonstrate an exact method for solving the close-coupled equations for rotationally inelastic scattering in the body-fixed (BF) coordinate representation, using a slight modification of the exponential method which allows application of the known boundary conditions for the space-fixed (SF) coordinate frame. The nature of the coupling in the BF frame suggests approximations which reduce the problem to a set of problems each of a smaller dimensionality. Using an atom-rigid rotor model potential, we have compared the decoupling approximation suggested by Pack and by McGuire and Kouri to the fully coupled problem. We find the centrifugal decoupling (CD) approximation to work best at low total angular momenta J, and for low rotor states j. Opacity functions for inelastic transitions are generally better than ones for elastic transitions, due to errors in the phases of elastic S-matrix elements. However, at high J, CD often severely underestimates the inelastic transition probabilities.
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