Theory of angular momentum decoupling approximations for rotational transitions in scattering

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Abstract
A systematic method is discussed for decoupling the internal angular momentum of molecules involved in a collision from their relative angular momentum. This leads to a large class of rotational approximations of varying degrees of complexity and accuracy. These approximations may be used directly for computing rotational transitions or they may be used for reducing the rotational complexity involved in accurate vibrational calculations. It is shown how this approach may be used to study the infinite−order sudden approximation and how that approximation may be extended to more complex potentials. It is shown also how one may use results of the jz−conserving approximation to obtain more complete information on the scattering matrix. The present approach may be used to deduce new angular momentum decoupling approximations and analyze such approximations arrived at through other considerations.